JP6233038B2 - Assembly yield prediction apparatus, assembly yield prediction program, and assembly yield prediction method - Google Patents

Description

  The present invention relates to an assembly yield prediction apparatus, an assembly yield prediction program, and an assembly yield prediction method.

  Products such as mobile phones, smartphones, and PDA (Personal Digital Assistants) housings are manufactured by assembling a plurality of types of parts. Since there is a manufacturing variation (distribution) when manufacturing parts, each part cannot be manufactured as designed. Therefore, at the time of product inspection, the dimensions of a plurality of check points (inspection points) included in the assembled product are measured. If the dimensions of all the check points are within the predetermined allowable range, it is determined that the assembled product is a non-defective product. If the dimensions are not within the allowable range, the assembled product is defective. It is determined that there is.

  Here, as shown in FIG. 22, the check location is a part of the product generated by assembling the parts, for example, a gap between the parts and an overlapping part of the parts. FIG. 22 is a diagram for explaining the partial dimensions of the product, the check location of the product, and the dimensions of the check location. In the example shown in FIG. 22, the product P is an assembly of two parts A and B, and has two check points # 1 and # 2. Further, the parts A1 and A2 of the part A and the parts B1 and B2 of the part B are parts that affect the dimensions of the check points # 1 and # 2 of the product P. More specifically, the size of the portion A1 and the size of the portion B1 affect the size of the check location # 1 (= the size of the portion B1−the size of the portion A1). Further, the size of the portion A2 and the size of the portion B2 affect the size of the check location # 2 (= the size of the portion A2 + the size of the portion B2).

  In the following, the probability that the dimensions of all the check points included in the product fall within the allowable range, that is, the proportion of the manufactured product is a non-defective product is referred to as “product yield” or “product assembly yield”.

  Conventionally, in order to keep the product yield high, in the product design stage, for example, as shown in FIG. 23, the yield information and product yield at the check location are predicted, and the result of the prediction is reflected in the design. Further, at the product assembly stage, for example, as shown in FIG. 24, yield information and product yield at the check location are calculated, and the result of the calculation is reflected in the manufacturing process. FIG. 23 is a diagram showing an example of a yield prediction procedure at the product design stage, and FIG. 24 is a diagram showing an example of a yield prediction procedure at the product assembly stage.

  In the example shown in FIG. 23 (design stage), the design data D1 includes design values for parts, variations in the design values, assembly drawings of products, design values for check points, and tolerances for check points. The range is acquired in advance. Here, the design stage is a stage where a product is being designed, and the parts are not actually manufactured at the design stage. For this reason, design value variation (manufacturing variation) is assumed from past empirical information or simulation results, and is obtained as a partial univariate normal distribution. The design value at the check location is the size of the check location when each part is assumed to be manufactured according to the design value.

At this time, assembly yield analysis is performed based on the design data described above (see S1 in FIG. 23), and the distribution of dimensions and yield information D2 for all the check locations # 1, # 2,. Sensitivity information D3 indicating the degree of influence of the change in the part size of the part on the size of the check location #i (i = 1, 2,...) Is obtained. The yield information of each check location #i is obtained as the probability P _i that the size of each check location #i falls within the allowable range based on the distribution of the size of each check location #i. The sensitivity information D3 is information indicating how many mm the check location changes when, for example, the part dimension of the component changes by 1 mm.

Assuming that each check point #i is independent, the product yield D4 is simplified by the following equation (1) based on the probability P _i that the size of each check point #i falls within the allowable range. Is approximated and predicted (see S2 in FIG. 23).
Product yield _{(D4) = Π i P i} (1)

Further, at the design stage, if the yield (probability P _i ) of all the check points has cleared the target yield, the product to be designed is manufactured with the target yield by using the current design data. It is judged and the design is finished. On the other hand, if there is a check location that does not clear the target yield even at one location, the design is changed until the yield of all the check locations clears the target yield. When the design is changed, the sensitivity information described above is used. As a result, a design that assumes manufacturing variations of each component is performed.

  In the example (assembly stage) shown in FIG. 24, parts for actually assembling a product are manufactured. In other words, the assembly stage is a stage in which a product is mass-produced in a factory or the like, and in the assembly stage, unlike the design stage, parts for assembling the product are already manufactured. For this reason, in addition to the design data D1 obtained in the above-described design stage, information D5 of actually manufactured parts is obtained. At this time, the component information D5 is estimated from the sample measurement result of the manufactured component, and is partial size of each component and variation information (for example, average and variance) of the partial size. The variation information obtained here is a distribution of partial dimensions, that is, a univariate distribution and not a multivariate distribution.

At this time, an assembly yield analysis is performed based on the above-described design data and manufactured part information (see S3 in FIG. 24), and the dimensions of each of the check points # 1, # 2,. Distribution and yield information D6 is obtained. The yield information of each check location #i is obtained as the probability P _i that the size of each check location #i falls within the allowable range based on the distribution of the size of each check location #i. Then, assuming that each check point #i is independent, the product yield D7 is simplified by the above equation (1) based on the probability P _i that the size of each check point #i falls within the allowable range. Is approximated and predicted (see S4 in FIG. 24).

  Also, at the assembly stage, if the distribution and yield of all the check points are within the allowable range assumed in the design, it is determined that the product is manufactured at the target yield by the current manufacturing process, and the current manufacturing is performed. Product production by the process continues. On the other hand, if there is a check location where the distribution and yield are not within the allowable range even at one location, change the manufacturing process until the distribution and yield of all check locations are within the allowable range (for example, mold) Adjustment) is performed.

Japanese Patent Laid-Open No. 10-40289 JP-A-10-105594

  With the technology described above, the same parts are always manufactured with the same distribution (there is no manufacturing process variation), and there is no or little correlation between the parts of the parts, so that the product design and assembly are not affected. It is done. For this reason, it is considered that the product yield can be increased if the high yield of all the check points included in the product is achieved, and it is not important to accurately predict the product yield. Therefore, because there are parts of parts that affect multiple check points, the correlation between the check points actually exists, but the correlation between the check points is ignored, and the product can be simplified by the above formula (1). Yield is calculated.

  However, in recent years, with the miniaturization of products and the limitations of manufacturing technology, the above assumptions have been lost, and it has become impossible to achieve a high yield at all check points. Therefore, it is important to accurately predict the product yield in order to increase the product yield. However, in the above-described technology, the product yield is predicted under the assumption that each part or each check point is independent without considering the correlation between the parts of each part of the product or between the check points. Therefore, there is a problem that the prediction accuracy of the product yield is extremely poor.

In one aspect, an object of the present invention is to accurately predict an assembly yield of a product.
In addition, the present invention is not limited to the above-mentioned object, and is an operational effect derived from each configuration shown in the best mode for carrying out the invention described later, and has an operational effect that cannot be obtained by conventional techniques. It can be positioned as one of the purposes.

  The assembly yield prediction apparatus of the present case predicts an assembly yield of a product assembled by a plurality of parts, and has an acquisition unit, a multivariate distribution calculation unit, and a prediction unit. Here, the acquisition unit acquires a multivariate distribution parameter of partial dimensions including correlation information between a plurality of partial dimensions in each part. In addition, the multivariate distribution calculation unit is configured to determine a degree of influence of the multivariate distribution parameter of the partial dimension acquired by the acquisition unit and the change of the partial dimension of each part on the dimensions of a plurality of check points in the product. The multivariate distribution parameter of the check spot size is calculated based on the sensitivity information indicating. The multivariate distribution parameter of the check location dimension is the correlation information generated between the dimensions of the plurality of check locations due to the change in the size of each part in the same part affecting the dimensions of the plurality of check locations. Including. Furthermore, the prediction unit predicts the assembly yield of the product based on the multivariate distribution parameter of the check spot size calculated by the multivariate distribution calculation unit.

  According to one embodiment, the assembly yield of a product can be accurately predicted.

It is a block diagram which shows the hardware structural example and functional structural example of the assembly yield prediction apparatus which concern on this embodiment. It is a block diagram which shows an example of a structure of the yield calculation process part shown in FIG. It is a block diagram which shows an example of a structure of the Monte Carlo process part shown in FIG. It is a block diagram which shows the other example of a structure of the Monte Carlo process part shown in FIG. It is a figure which illustrates roughly operation | movement of the assembly yield prediction apparatus which concerns on this embodiment in the product design stage. It is a figure which illustrates roughly operation | movement of the assembly yield prediction apparatus which concerns on this embodiment in the assembly stage of a product. It is a flowchart explaining operation | movement of the assembly yield prediction apparatus which concerns on this embodiment in the design stage of a product. It is a flowchart explaining operation | movement of the assembly yield prediction apparatus which concerns on this embodiment in the assembly stage of a product. It is a flowchart explaining the yield calculation process of step S22 shown in FIG. It is a flowchart explaining the yield calculation process of step S24 shown in FIG. It is a flowchart explaining the high-speed Monte Carlo process performed by the Monte Carlo process part shown in FIG. It is a figure which shows an example of the sensitivity information which is input data to the assembly yield prediction apparatus of this embodiment. It is a figure which shows an example of the design data (The design value and variation information of a part) which are input data to the assembly yield prediction apparatus of this embodiment. It is a figure which shows an example of the design data (design value of a check location, and tolerance | permissible_range) which is input data to the assembly yield prediction apparatus of this embodiment. It is a figure which shows an example of the component sample measurement information which is input data to the assembly yield prediction apparatus of this embodiment. It is a figure which shows the other example of the component sample measurement information which is input data to the assembly yield prediction apparatus of this embodiment. It is a figure which shows an example of distribution of the check location which is output data from the assembly yield prediction apparatus of this embodiment, and a yield. It is a figure which shows an example of the average vector and dispersion | distribution covariance matrix of the part which are the intermediate data (multivariate distribution parameter of a partial dimension) of the process by the assembly yield prediction apparatus of this embodiment. 5 is a flowchart illustrating a processing procedure by a product yield calculation unit (first yield calculation unit) of the Monte Carlo processing unit illustrated in FIGS. 3 and 4. It is a figure explaining manufacturing process variation. It is a figure explaining manufacturing process variation. It is a figure explaining the partial dimension of a product, the check location of a product, and the dimension of the said check location. It is a figure which shows an example of the prediction procedure of the yield in the product design stage. It is a figure which shows an example of the prediction procedure of the yield in the assembly stage of a product.

  Hereinafter, embodiments of an assembly yield prediction apparatus, an assembly yield prediction program, and an assembly yield prediction method disclosed in the present application will be described in detail with reference to the drawings. However, the embodiment described below is merely an example, and there is no intention to exclude application of various modifications and techniques not explicitly described in the embodiment. That is, the present embodiment can be implemented with various modifications without departing from the spirit of the present embodiment. Each figure is not intended to include only the components shown in the figure, and may include other functions. And each embodiment can be suitably combined in the range which does not contradict a processing content.

[1] Configuration of the present embodiment First, the configuration of the present embodiment will be described with reference to FIGS.
FIG. 1 is a block diagram illustrating a hardware configuration example and a functional configuration example of an assembly yield prediction apparatus 1 according to the present embodiment. FIG. 2 is a block diagram showing an example of the configuration of the yield calculation processing units 20 and 412 shown in FIG. FIG. 3 is a block diagram illustrating an example of the configuration of the Monte Carlo processing unit illustrated in FIG. 2 (see reference numeral 22). FIG. 4 is a block diagram showing another example of the configuration of the Monte Carlo processing unit shown in FIG. 2 (see reference numeral 22 ').

  As shown in FIG. 1, the assembly yield predicting apparatus 1 predicts assembly yields 60 and 68 of a product P (see FIG. 22) assembled by a plurality of parts A and B, for example. The assembly yield prediction apparatus 1 includes at least a processing unit 2 such as a CPU (Central Processing Unit), an MPU (Micro-Processing Unit), a computer, a RAM (Random Access Memory), an HDD (Hard Disk Drive), an SSD (Solid). And a storage unit 3 such as (State Device).

  The processing unit 2 reads a predetermined application program (assembly yield prediction program) from the storage unit 3 and executes it to thereby execute a multivariate distribution parameter determination unit 10, a yield calculation processing unit 20, which will be described later, and multivariate distribution parameter estimation. Functions as the unit 30 and the confidence interval calculation unit 40. The predetermined application program is, for example, a flexible disk, CD (CD-ROM, CD-R, CD-RW, etc.), DVD (DVD-ROM, DVD-RAM, DVD-R, DVD-RW, DVD + R, DVD + RW). Etc.), and is provided in a form recorded on a computer-readable recording medium such as a Blu-ray disc. In this case, the processing unit 2 reads the program from the recording medium, transfers it to the storage unit 3 as an internal storage device or an external storage device, and uses it.

  In addition to storing the predetermined application program, the storage unit 3 stores various information necessary for processing by the processing unit 2. For example, the storage unit 3 uses, as the various information, the part variation information 51 and the design value 52; the sensitivity information 53 of the part; the design value 54 of the check location and the allowable range 55, assembling yield prediction processing at the design stage. Save in advance. In addition, the storage unit 3 stores in advance the part sample measurement information 61 as the various information before the assembly yield prediction process at the assembly stage. Further, the storage unit 3 includes, as the various information, etc., check location yields 58 and 69; product yields 60 and 68; check location yield confidence intervals 70; product yields, which are prediction results by the assembly yield prediction device 1. The confidence interval 71 is saved. In addition, the storage unit 3 stores information obtained during the prediction process by the assembly yield prediction apparatus 1 (reference numerals 56, 57, 59, 59 ', 59 ", 62-67 in FIGS. 1 to 17) as the various information. , 67 ', 72-76).

  Hereinafter, the functions realized by the processing unit 2 as the multivariate distribution parameter determination unit 10, the yield calculation processing unit 20, the multivariate distribution parameter estimation unit 30, and the confidence interval calculation unit 40 will be described with reference to FIGS. While explaining.

[1-1] About the multivariate distribution parameter determination unit (acquisition unit) 10 and the multivariate distribution parameter estimation unit (acquisition unit) 30 The multivariate distribution parameter determination unit (acquisition unit) 10 is preliminarily used in the design stage of the product P. A multivariate distribution parameter 56 of partial dimensions including correlation information (correlation, relationship) between a plurality of partial dimensions in the parts A and B based on the assumed manufacturing variation 51 of the product P (see FIGS. 2 and 7). Determine and get. Manufacturing variation is a deviation from a design value (see reference numeral 52) that occurs at random during manufacturing, and is caused by various factors such as differences in material, temperature, humidity, and manufacturing machine. For this reason, in the design stage, the manufacturing variation information 51 is assumed from past empirical information or simulation results. The design value 52 and the variation information 51 for the part will be described later with reference to FIG. Further, the multivariate distribution parameter 56 of partial dimensions is acquired as, for example, an average (average vector) and a variance covariance matrix that are parameters of a multivariate normal distribution (simultaneous distribution) of partial dimensions.

  The multivariate distribution parameter estimation unit (acquisition unit) 30, in the assembly stage of the product P, is based on the part sample measurement information 61 that is an actual measurement value of each manufactured part. A multivariate distribution parameter 63 (see FIGS. 2, 8, and 9) having partial dimensions including correlation information (correlation, relationship) is estimated and acquired. The multivariate distribution parameter estimation unit 30 also outputs a measurement sample number (sample number) 62 in the component sample measurement information 61. The component sample measurement information 61 will be described later with reference to FIGS. 15 and 16. Similarly to the multivariate distribution parameter 56, the multivariate distribution parameter 63 of the partial size is acquired as, for example, an average and a variance covariance matrix that are parameters of the multivariate normal distribution of the partial size.

  Here, the partial dimensions are, for example, the dimensions of the portions A1 and A2 and the portions B1 and B2 described above with reference to FIG. That is, the product P is an assembly of two parts A and B, for example, and has two check points # 1 and # 2. Further, the parts A1 and A2 of the part A and the parts B1 and B2 of the part B are parts that affect the dimensions of the check points # 1 and # 2 of the product P.

[1-2] About Yield Calculation Processing Unit 20 The yield calculation processing unit 20 calculates multi-variate distribution parameters 57 and 67 for check points, which will be described later, check point yields 58 and 69, and product yields 60 and 68. As shown in FIG. 2, a check point calculation unit 21 and a Monte Carlo processing unit 22 (22 ') are included. The check location calculation unit 21 includes a multivariate distribution calculation unit 211 and a check location yield calculation unit 212. Note that the yield calculation processing unit 412 in the confidence interval calculation unit 40 described later is also configured in the same manner as the yield calculation processing unit 20 shown in FIG. A yield 66 and a product yield 65 are calculated. Here, the configuration of the yield calculation processing unit 412 as well as the configuration of the yield calculation processing unit 20 will be described.

  The multivariate distribution calculation unit (multivariate distribution calculation unit) 211 is a multivariate distribution parameter 56 of partial dimensions acquired by the multivariate distribution parameter determination unit 10, sensitivity information 53, Based on the design value 52 and the design value 54 of the check location, a multivariate distribution parameter 57 of the check location size is calculated. Further, the multivariate distribution calculation unit 211, in the assembly stage of the product P, the multivariate distribution parameter 63 of the partial dimension acquired by the multivariate distribution parameter estimation unit 30, the sensitivity information 53, the design value 52 of the part, Based on the design value 54 of the check location, a multivariate distribution parameter 67 of the check location size is calculated. Further, the multivariate distribution calculation unit 211 belonging to the yield calculation processing unit 412 calculates the multivariate distribution parameter 67 ′ of the check spot size for each bootstrap sample 64 as described later with reference to FIG.

  Here, the sensitivity information 53 is the degree of the influence (sensitivity) of the change in the size of each part in each part on the size of the check location #i (i = 1, 2,. , Influence degree). The sensitivity information 53 will be described later with reference to FIG.

  Further, the check spot size is a dimension for each of the check spots # 1, # 2,... Described above with reference to FIG. Then, the multivariate distribution parameters 57 and 67 (67 ′) of the check spot size are acquired as, for example, a mean vector and a variance covariance matrix that are parameters (intermediate data) of the multivariate normal distribution of the check spot size, respectively. .

  Such multivariate distributions 57 and 67 (67 ') of the check location dimensions are obtained due to the fact that the change of each partial size in the same part affects the size of each check location #i. It contains correlation information (correlation, relationship) that occurs between the dimensions of locations. The average vector and the variance-covariance matrix, which are the distribution parameters 57 and 67 (67 ′) of the multivariate distribution of the check spot size, will be described later with reference to FIG.

  The check location yield calculation unit (second yield calculation unit) 212 is a multivariate distribution parameter 57 of the check location dimensions calculated by the multivariate distribution calculation unit 211 and the dimensions of a plurality of check locations in the design stage of the product P. Based on the allowable range 55, the assembly yield 58 of each check location #i is calculated. In addition, the check location yield calculation unit 212 determines, based on the multivariate distribution parameter 67 of the check location dimension calculated by the multivariate distribution calculation unit 211 and the allowable size range 55 of the check location, in the assembly stage of the product P. The assembly yield 69 for the check location #i is calculated. Furthermore, the check location yield calculation unit 212 belonging to the yield calculation processing unit 412 includes the multivariate distribution parameter 67 ′ of the check location size calculated for each bootstrap sample 64 by the multivariate distribution calculation unit 211 and the size of the check location. Based on the allowable range 55, the assembly yield 66 of each check point #i is calculated for each bootstrap 64.

  Note that the dimensional tolerance 55 for the check location may be referred to as the tolerance 55 for the check location. The design value 54 of the check location is the size of the check location when it is assumed that each part is manufactured according to the design value 52 as described above. The design value 54 and the dimension allowable range 55 of the check location will be described later with reference to FIG.

  The Monte Carlo processing unit (prediction unit) 22 or 22 ′ determines the assembly yield (product yield) of the product P based on the multivariate distribution parameter 57 of the check point size calculated by the multivariate distribution calculation unit 211 in the design stage of the product P. Tome) 60 is predicted. In addition, the Monte Carlo processing unit 22 or 22 ′ predicts the product yield 68 based on the multivariate distribution parameter 67 of the check spot size calculated by the multivariate distribution calculation unit 211 in the assembly stage of the product P. Furthermore, the Monte Carlo processing unit 22 or 22 ′ belonging to the yield calculation processing unit 412 is configured to output a multivariate distribution parameter 67 calculated by the multivariate distribution calculation unit 211 for each bootstrap sample 64 as described later with reference to FIG. ', The product yield 65 of each bootstrap sample 64 is predicted.

Here, the Monte Carlo processing unit 22 includes a Monte Carlo sample generation unit 221 and a product yield calculation unit 222, as shown in FIG.
The Monte Carlo sample generation unit (first sample generation unit) 221 includes a plurality of Monte Carlo samples 59 each including a set of dimension data of a plurality of check locations based on the multivariate distribution parameter 57 of the check location dimensions in the design stage of the product P. Are generated by Monte Carlo simulation. Further, the Monte Carlo sample generation unit 221 performs a Monte Carlo simulation on a plurality of Monte Carlo samples 59 ′ each including a set of dimension data of a plurality of check locations based on the multivariate distribution parameter 67 of the check location dimensions at the assembly stage of the product P. Generate by. Further, the Monte Carlo sample generation unit 221 belonging to the yield calculation processing unit 412 has a plurality of check points based on the multivariate distribution parameter 67 ′ of the check point size calculated for each bootstrap 64 by the multivariate distribution calculation unit 211. A plurality of Monte Carlo samples 59 ″ each including a set of dimension data are generated by Monte Carlo simulation.

  The product yield calculation unit (first yield calculation unit) 222 has a plurality of check locations and a plurality of check locations included in the Monte Carlo sample 59 generated by the Monte Carlo sample generation unit 221 at the design stage of the product P. Are compared with each other and the assembly yield 60 of the product P is calculated based on the result of the comparison. The product yield calculation unit 222 also includes dimensions of a plurality of check points included in the Monte Carlo sample 59 ′ generated by the Monte Carlo sample generation unit 221 and a dimension allowable range 55 of the plurality of check points in the assembly stage of the product P. And the assembly yield 68 of the product P is calculated based on the result of the comparison. Further, the product yield calculation unit 222 belonging to the yield calculation processing unit 412 includes a plurality of check point dimensions included in the Monte Carlo sample 59 ″ generated by the Monte Carlo sample generation unit 221 and a dimension tolerance range of the plurality of check points. 55, and the assembly yield 65 of the product P is calculated based on the comparison result.

  On the other hand, the Monte Carlo processing unit 22 'is for realizing the same processing as the Monte Carlo processing unit 22 at a higher speed. As shown in FIG. 4, a normalization unit 223, an eigenvector / eigenvalue calculation unit 224, and a Monte Carlo sample generation Section 221 'and product yield calculation section 222'.

  The normalizing unit 223 normalizes the multivariate distribution parameter 57 of the check spot size and the dimension tolerance ranges 55 of the plurality of check spots in the design stage of the product P. Further, the normalizing unit 223 normalizes the multivariate distribution parameter 67 of the check spot size and the dimension tolerance range 55 of the plurality of check spots in the assembly stage of the product P. Further, the normalization unit 223 belonging to the yield calculation processing unit 412 normalizes the multivariate distribution parameter 67 ′ of the check spot size and the dimension tolerances 55 of the plurality of check spots.

  The eigenvector / eigenvalue calculation unit 224 obtains a plurality of eigenvectors from the multivariate normal distribution of the check spot size normalized by the normalization part 223 (variance covariance matrix 74 of the multivariate normal distribution of the check spot after normalization). The eigenvalue 75 corresponding to each vector is calculated by singular value decomposition.

  The Monte Carlo sample generation unit (first sample generation unit) 221 ′ generates, by Monte Carlo simulation, a plurality of Monte Carlo samples 76 each including a set of size data of a plurality of check locations in the following space. The space is spanned by eigenvectors whose cumulative contribution rate defined by eigenvalues exceeds a predetermined threshold among a plurality of eigenvectors.

  The product yield calculation unit (first yield calculation unit) 222 ′ normalizes the dimensions of a plurality of check points included in the plurality of Monte Carlo samples 76 generated by the Monte Carlo sample generation unit 221 ′ and the normalization unit 223. The dimensional tolerances 72 of the plurality of check points are compared. Then, the product yield calculation unit 222 ′ calculates assembly yields 60 and 68 (65) of the product P based on the comparison result.

[1-3] About the confidence interval calculation unit (first confidence interval calculation unit and second confidence interval calculation unit) 40 The confidence interval calculation unit 40 functions as a first confidence interval calculation unit and a second confidence interval calculation unit. Fulfill.
The first confidence interval calculation unit is a multivariate distribution parameter of partial dimensions estimated from the component sample measurement information 61 due to the small number of measurement samples (sample number) 62 of the component sample measurement information (actual measurement value) 61. The error occurring at 63 is estimated. Then, the first confidence interval calculation unit 40 calculates an assembly yield confidence interval 70 for each check location #i based on the estimated error and the sensitivity information 53.

  Further, the second confidence interval calculation unit is a multivariate of partial dimensions estimated from the component sample measurement information 61 due to the small number of measurement samples (number of samples) 62 of the component sample measurement information (actual measurement value) 61. An error occurring in the distribution parameter 63 is estimated. Then, the second confidence interval calculation unit 40 calculates the estimated error, the sensitivity information 53, and the multivariate distribution parameter 67 ′ of the check spot size calculated by the multivariate distribution calculation unit 211 for each bootstrap sample 64 described later. Based on the above, the confidence interval 71 of the assembly yield of the product P is calculated. The confidence interval is a range in which the yield value enters with a predetermined probability. For example, when the predetermined probability is 95%, when the yield value falls within the range of 0 to 0.5 with a probability of 95% or more, the range 0 to 0.5 is set as the confidence interval.

  As shown in FIG. 2, the confidence interval calculation unit 40 includes a bootstrap yield calculation unit 41, a check location yield confidence interval calculation unit 42, and a product yield confidence interval calculation unit 43. Further, the bootstrap yield calculation unit 41 includes a bootstrap sample generation unit 411 and a yield calculation processing unit 412.

[1-3-1] Regarding First Confidence Interval Calculation Unit First, a bootstrap sample generation unit 411, a yield calculation processing unit (third step) when the confidence interval calculation unit 40 functions as a first confidence interval calculation unit. The functions as the yield calculation unit 412 and the check location yield confidence interval calculation unit 42 will be described.

  At this time, the bootstrap sample generation unit (second sample generation unit) 411, based on the number of samples 62 and the multivariate distribution parameter 63 of the partial size, distributes parameters (average vector, variance) of the multivariate distribution parameter 63 of the partial size. Bootstrap samples 64 for the (covariance matrix) are generated by the parametric bootstrap method.

  The yield calculation processing unit (third yield calculation unit) 412 is configured in the same manner as the yield calculation processing unit 20 described above with reference to FIG. Then, the multivariate distribution calculation unit 211 of the yield calculation processing unit 412 determines, for each bootstrap sample 64 generated by the bootstrap sample generation unit 411, a multivariate distribution parameter 67 of the check spot size based on the sensitivity information 53. 'Is calculated. Also, the check location yield calculation unit 212 of the yield calculation processing unit 412 determines each check location based on the calculated multivariate distribution parameter 67 ′ of the check location dimensions and the dimensional tolerances 55 of the plurality of check locations. The assembly yield 66 for #i is calculated.

  The check location yield confidence interval calculation unit (check location yield confidence interval calculation unit) 42 checks each check location #i calculated for each bootstrap sample 64 by the yield calculation processing unit (third yield calculation unit) 412. Based on the assembly yield 66, an assembly yield confidence interval 70 for each check location #i is calculated. A specific method for calculating the confidence interval 70 will be described later.

[1-3-2] Regarding the Second Confidence Interval Calculation Unit Further, when the confidence interval calculation unit 40 functions as the second confidence interval calculation unit, the bootstrap sample generation unit 411, the yield calculation processing unit (fourth step The functions as the yield calculation unit 412 and the product yield confidence interval calculation unit 43 will be described.

  At this time, the bootstrap sample generation unit (second sample generation unit) 411 generates the bootstrap sample 64 by the parametric bootstrap method in the same manner as the bootstrap sample generation unit 411 of the first confidence interval calculation unit.

  The yield calculation processing unit (fourth yield calculation unit) 412 includes, for example, the Monte Carlo processing unit 22 described above with reference to FIG. In this case, the multivariate distribution calculation unit 211 of the yield calculation processing unit 412 determines the parameter of the multivariate distribution of the check spot size for each bootstrap sample 64 generated by the bootstrap sample generation unit 411 based on the sensitivity information 53. 67 'is calculated. In addition, the Monte Carlo sample generation unit 221 of the yield calculation processing unit 412 has a plurality of Monte Carlo samples each including a set of dimensional data of a plurality of check locations based on the calculated parameter 67 ′ of the multivariate distribution of the check location dimensions. 59 ″ is generated by Monte Carlo simulation. Then, the product yield calculation unit 222 of the yield calculation processing unit 412 includes dimensions of a plurality of check points included in the generated plurality of Monte Carlo samples 59 ″ and a plurality of checks. Each part is compared with the dimension allowable range 55, and the assembly yield 65 of the product P is calculated based on the comparison result.

  The product yield confidence interval calculation unit (product yield confidence interval calculation unit) 43 is an assembly yield 65 of the product P calculated for each bootstrap sample 64 by the yield calculation processing unit (fourth yield calculation unit) 412. Based on the above, the confidence interval 71 of the assembly yield of the product P is calculated. A specific method for calculating the confidence interval 71 will be described later.

  Note that the yield calculation processing unit (fourth yield calculation unit) 412 may include the Monte Carlo processing unit 22 ′ described above with reference to FIG. Also in this case, the multivariate distribution calculation unit 211 of the yield calculation processing unit 412 calculates the parameter 67 ′ of the multivariate distribution of the check spot size based on the sensitivity information 53 for each bootstrap sample 64, as described above. . In addition, the normalization unit 223 normalizes the calculated multivariate distribution parameter 67 ′ of the check spot size and the dimension tolerances 55 of the plurality of check spots. Further, the eigenvector / eigenvalue calculation unit 224 converts the normalized check point size multivariate normal distribution (variance covariance matrix 74 of the check point multivariate normal distribution after normalization) into a plurality of eigenvectors and each vector. The corresponding eigenvalue 75 is calculated by singular value decomposition. In addition, the Monte Carlo sample generation unit 221 ′ generates, by Monte Carlo simulation, a plurality of Monte Carlo samples 76 each including a set of dimension data of a plurality of check locations in the space. Then, the product yield calculation unit 222 ′ compares the dimensions of the plurality of check locations included in the generated plurality of Monte Carlo samples 76 with the normalized size tolerance ranges 72 of the plurality of check locations, respectively. Based on the comparison result, the assembly yield 65 is calculated for each bootstrap sample 64.

[2] Operation of the present embodiment Next, the operation of the assembly yield prediction apparatus 1 according to the present embodiment will be described with reference to FIGS.
[2-1] Outline of Operation of Assembly Yield Prediction Device 1 First, an outline of operation of the assembly yield prediction device 1 according to the present embodiment will be described with reference to FIGS. 5 and 6. FIG. 5 is a diagram schematically illustrating the operation of the assembly yield prediction apparatus 1 according to the present embodiment at the design stage of the product P. FIG. 6 is a diagram schematically illustrating the operation of the assembly yield prediction apparatus 1 according to the present embodiment at the assembly stage of the product P.

  As shown in FIG. 5, at the design stage of the product P, the assembly yield prediction device 1 determines the distribution of check points based on part of the design data (see reference numerals 51, 52, 54, 55) and the sensitivity information 53. (Multivariate distribution parameter) 57 and yield 58 and product yield 60 are predicted and calculated. The part of the design data includes a manufacturing variation 51 of the part portion, a design value 52 of the part portion, a design value 54 of the check location, and an allowable range (dimension allowable range) 55.

  Here, as described above, the manufacturing variation 51 is variation information of partial dimensions of each part in the product P assumed in advance. Based on the manufacturing variation 51 and the design value 52, the multivariate distribution parameter 56 of partial dimensions including correlation information (correlation, relationship) between a plurality of partial dimensions in each part is the multivariate distribution parameter in the assembly yield prediction apparatus 1. It is determined by the determination unit 10. Further, as described above, the sensitivity information 53 indicates the degree of influence (sensitivity, influence degree) that the change in the size of each part in each part has on the size of the check location #i in the product P. The sensitivity information 53 is acquired and output by an assembly yield analysis tool based on, for example, design data (see, for example, S1 in FIG. 23).

  Then, the yield calculation processing unit 20 in the assembly yield prediction apparatus 1 assembles the product P assembled by a plurality of parts based on the design values 52 and 54, the allowable range 55, and the multivariate distribution parameter 56 of the partial dimensions. The yield 60, the check spot distribution 57, and the yield 58 are predicted and calculated. The check point distribution 57 and the yield 58 are used when the design of the product P is changed.

  As described above, according to the assembly yield prediction apparatus 1 of the present embodiment, the product yield 60 is predicted in the design stage of the product P while taking into account the correlation between the parts of each part of the product P and the check points. Is done. For this reason, the product yield 60 can be accurately predicted. Therefore, a designer or the like can make a design change based on the product yield 60 predicted with high accuracy so as to reliably optimize (maximize) the product yield 60.

  On the other hand, as shown in FIG. 6, at the assembly stage of the product P, the assembly yield prediction apparatus 1 includes a part of design data (see reference numerals 52, 54, and 55), sensitivity information 53, and component sample measurement information 61. Based on the check point distribution (multivariate distribution parameter) 67, the yield 69 and the confidence interval 70, the assembly yield 68 and the confidence interval 71 of the product P are predicted and calculated. As part of the design data, a design value 52 for a part, a design value 54 for a check point, and an allowable range (dimension allowable range) 55 are included.

  In the assembly stage, parts for actually assembling products are manufactured. That is, the assembly stage is a stage in which a product is mass-produced in a factory or the like. Unlike the design stage, parts for assembling the product P are already manufactured in the assembly stage. For this reason, the part sample measurement information 61 is obtained from the actually manufactured part. Based on the part sample measurement information 61, the multivariate distribution parameter 63 of partial dimensions including correlation information (correlation, relationship) between a plurality of partial dimensions in each part is used to estimate the multivariate distribution parameters in the assembly yield prediction apparatus 1. Estimated by the unit 30. At this time, the measurement sample number (sample number) 62 in the component sample measurement information 61 is also acquired by the multivariate distribution parameter estimation unit 30.

  Then, a product assembled by a plurality of parts based on the design values 52 and 54, the sensitivity information 53, the allowable range 55, and the multivariate distribution parameter 63 of the partial dimensions by the yield calculation processing unit 20 in the assembly yield prediction apparatus 1. P assembly yield 68, check point distribution 67 and yield 69 are predicted and calculated. The check point distribution 67 and the yield 69 are used when the manufacturing process of the product P is changed (for example, the mold is adjusted).

  Further, the confidence interval calculation unit 40 in the assembly yield prediction apparatus 1 checks the check location step based on the design values 52 and 54, the sensitivity information 53, the allowable range 55, the number of measurement samples 52, and the multivariate distribution parameter 63 of the partial dimensions. The confidence interval 70 of the yield 69 and the confidence interval 71 of the product yield 68 are predicted and calculated.

  As described above, according to the assembly yield prediction apparatus 1 of the present embodiment, the product yield 68 is predicted in the assembly stage of the product P while taking into account the correlation between the parts of each part of the product P and the check points. Is done. For this reason, the product yield 68 can be accurately predicted. Therefore, the designer or the like may change the manufacturing process (for example, mold adjustment) to reliably optimize (maximize) the product yield 68 based on the product yield 68 predicted with high accuracy. it can.

  In addition, according to the assembly yield prediction apparatus 1 of the present embodiment, at the assembly stage of the product P, the confidence interval 70 of the check location yield is considered while taking into account the correlation between the parts of each part of the product P and the check location. And a confidence interval 71 of the product yield is predicted. Therefore, it is possible to accurately predict the confidence interval 70 of the check location yield and the confidence interval 71 of the product yield. Therefore, the designer or the like refers to the confidence interval 70 of the check location yield 69 or the confidence interval 71 of the product yield 68 predicted with high accuracy, thereby determining how much the check location yield 69 or the product yield 68 is. It is possible to accurately determine whether there is a possibility of blurring.

[2-2] Operation of the assembly yield prediction apparatus 1 in the design stage Next, the assembly yield prediction in the design stage of the product P according to the present embodiment according to the flowchart (steps S11 to S15) shown in FIG. The operation of the device 1 will be described. Note that the yield calculation process P1 illustrated in FIG. 7 includes the processes of steps S12 to S15 executed in the yield calculation processing unit 20. Further, the Monte Carlo process P2 shown in FIG. 7 includes the processes of steps S14 and S15 executed in the Monte Carlo processing unit 22.

  In the design stage of the product P, first, the multivariate distribution parameter 56 of the partial dimension is set by the multivariate distribution parameter determination unit 10 based on the presumed manufacturing variation information 51 of the product P and the design value 52 of the part. It is determined (step S11). As described above, the parameter 56 is, for example, the average (average vector) and variance-covariance matrix of the multivariate normal distribution (simultaneous distribution) of partial dimensions.

  Based on the multivariate distribution parameter 56 determined in step S11, the design value 52 and sensitivity information 53 of the portion, and the design value 54 of each check location #i, the multivariate distribution calculation unit 211 increases the size of the check location. A variable distribution parameter 57 is calculated (step S12). The parameter 57 is also the average (average vector) and variance-covariance matrix of the multivariate normal distribution (simultaneous distribution) of the check spot size, for example.

  Then, based on the multivariate distribution parameter 57 calculated in step S12 and the allowable range 55 of each check location #i, the check location yield calculation unit 212 uses the assembly yield (check location step) of each check location #i. ) 58 is calculated (step S13). At this time, the check location yield 58 is calculated from the relationship between the multivariate distribution parameter 57 of each check location #i and the allowable range 55 of each check location #i.

  On the other hand, in the Monte Carlo processing unit 22, an assembly yield (product yield) 60 of the product P is predicted based on the multivariate distribution parameter 57 calculated in step S12 and the allowable range 55 of each check location #i. (See Monte Carlo processing P2). At this time, first, in the Monte Carlo sample generation unit 221, based on the multivariate distribution parameter 57 of each check location #i, a plurality of Monte Carlo samples 59 each including a set of dimensional data of a plurality of check locations is generated by Monte Carlo simulation. (Step S14).

  Thereafter, the product yield calculation unit 222 compares, for each Monte Carlo sample, the dimensions of the plurality of check locations included in each Monte Carlo sample 59 generated in step S14 and the dimension tolerances 55 of the plurality of check locations. The By this comparison, it is checked for every Monte Carlo sample whether all the check points are included in the allowable range. Then, the product yield 60 is calculated as a ratio of the Monte Carlo samples 59 in which all the check spot dimensions are included in the allowable range 55 among the plurality of generated Monte Carlo samples 59 (step S15). The ratio corresponds to the probability that all check spot dimensions are included in the allowable range 55 in one Monte Carlo sample 59.

[2-3] Operation of the assembly yield prediction apparatus 1 at the assembly stage Next, the assembly yield prediction according to the present embodiment at the assembly stage of the product P according to the flowchart (steps S21 to S26) shown in FIG. The operation of the device 1 will be described. Note that the confidence interval calculation process P3 illustrated in FIG. 8 includes the processes of steps S23 to S26 executed in the confidence interval calculation unit 40. The bootstrap yield calculation process P4 shown in FIG. 8 includes steps S23 and S24 executed in the bootstrap yield calculator 41.

  In the assembly stage of the product P, first, the multivariate distribution parameter 63 of the partial dimension is estimated and acquired by the multivariate distribution parameter estimation unit 30 based on the part sample measurement information 61 which is an actual measurement value of each manufactured part. The The multivariate distribution parameter estimation unit 30 also outputs the number of measurement samples (number of samples) 62 in the component sample measurement information 61 (step S21). As described above, the parameter 63 is, for example, the average (average vector) and variance-covariance matrix of the multivariate normal distribution (simultaneous distribution) of partial dimensions.

  On the basis of the multivariate distribution parameter 63 estimated in step S21, the design value 52 and sensitivity information 53 of the portion, the design value 54 and the allowable range 55 of each check point #i, The multivariate distribution parameter 67, the product yield 68, and the check location yield 69 of the check location #i are predicted and calculated (step S22). The yield calculation process in step S22 will be described later with reference to FIG.

  Then, in the bootstrap sample generation unit 411, based on the number of samples 62 and the multivariate distribution parameter 63 from step S21, the bootstrap sample 64 for the multivariate distribution parameter 63 of the partial dimension is generated by the parametric bootstrap method. (Step S23).

  Thereafter, in the yield calculation processing unit 412, for each bootstrap sample generated in step S23, based on the design value 52 and sensitivity information 53 of the part, the design value 54 and the allowable range 55 of each check point #i. The check location yield 66 and the product yield 65 of each bootstrap sample 64 are calculated (step S24). The yield calculation process in step S24 will be described later with reference to FIG.

  Then, in the check location yield confidence interval calculation unit 42, the assembly yield reliability of each check location #i is based on the check location yield 66 of each bootstrap sample 64 calculated for each bootstrap sample in step S24. The section 70 is calculated (step S25). A specific method for calculating the confidence interval 70 will be described later.

  In addition, the product yield confidence interval calculation unit 43 calculates a product yield confidence interval 71 based on the product yield 65 of each bootstrap sample 64 calculated for each bootstrap sample in step S24 (step S24). S26). A specific method for calculating the confidence interval 71 will be described later.

[2-3-1] Yield Calculation Processing in Step S22 shown in FIG. 8 Next, according to the flowchart (Steps S221 to S224) shown in FIG. 9, the yield calculation processing in Step S22 shown in FIG. The operation of the calculation processing unit 20 will be described. Note that the Monte Carlo process P5 shown in FIG. 9 includes the processes of steps S223 and S224 executed in the Monte Carlo processing unit 22.

  In step S22, first, based on the multivariate distribution parameter 63 estimated in step S21, the partial design value 52 and sensitivity information 53, and the design value 54 of each check location #i, the multivariate distribution calculation unit 211 Thus, the multivariate distribution parameter 67 of the check spot size is calculated (step S221). The parameter 67 is also the average (average vector) and variance-covariance matrix of the multivariate normal distribution (simultaneous distribution) of the check spot size, for example.

  Then, based on the multivariate distribution parameter 67 calculated in step S221 and the allowable range 55 of each check location #i, the check location yield calculation unit 212 uses the assembly yield (check location step) of each check location #i. 69) is calculated (step S222). At this time, the check location yield 69 is calculated from the relationship between the multivariate distribution parameter 67 of each check location #i and the allowable range 55 of each check location #i.

  On the other hand, in the Monte Carlo processing unit 22, an assembly yield (product yield) 68 of the product P is predicted based on the multivariate distribution parameter 67 calculated in step S221 and the allowable range 55 of each check location #i. (See Monte Carlo Process P5). At this time, first, the Monte Carlo sample generation unit 221 generates, based on the multivariate distribution parameter 67 of each check location #i, a plurality of Monte Carlo samples 59 ′ each including a set of dimensional data of a plurality of check locations by Monte Carlo simulation. (Step S223).

  Thereafter, the product yield calculation unit 222 compares, for each Monte Carlo sample, the dimensions of the plurality of check locations included in each Monte Carlo sample 59 ′ generated in step S223 and the dimension tolerances 55 of the plurality of check locations. Is done. By this comparison, it is checked for every Monte Carlo sample whether all the check points are included in the allowable range. Then, the product yield 68 is calculated as a ratio of the Monte Carlo samples 59 ′ in which all the check spot dimensions are included in the allowable range 55 among the plurality of generated Monte Carlo samples 59 ′ (Step S224). This ratio corresponds to the probability that all the check spot dimensions are included in the allowable range 55 in one Monte Carlo sample 59 ′.

[2-3-2] Yield Calculation Processing in Step S24 shown in FIG. 8 Next, according to the flowchart shown in FIG. 10 (Steps S241 to S244), the yield calculation processing in Step S24 shown in FIG. The operation of the calculation processing unit (third yield calculation unit and fourth yield calculation unit) 412 will be described. The Monte Carlo process P6 shown in FIG. 9 includes the processes of Steps S243 and S244 executed in the Monte Carlo processing unit 22.

  The process in step S24 is executed for each bootstrap sample generated in step S23. In step S24, first, based on the bootstrap sample 64 generated in step S21, the partial design value 52 and the sensitivity information 53, and the design value 54 of each check point #i, the multivariate distribution calculation unit 211 performs. Then, the multivariate distribution parameter 67 ′ of the check spot size is calculated (step S241). The parameter 67 ′ is also, for example, the average (average vector) and variance-covariance matrix of the multivariate normal distribution (simultaneous distribution) of the check spot size.

  Then, based on the multivariate distribution parameter 67 ′ calculated in step S 241 and the allowable range 55 of each check location #i, the check location yield calculation unit 212 uses the assembly yield (check location) of each check location #i. Yield) 66 is calculated (step S242). At this time, the check location yield 66 of each bootstrap sample 64 is calculated from the relationship between the multivariate distribution parameter 67 ′ of each check location #i and the allowable range 55 of each check location #i.

  On the other hand, in the Monte Carlo processing unit 22, the product yield 65 of each bootstrap sample 64 is predicted based on the multivariate distribution parameter 67 ′ calculated in step S241 and the allowable range 55 of each check location #i. (See Monte Carlo processing P6). At this time, first, the Monte Carlo sample generation unit 221 generates a plurality of Monte Carlo samples 59 ″ each including a set of dimension data of a plurality of check locations based on the multivariate distribution parameter 67 ′ of each check location #i by Monte Carlo simulation. (Step S243).

  Thereafter, the product yield calculation unit 222 compares, for each Monte Carlo sample, the dimensions of the plurality of check points included in each Monte Carlo sample 59 ″ generated in step S243 and the dimension tolerances 55 of the plurality of check parts. By the comparison, for each Monte Carlo sample, it is checked whether or not all the check points are within the allowable range, and the product yield 65 of each bootstrap sample 64 is generated in the generated plurality of samples. Of the Monte Carlo samples 59 ″, the size of all the check points is calculated as a ratio of the Monte Carlo samples 59 ″ included in the allowable range 55 (step S244). The ratio is calculated for all the check points in one Monte Carlo sample 59 ″. This corresponds to the probability that the dimension falls within the allowable range 55.

[2-4] High-speed Monte Carlo processing (operation of Monte Carlo processing unit 22 ') Next, high-speed Monte Carlo processing executed by the Monte Carlo processing unit 22' shown in FIG. 4 according to the flowchart (S31 to S34) shown in FIG. explain. That is, the operation when the Monte Carlo processing P2, P5, and P6 shown in FIGS. 7, 9, and 10 are executed by the Monte Carlo processing unit 22 ′ shown in FIG. 4 (operation of the Monte Carlo processing unit 22 ′) will be described. .

  The Monte Carlo processing unit 22 ′ changes the processing executed by the above-described Monte Carlo processing unit 22 with respect to the following items (a1) and (a2), while maintaining the prediction accuracy of the product yields 60, 68, and 65. It is possible to increase the speed of the Monte Carlo processes P2, P5, and P6.

(A1) The variance / covariance matrix of the check location is adjusted (normalized) by the size of the allowable range 55 for each check location #i (i = 1, 2,..., N; n is an integer of 2 or more).
(A2) The Monte Carlo sample 76 of the check point #i is generated approximately in a space spanned by the upper D eigenvectors of the normalized eigenvectors of the variance-covariance matrix of the check points with the largest eigenvalue. Here, D is an integer less than n (D <n), and is the minimum number of eigenvectors whose cumulative contribution rate defined by the eigenvalue exceeds a predetermined threshold.

  In the Monte Carlo processing unit 22 ′ that has been changed as described above, since the number of dimensions is reduced from n to D, the amount of calculation per one Monte Carlo sample is reduced, so the Monte Carlo processing P2, P5, and P6 are accelerated. can do. In addition, a direction in which the quality of the check point is likely to change (direction with yield sensitivity) is specified from the eigenvector, and the number of Monte Carlo samples 76 to be generated is determined according to the number of dimensions of the sensitive area. Is done. The smaller the number of dimensions in the sensitive area, the more accurately the product yields 60, 68 and 65 can be predicted with a smaller number of samples. For the above reasons, according to the Monte Carlo processing unit 22 ′ of the present embodiment, it is possible to increase the speed of the Monte Carlo processes P2, P5, and P6 while maintaining the prediction accuracy of the product yields 60, 68, and 65.

  As shown in FIG. 11, in the Monte Carlo processing unit 22 ′, the product yield 60 is based on the multivariate distribution parameters 57, 67, 67 ′, the design value 54 and the allowable range 55 of each check point #i. , 68, 65 are predicted.

  First, the normalization unit 223 normalizes the multivariate distribution parameters 57, 67, 67 ′ of the check spot size, the design value 54 of the check spot, and the dimension allowable range 55 (step S31). That is, coordinate conversion is performed so that the design value 54 of each check location #i is 0 and the size of the allowable range 55 of each check location #i is 1. In addition, multivariate distribution parameters (average, variance-covariance matrix) 57, 67, 67 'are also converted into the coordinate system after the coordinate conversion.

  Thereafter, in the eigenvector / eigenvalue calculation unit 224, a plurality of normal distributions of the check spot size normalized in step S31 (variance covariance matrix 74 of the multivariate normal distribution of the check spot after normalization) are used. The eigenvector and the eigenvalue 75 corresponding to each vector are calculated by singular value decomposition (step S32).

  Then, in the Monte Carlo sample generation unit 221 ′, the Monte Carlo sample 76 at the check location is determined based on the average 73 of the multivariate normal distribution at the check location after normalization at Step S31 and the eigenvector and eigenvalue 75 calculated at Step S32. It is generated (step S33).

  At this time, among the plurality of eigenvectors, the D eigenvectors whose cumulative contribution rate defined by the eigenvalue exceeds a predetermined threshold are extracted. In a space spanned by the extracted D eigenvectors, a plurality of Monte Carlo samples 76 each including a set of dimension data of a plurality of check locations are generated by Monte Carlo simulation. In this way, the check point sample 76 is approximately generated using the eigenvector having a large eigenvalue.

  Then, in the product yield calculation unit 222 ′, for each Monte Carlo sample, based on the allowable range (after normalization) 72 of the check location #i obtained in Step S31 and the Monte Carlo sample 76 generated in Step S33, Product yields 60, 68, 65 are calculated (step S34).

  At this time, the dimensions of the plurality of check locations included in each Monte Carlo sample 76 generated in step S33 are compared with the dimension tolerance ranges 72 of the plurality of check locations normalized in step S31. By this comparison, it is checked whether or not all the check points are included in the allowable range 72 for each Monte Carlo sample. The product yields 60, 68, and 65 are calculated as the proportion of the Monte Carlo samples 76 in which all the check spot dimensions are included in the allowable range 55 among the plurality of generated Monte Carlo samples 76. This ratio corresponds to the probability that all check spot dimensions are included in the allowable range 72 in one Monte Carlo sample 76.

[2-5] Details of Assembly Yield Prediction Device 1 Next, details of the assembly yield prediction device 1 of the present embodiment will be described with reference to FIGS. Hereinafter, as details of the assembly yield prediction apparatus 1, for example, specific examples of input data, output data, and intermediate data, and more specific operations of components of the assembly yield prediction apparatus 1 will be described.

[2-5-1] Sensitivity Information 53 (Input Data) First, an example of sensitivity information 53 that is input data to the assembly yield prediction apparatus 1 of the present embodiment will be described with reference to FIG. FIG. 12 is a diagram illustrating an example of the sensitivity information 53.

  As described above, the sensitivity information 53 is information regarding a value indicating how many mm the check location changes when the partial dimension of the component changes by 1 mm, for example. The sensitivity information 53 includes sensitivities (influences) with respect to all check locations in all parts of all types of components. The sensitivity information 53 is expressed by a matrix as shown in FIG. 12, for example.

In FIG. 12, the product P is assembled from three types of parts A, B, and C, has n check points, and each of the parts A, B, and C has p parts, q parts, and r parts. The sensitivity information 53 is illustrated. The sensitivity information 53 shown in FIG. 12 is a matrix with n rows and m columns, and m = p + q + r. A _{i, j} is the sensitivity to the check point #i (i is an integer from 1 to n) of the part #j (j is an integer from 1 to m).

[2-5-2] Design Data (Input Data) Next, design data that is input data to the assembly yield prediction apparatus 1 of the present embodiment will be described with reference to FIGS. 13 and 14. FIG. 13 is a diagram illustrating an example of the design value 52 and the variation information 51 of a portion that is design data. FIG. 14 is a diagram illustrating an example of the design value 54 and the allowable range 55 of the check location #i, which is design data.

  The design value 52 of the part #j of each part A to C is a value of the dimension (partial dimension) of each part #j determined by design, for example, as shown in FIG. Further, the variation 51 represents the size error of each part #j, and is represented by, for example, tolerance, standard deviation, or variance as shown in FIG. When it is assumed that the distribution of the variation 51 is a normal distribution, the tolerance is often set to 3σ. Here, 1σ is a standard deviation of the assumed normal distribution. When the variation range is represented by a tolerance, the design value 52 is set so as to be the middle value of the variation range. The value from the design value 52 to the boundary of the variation range is a tolerance.

  The design value 54 of each check point #i is the value of the dimension of the check point #i when it is assumed that the parts #j of the parts A to C are all manufactured according to the design value as described above. For example, as shown in FIG. Further, the allowable range 55 of each check location #i represents a range of dimensions that each check location #i must satisfy in order for the product P to be a non-defective product. For example, as shown in FIG. And the upper limit.

[2-5-3] Component Sample Measurement Information 61 (Input Data) Next, with reference to FIG. 15 and FIG. 16, component sample measurement information which is input data to the assembly yield prediction apparatus 1 of the present embodiment. 61 will be described. FIG. 15 is a diagram illustrating an example of the component sample measurement information 61, and FIG. 16 is a diagram illustrating another example of the component sample measurement information 61.

  For example, as shown in FIG. 15 or FIG. 16, the part sample measurement information 61 includes a part name, a part name, a part size, variation, a sample number (sample number), and the like obtained as a sample measurement result of an actually manufactured part. Information. In the part sample measurement information 61 shown in FIG. 15, the size and variation of each part #j are expressed by the average (average vector) of each part #j and the variance-covariance matrix. Also, as in the part sample measurement information 61 shown in FIG. 16, the size and variation of each part #j are given as raw measurement data (actual measurement values) based on the average vector and the variance-covariance matrix. Good. In the matrix representing the measurement data of the part in the part sample measurement information 61 shown in FIG. 16, for example, the jth row corresponds to the measurement data of the part #j, and one column indicates each part of the same part (individual). Corresponds to the measured value.

[2-5-4] Output Data Next, output data from the assembly yield prediction apparatus 1 of the present embodiment will be described.
The assembly yield (product yield) 60, 68 (65) of the product P is output data from the assembly yield prediction device 1 of the present embodiment, and is one predicted value (for example, 97.5%).
The check location yield confidence interval 70 and the product yield confidence interval 71 are also output data from the assembly yield prediction apparatus 1 of the present embodiment. The confidence intervals 70 and 71 will be described later.

  Furthermore, the distribution and yield of each check location #i (multivariate distribution parameters 57 and 67 (67 ′) and check location yields 58 and 69 (66)) are also obtained from the assembly yield prediction device 1 of the present embodiment. Output data, for example, output as shown in FIG. FIG. 17 is a diagram illustrating an example of the distribution information and the yield information of the check location #i output from the assembly yield prediction apparatus 1 according to the present embodiment.

  The distribution information of the check location #i is a parameter representing the size distribution of the check location #i. As shown in FIG. 17, the distribution information is usually the average and variance values of the check spot dimensions. Further, the yield information of the check location #i is a value corresponding to the assembly yield value of the check location #i, that is, the probability that the size of the check location #i falls within the allowable range 55.

[2-5-5] Intermediate Data Next, intermediate data (multivariate distribution parameters of partial dimensions) of processing by the assembly yield prediction apparatus 1 of the present embodiment will be described with reference to FIG. FIG. 18 is a diagram illustrating an example of the average vector and the variance-covariance matrix of the portion that is the multivariate distribution parameter 57, 67, 67 ′ of the partial size of the intermediate data.

As shown in FIG. 18, the multivariate distribution parameter of the partial size includes the partial average vector X (in FIG. 18, a horizontal bar is added to X but omitted in the specification) and the variance covariance matrix Σ. Expressed as _X. At this time, a normal distribution is assumed as the multivariate distribution. As shown in FIG. 18, the average vector X is obtained by integrating the dimensional average values of all the parts # 1 to #m of all types of parts. The variance-covariance matrix Σ _X is obtained by integrating the variances of all parts # 1 to #m of all types of parts.

[2-5-6] Multivariate Distribution Parameter Determination Unit 10 Next, a more specific operation of the multivariate distribution parameter determination unit 10 in the assembly yield prediction apparatus 1 of the present embodiment will be described.

(B1) When the dimensional variation information 51 of the part #j (j is an integer of 1 to m) is given as a tolerance, the multivariate distribution parameter determination unit 10 calculates the following equation (Equation 1) from the given tolerance: The partial variance-covariance matrix Σ _x (multivariate distribution parameter 56) shown in FIG.

However, t _j is the tolerance of the dimension of the part #j, and the above equation (Equation 1) shows an example in which the tolerance is 3σ.
Further, the multivariate distribution parameter determination unit 10 sets the average vector X (multivariate distribution parameter 56) of the part to be the design value of the part #j corresponding to each element (average value of the dimension of the part #j). Generate.

(B2) When the variation information 51 of the size of the part #j is given by the average and variance of the normal distribution of each part #j, the multivariate distribution parameter determination unit 10 calculates the following equation (Equation 2 The partial variance-covariance matrix Σ _x (multivariate distribution parameter 56) shown in FIG.

However, σ _j ² is the variance of the dimension of the part #j.
Further, the multivariate distribution parameter determination unit 10 sets the average vector X (multivariate distribution parameter 56) of the part to the average of the normal distribution of the part #j corresponding to each element (the average value of the dimension of the part #j). Generate as follows.

(B3) When the variation information 51 of the size of the part #j is given by the average vector of the normal distribution and the variance-covariance matrix for each type of part, the multivariate distribution parameter determination unit 10 gives the given type #k A variance-covariance matrix Σ _x (multivariate distribution parameter 56) represented by the following equation (Equation 3) is generated from the variance-covariance matrix Σ _k (where k is an integer of 1 to the number of types of parts).

  Further, the multivariate distribution parameter determination unit 10 generates a partial average vector X (multivariate distribution parameter 56) from the average vector of each type #k as shown in the following equation (Equation 4).

[2-5-7] Multivariate Distribution Parameter Estimation Unit 30 Next, a more specific operation of the multivariate distribution parameter estimation unit 30 in the assembly yield prediction apparatus 1 of the present embodiment will be described.

(C1) When the part sample measurement information 61 is expressed by a partial average vector and a variance-covariance matrix (see, for example, FIG. 15), the multivariate distribution parameter estimation unit 30 uses the average vector as the part sample measurement information 61. And the variance-covariance matrix are output as they are as the estimated values of the multivariate distribution parameters. In this case, the multivariate distribution parameter estimation unit 30 uses the estimated values of the average vector and the variance-covariance matrix of each component as in the case of the item (b3) by the multivariate distribution parameter determination unit 10. And a variance-covariance matrix Σ _X (multivariate distribution parameter 63).

(C2) When the component sample measurement information 61 is raw sample measurement data (see, for example, FIG. 16), the multivariate distribution parameter estimation unit 30 calculates the sample average vector and unbiased variance from the measurement result as the component sample measurement information 61. Calculate the covariance matrix. Then, the multivariate distribution parameter estimation unit 30 sets the calculated sample average vector and the unbiased covariance matrix as the multivariate distribution parameter estimation value, and uses the estimated value to calculate the average vector as in the case of the item (c1). X and the variance-covariance matrix Σ _X (multivariate distribution parameter 63) are generated. Note that the sample mean vector and the unbiased variance covariance matrix are calculated by a general calculation method.

[2-5-8] Check Point Multivariate Distribution Calculation Unit 211 Next, a more specific operation of the check point multivariate distribution calculation unit 211 in the assembly yield prediction apparatus 1 of the present embodiment will be described. .

The distribution of the check spot size is a multivariate normal distribution, and the multivariate distribution calculation unit 211 of the check spot has an average vector Z and a variance covariance matrix Σ _Z (multivariate distribution parameters 57, 67, 67 of the multivariate normal distribution). ′) Is analytically calculated from the multivariate distribution parameters 56 and 63 (64) of the part, the sensitivity information 53, and the design value 54 of the check location by the following equation (Equation 5).

上式（数６）の平均ベクトルＺの要素Ｚ_iは、チェック箇所＃ｉの寸法の平均である。また、Ｙは下式（数７）で与えられる設計値ベクトルである。 However, the average vector Z is given by the following equation (Equation 6).

The element Z _i of the average vector Z in the above equation (Formula 6) is the average of the dimensions of the check location #i. Y is a design value vector given by the following equation (Equation 7).

上式（数７）の設計値ベクトルＹの要素Ｙ_iは、チェック箇所＃ｉの設計値である。さらに、上式（数５）において、Ａは感度行列（図１２参照）、Ｘは部分寸法の平均ベクトル、μは部分の設計値のベクトル、Σ_Ｘは部分の分散共分散行列である。
そして、分散共分散行列Σ_Ｚのｉ番目の対角成分Σ_Ｚ,iiがチェック箇所＃ｉの分散となる。

The element Y _i of the design value vector Y in the above equation (Equation 7) is the design value of the check location #i. Further, in the above equation (Equation 5), A is a sensitivity matrix (see FIG. 12), X is an average vector of partial dimensions, μ is a vector of partial design values, and Σ _X is a partial covariance matrix.
Then, i-th diagonal element sigma _Z covariance matrix sigma _{Z, ii} is the variance of the check point #i.

[2-5-9] Check Point Yield Calculation Unit 212 Next, a more specific operation of the check point yield calculation unit 212 in the assembly yield prediction apparatus 1 of the present embodiment will be described.

  The check location yield calculation unit 212 uses analytically calculated check location multivariate distribution parameters 57, 67, and 67 ', the check location tolerance 55, and the cumulative distribution function of the normal distribution. The probability that the size of each check location #i falls within the allowable range 55 is calculated as the check location yield 58, 69, 66. Here, the cumulative distribution function of the normal distribution is normally prepared as a function or a library in a tool or the like that performs statistical processing.

Here, the distribution of the i th check location #i is a univariate normal distribution, the average of the check location # i is the i th element of the average vector Z, and the variance of the check location # i is wherein an i-th diagonal element of variance-covariance matrix sigma _Z. From these pieces of information and the allowable range 55 of the check location #i, the yield calculation unit 212 determines the probability that the size of the check location #i falls within the allowable range 55, that is, the assembly yields 58 and 69 of the check location #i. , 66 is calculated.

[2-5-10] Monte Carlo processing unit 22 that does not perform high-speed Monte Carlo processing Next, the Monte Carlo processing unit 22 (Monte Carlo sample generation unit 221) when high-speed Monte Carlo processing is not performed in the assembly yield prediction device 1 of this embodiment. ) Will be described in more detail.

The Monte Carlo sample generation unit 221 generates M sets of Monte Carlo samples 59, 59 ′, 59 ″ according to the procedures of the following items (d1) to (d3). The value of M is changed according to the number n of check points. For example, M = 100 ⁿ .

(D1) The Monte Carlo sample generation unit 221 generates n × M random numbers that independently follow a standard normal distribution with an average of 0 and a variance of 1.
(D2) The Monte Carlo sample generation unit 221 generates an n-by-M matrix R _n having the random numbers generated in the item (d1) as elements.
(D3) The Monte Carlo sample generation unit 221 performs matrix calculation according to the following equation (Equation 8), and each column is a set of (check location # 1,..., Check location #n) samples in n rows An M-column matrix _RA is generated.

上式（数８）において、右辺第２項の（Ｚ,…,Ｚ）は、全ての列が平均ベクトルＺであるｎ行Ｍ列の行列である。また、Ｕ_ｎは分散共分散行列Σ_Ｚ′の固有ベクトルｕ₁,…,ｕ_nを固有値の大きい順にならべたもの、つまりＵ_ｎ＝（ｕ₁,…,ｕ_n）である。さらに、Λ_ｎは、下式（数９）に示すような、固有値の平方根を対角要素にもつｎ行ｎ列の行列である。

In the above equation (Equation 8), the second term (Z,..., Z) in the right-hand side is a matrix of n rows and M columns in which all the columns are the average vector Z. Further, eigenvectors u ₁ of _{U n} is the variance-covariance matrix sigma _{Z ',} ..., which arranged the u _n in descending order of eigenvalue, i.e. _U n = (u _1, ..., u _n) it is. Furthermore, Λ _n is an n-by-n matrix having the square root of the eigenvalue as a diagonal element as shown in the following equation (Equation 9).

The matrix R _A generated as described above is output to the product yield calculation unit 222 as M sets of Monte Carlo samples 59, 59 ′, 59 ″. In the product yield calculation unit 222, the product yield is based on the matrix R _A. 60, 68, and 65. The processing by the product yield calculation unit 222 is the same as the processing by the product yield calculation unit 222 ′ in the Monte Carlo processing unit 22 ′ that performs high-speed Monte Carlo processing, which will be described later. The processing by the residue calculation unit 222 will be described later with reference to FIG.

[2-5-11] Normalization Unit 223 Next, a more specific operation of the normalization unit 223 in the assembly yield prediction apparatus 1 of the present embodiment, that is, a normalization process performed by high-speed Monte Carlo processing will be described. .

The normalizing unit 223 calculates an average vector Z ′ and a variance covariance matrix ΣZ _′ , which are multivariate normal distribution parameters (reference numerals 73 and 74) of the check points after normalization, according to the following equation (Equation 10). .

In the above equation (Equation 10), the matrix G is given by the following equation (Equation 11). In the following equation (Equation 11), d _i is the size of the allowable range 55 of the i-th check location #i.

In addition, the normalization unit 223 also normalizes the check spot allowable range 55 as in the following equation (Equation 12), and calculates a normalized allowable range 72. Here, assuming that the lower limit and upper limit of the allowable range of the check point #i before normalization are Ll _i and Lh _i , respectively, the normalization unit 223 lowers the lower limit Ll _i ′ of the allowable range of the check point #i after normalization. The upper limit Lh _i ′ is calculated as shown in the following equation (Equation 12).

  In addition, since the size of the allowable range differs depending on the check location, even if the dimensions at the plurality of check locations are shifted by, for example, the same 0.1 mm, the influence on good / bad varies depending on the check location. Therefore, the purpose of normalization is to make the influence on the yield of each check point the same.

[2-5-12] Eigenvalue / Eigenvector Calculation Unit 224 Next, more specific operation of the eigenvalue / eigenvector calculation unit 224 in the assembly yield prediction apparatus 1 of the present embodiment, that is, the eigenvalue The eigenvector calculation process will be described.

Eigenvalues and Eigenvectors calculation unit 224, the variance-covariance matrix sigma _Z check point after normalization _'(reference numeral 74), the eigenvector u _1, ..., eigenvalues lambda ₁ corresponding to _{u n} and the eigenvectors, ..., lambda _n is calculated by singular value decomposition (see reference numeral 75). However, the eigenvectors u _i are arranged in descending order of the eigenvalues λ _i and the size of each eigenvector u _i is normalized to 1.

Further, the eigenvalue / eigenvector calculation unit 224 has a minimum value D (D is less than n) in which the “cumulative contribution rate C (D)” defined by the following equation (Equation 13) exceeds a predetermined threshold (for example, 0.95). obtains an integer), u _1, ..., a _{u D} and each column, the matrix _U D = (u ₁ u-row column D, ..., and generates a _{u D).}

[2-5-13] Monte Carlo sample generation part 221 'at the check location Next, more specific operation of the Monte Carlo sample generation unit 221' at the check location in the assembly yield prediction apparatus 1 of the present embodiment, that is, the high-speed Monte Carlo sample generation unit 221 '. The Monte Carlo generation process performed in the process will be described.

The Monte Carlo sample generation unit 221 ′ generates M sets of Monte Carlo samples 59, 59 ′, 59 ″ according to the procedures of the following items (e1) to (e3). The value of M is the value of D (<n) described above. For example, M = 100 ^D.

(E1) The Monte Carlo sample generation unit 221 ′ generates D × M random numbers that independently follow a standard normal distribution with an average of 0 and a variance of 1.
(E2) The Monte Carlo sample generation unit 221 ′ generates a D-row and M-column matrix R having the random numbers generated in the item (e1) as elements.
(E3) The Monte Carlo sample generation unit 221 ′ performs matrix calculation according to the following equation (Equation 14), and each column is a set of (check location # 1,..., Check location #n) samples n _A matrix M of rows M columns is generated.

上式（数１４）において、右辺第２項の（Ｚ,…,Ｚ）は、全ての列が平均ベクトルＺであるｎ行Ｍ列の行列である。また、Ｕ_Ｄは、固有値・固有ベクトル計算部２２４で上述のごとく生成されるｕ行Ｄ列の行列Ｕ_Ｄ＝（ｕ₁,…,ｕ_Ｄ）である。さらに、Λは、下式（数１５）に示すような、固有値の平方根を対角要素にもつＤ行Ｄ列の行列である。

In the above equation (Expression 14), the second term (Z,..., Z) in the right-hand side is a matrix of n rows and M columns in which all columns are average vectors Z. U _D is a matrix U _D = (u ₁ ,..., U _D ) with u rows and D columns generated by the eigenvalue / eigenvector calculation unit 224 as described above. Furthermore, Λ is a matrix of D rows and D columns having the square root of the eigenvalue as a diagonal element as shown in the following equation (Equation 15).

The generated matrix _{R A} as described above 'is output to, product yield calculation unit 222' product yield calculation unit 222 as M sets of Monte Carlo samples 76 in, based on the matrix _{R A} product yield 60 and 68, 65 is calculated.

[2-5-14] Product Yield Calculation Units 222 and 222 ′ Next, referring to FIG. 19, the product yield calculation units 222 and 222 ′ in the assembly yield prediction apparatus 1 of the present embodiment A specific operation will be described. FIG. 19 is a flowchart for explaining the processing procedure by the product yield calculation units 222 and 222 ′ of the Monte Carlo processing units 22 and 22 ′ shown in FIGS.

Each column of the matrix _RA of n rows and M columns is a sample of a set (check location # 1,..., check location #n). Product yield calculation unit 222 and 222 'are each Monte Carlo sample generating unit 221, 221' whether it is within the allowable range of the check point for each column (one sample) of the matrix _{R A} of n rows and M columns from To check. Then, the product yield calculators 222 and 222 ′ calculate the ratio of the number of samples determined to be within the allowable range with respect to the total number of samples M as product yields 60, 68, and 65.

Hereinafter, the product yield calculation procedure by the product yield calculators 222 and 222 ′ will be described with reference to the flowchart shown in FIG. 19 (steps S41 to S50).
First, product yield calculation unit 222 and 222 'sets a "0" to "j" indicating the process target column of the matrix _{R A,} after setting the "good" to "0" (step S41) , J is incremented by 1 (step S42). Here, “good” is a parameter indicating the number of samples in which all the check spot dimensions are within the allowable range.

Thereafter, the product yield calculation units 222 and 222 ′ determine whether j exceeds the total number of samples (the number of columns of the matrix _RA ) M (step S43). If j exceeds the total number of samples M, that is, if j> M (YES route of step S43), the processing for all samples of the matrix _RA has been completed, so the product yield calculation units 222, 222 ' Calculates “good / M” as product yields 60, 68, 65 (step S50).

When j does not exceed the total number of samples M, that is, when j ≦ M (NO route of step S43), the product yield calculation unit 222, 222 ′ indicates the check location in the processing target column (sample) #j. “0” is set to “i” (step S44). Thereafter, the product yield calculation unit 222, 222 ′ increments i by 1 (step S45), and then the element (dimension) R _{A, ij} of the check location #i and the check location #i in the processing target column #j. Are compared with the permissible ranges (lower limit Ll _i and upper limit Lh _i ) (step S46).

As a result of the comparison, if the dimension _{RA, ij} is outside the allowable range (NO route of step S46), the product yield calculation units 222, 222 'end the process for the current processing target column #j, and step S42 Then, the process for the next sample is performed.

As a result of the comparison, when the dimension _{RA, ij} is within the allowable range (YES route of step S46), the product yield calculation unit 222, 222 'determines whether i has reached the number n of check points. (Step S47). If i has not reached the number of check points n (NO route of step S47), the product yield calculation units 222 and 222 'proceed to the process of step S45 and perform the process for the next check point.

  When i has reached the number of check points n (YES route of step S47), the product yield calculation unit 222, 222 ′ determines that all the check points of the current processing target column (sample) are within the allowable range. Then, “1” is added to “good” (step S48). Then, the product yield calculators 222 and 222 ′ determine whether j has reached the total number of samples M (step S49).

If j has not reached the total number M of samples (NO route of step S49), the product yield calculation units 222 and 222 'proceed to the process of step S42 and perform the process for the next check location. On the other hand, if j has reached the total number of samples M (YES route in step S49), the processing for all samples in the matrix _RA has been completed, so that the product yield calculation units 222 and 222 ' “Good / M” is calculated as 60, 68, 65 (step S50).

[2-5-15] About Bootstrap Sample Generation Unit 411 Next, a more specific operation of the bootstrap sample generation unit 411 in the assembly yield prediction apparatus 1 of the present embodiment will be described.

The bootstrap sample generation unit 411 uses the parametric bootstrap method from the multivariate distribution parameter (mean, variance-covariance matrix) 63 and the sample number 62 of partial dimensions, and uses the multivariate distribution parameter (mean vector, variance-covariance matrix). ) Is generated. The processing by the bootstrap sample generation unit 411 is performed according to the procedures of the following items (f1) to (f5). Here, the average vector of the multivariate distribution of the partial size of the component type #k (k = 1, 2,...) Is X _k , the variance-covariance matrix of the multivariate distribution is Σ _k , and the number of samples is N _k . . As for the parametric bootstrap method, for example, Sadanori Konishi (Author), Yoshimichi Ochi (Author), Hirohiro Omori (Author) “Method of Computational Statistics—Bootstrap / EM Algorithm / MCMC (Science of Series Prediction and Discovery) 5) See (Asakura Shoten).

(F1) The bootstrap sample generation unit 411 generates N _k sets of random numbers that independently follow the multivariate normal distribution of the mean X _k and the variance-covariance matrix Σ _k .
(F2) The bootstrap sample generation unit 411 calculates the sample average X _k ^* and the unbiased covariance matrix Σ _k ^* of the N _k sets of random numbers generated in the item (f1).
(F3) The bootstrap sample generation unit 411 repeatedly executes the processes of the items (f1) and (f2) as many as the number of types of parts.
(F4) The bootstrap sample generation unit 411 uses a function similar to that of the multivariate distribution parameter determination unit 10 based on the sample mean X _k ^* and the unbiased covariance matrix Σ _k ^* (k = 1, 2,...) Determine the mean vector X ^* and the variance-covariance matrix Σ _X ^* as the set of bootstrap samples 64.
(F5) The bootstrap sample generation unit 411 repeatedly executes the processes of the items (f1) to (f4) as many times as necessary (for example, B set; B is an integer of 2 or more).

[2-5-16] Regarding Yield Calculation Processing Unit 412 and Confidence Interval Calculation Units 42 and 43 Next, the yield calculation processing unit 412 in the assembly yield prediction apparatus 1 of the present embodiment, check location yield confidence interval calculation. Specific operations of the unit 42 and the product yield confidence interval calculation unit 43 will be described.

The yield calculation processing unit 412, the check location yield confidence interval calculation unit 42 and the product yield confidence interval calculation unit 43 follow the procedures of the following items (g1) to (g3), and check location yield confidence interval 70 and product. The calculation process of the yield confidence section 71 is performed. Here, B sets of bootstrap samples 64 prepared in advance by the bootstrap sample generation unit 411 are converted into an average vector X ^* (b) and a variance covariance matrix Σ _X ^* (b) (b = 1,..., B). And

(G1) The yield calculation processing unit 412 uses the bootstrap sample of b = 1, that is, the average vector X ^* (b) and the variance-covariance matrix Σ _X ^* (b) (b = 1) to determine the bootstrap sample. The product yield 65 and the yield 66 of each check point are calculated.
(G2) The yield calculation processing unit 412 repeatedly executes the process of the item (g1) for each of b = 2, 3,. As a result, B product yields and B sets of check location yields are calculated in total.
(G3) The confidence interval calculation units 42 and 43 start from the one with the smallest yield for each check point and product according to a predetermined confidence interval ratio α (for example, 0.95 (95%)). The ratio of [(1-α) / 2] to [1- (1-α) / 2] is calculated as the confidence interval of each yield.

[3] Effects of the present embodiment According to the assembly yield prediction apparatus 1 of the present embodiment, in the design stage of the product P, the product yield is considered while taking into account the correlation between the parts of each part of the product P and the check points. A residue 60 is predicted. For this reason, the product yield 60 can be accurately predicted. Therefore, a designer or the like can make a design change based on the product yield 60 predicted with high accuracy so as to reliably optimize (maximize) the product yield 60.

  Further, according to the assembly yield prediction apparatus 1 of the present embodiment, the product yield 68 is predicted in the assembly stage of the product P while taking into account the correlation between the parts of each part and the check location in the product P. . For this reason, the product yield 68 can be accurately predicted. Therefore, the designer or the like may change the manufacturing process (for example, mold adjustment) to reliably optimize (maximize) the product yield 68 based on the product yield 68 predicted with high accuracy. it can.

  Furthermore, according to the assembly yield prediction device 1 of the present embodiment, the confidence interval 70 of the check location yield is taken into consideration at the assembly stage of the product P while taking into account the correlation between the parts of each part of the product P and the check location. And a confidence interval 71 of the product yield is predicted. Therefore, it is possible to accurately predict the confidence interval 70 of the check location yield and the confidence interval 71 of the product yield. Therefore, the designer or the like refers to the confidence interval 70 of the check location yield 69 or the confidence interval 71 of the product yield 68 predicted with high accuracy, thereby determining how much the check location yield 69 or the product yield 68 is. It is possible to accurately determine whether there is a possibility of blurring.

  Further, according to the assembly yield prediction apparatus 1 of the present embodiment, the check location distribution 57 and the yield 58 are also accurately predicted and calculated in consideration of the correlation between the parts of the parts of the product P and the check locations. The Therefore, the designer or the like can change the design of the product P so as to improve the product yields 60 and 68 with reference to the check spot distribution 57 and the yield 58 predicted with high accuracy. .

  On the other hand, in the Monte Carlo processing unit 22 ′ of the present embodiment, by reducing the number of dimensions from n to D, the amount of calculation per one Monte Carlo sample is reduced, and the Monte Carlo processing P2, P5, and P6 can be speeded up. it can. Also, the direction in which the good / bad of the check location is likely to change is identified from the eigenvector, and the number of Monte Carlo samples 76 to be generated is determined according to the number of dimensions of the sensitive region. The smaller the number of dimensions in the sensitive area, the more accurately the product yields 60, 68 and 65 can be predicted with a smaller number of samples. Therefore, according to the Monte Carlo processing unit 22 ′ of the present embodiment, the Monte Carlo processes P 2, P 5, and P 6 can be speeded up while maintaining the prediction accuracy of the product yields 60, 68, 65. The speeding up of predictions 68 and 65 is also realized.

  With the recent miniaturization of products and the limitations of manufacturing technology, for example, as shown in FIGS. 20 and 21, variations in manufacturing processes are relatively increased with respect to component sizes. For this reason, even if it is going to manufacture the same kind of parts similarly by variation of a manufacturing process, it cannot manufacture in the same way. That is, it is impossible to manufacture the same type of components so that the distribution of the component dimensions is the same. Therefore, the distribution varies depending on the manufacturing conditions (manufacturing process), and it is necessary to accurately predict the assembly yield of the product for each combination of these parts. According to the assembly yield prediction apparatus 1 of the present embodiment, the product yield can be accommodated while taking into account the manufacturing process variability in consideration of the manufacturing variability of parts and the correlation between the parts of each part and the check location in the product P. 60 and 68 can be predicted with high accuracy. 20 and 21 are diagrams for explaining manufacturing process variations.

[4] Others While the preferred embodiment of the present invention has been described in detail above, the present invention is not limited to such a specific embodiment, and various modifications and changes can be made without departing from the spirit of the present invention. It can be changed and implemented.

[5] Supplementary Notes The following supplementary notes are further disclosed with respect to the embodiments including the above embodiments.
(Appendix 1)
An assembly yield prediction apparatus for predicting an assembly yield of a product assembled by a plurality of parts,
An acquisition unit for acquiring multivariate distribution parameters of partial dimensions including correlation information between a plurality of partial dimensions in each part;
Based on the multivariate distribution parameter of the partial dimensions acquired by the acquisition unit and the sensitivity information indicating the degree of influence of the change in the partial dimensions of the parts on the dimensions of a plurality of check points in the product, the same A multivariate distribution parameter of check location dimensions including correlation information generated between the dimensions of the plurality of check locations due to changes in the size of each part in the component affecting the dimensions of the plurality of check locations. A variable distribution calculator,
A prediction unit that predicts an assembly yield of the product based on a multivariate distribution parameter of the check spot size calculated by the multivariate distribution calculation unit;
An assembly yield prediction apparatus having:

(Appendix 2)
The prediction unit
A plurality of Monte Carlo samples each including a set of dimension data of the plurality of check locations based on the multivariate distribution parameter of the check location dimensions; a first sample generation unit that generates by Monte Carlo simulation;
The dimensions of the plurality of check locations included in the plurality of Monte Carlo samples generated by the first sample generation unit are respectively compared with the dimension tolerance ranges of the plurality of check locations, and the product based on the comparison result A first yield calculation unit for calculating the assembly yield of
The assembly yield prediction apparatus according to appendix 1, including:

(Appendix 3)
The prediction unit
A normalization unit that normalizes the multivariate distribution parameter of the check spot dimension and the dimension tolerance of the plurality of check spots;
An eigenvector / eigenvalue calculation unit that calculates a plurality of eigenvectors and eigenvalues corresponding to each vector by singular value decomposition from the multivariate distribution parameter of the check spot size normalized by the normalization unit;
Among the plurality of eigenvectors, in a space spanned by eigenvectors whose cumulative contribution rate defined by the eigenvalue exceeds a predetermined threshold, a plurality of Monte Carlo samples each including a set of dimension data of the plurality of check locations are obtained by Monte Carlo simulation. A first sample generation unit to generate;
The dimensions of the plurality of check points included in the plurality of Monte Carlo samples generated by the first sample generation unit are respectively compared with the dimension allowable ranges of the plurality of check points normalized by the normalization unit. A first yield calculation unit for calculating an assembly yield of the product based on the result of the comparison;
The assembly yield prediction apparatus according to appendix 1, including:

(Appendix 4)
Second yield calculation for calculating an assembly yield of each of the plurality of check locations based on the multivariate distribution parameter of the check location dimensions calculated by the multivariate distribution calculation unit and the size tolerance of the plurality of check locations. The assembly yield prediction apparatus according to any one of Supplementary Note 1 to Supplementary Note 3, further including a unit.

(Appendix 5)
The assembly yield prediction apparatus according to any one of Supplementary Note 1 to Supplementary Note 4, wherein the acquisition unit acquires a multivariate distribution parameter of the partial dimensions based on a manufacturing variation of the product assumed in advance.

(Appendix 6)
The assembly yield prediction apparatus according to any one of appendix 1 to appendix 4, wherein the acquisition unit acquires a multivariate distribution parameter of the partial dimension based on an actual measurement value of each manufactured part.

(Appendix 7)
An error occurring in the multivariate distribution parameter of the partial dimension due to the number of samples of the actual measurement value is estimated, and a confidence interval of the assembly yield of each of the plurality of check points is determined based on the estimated error and the sensitivity information. The assembly yield prediction apparatus according to appendix 6, further comprising a first confidence interval calculation unit for calculating.

(Appendix 8)
The first confidence interval calculation unit includes:
A second sample generation unit that generates a bootstrap sample for the multivariate distribution parameter of the partial dimension based on the number of samples and the multivariate distribution parameter of the partial dimension by a parametric bootstrap method;
For each of the bootstrap samples generated by the second sample generation unit, based on the sensitivity information, the change in the size of each part in the same part affects the size of the plurality of check points. A multivariate distribution parameter of a check spot size including correlation information generated between the dimensions of a plurality of check spots is calculated, and based on the calculated multivariate distribution parameter of the check spot dimension and the dimension tolerance of the plurality of check spots. A third yield calculator that calculates an assembly yield of each of the plurality of check points;
Check location yield for calculating an assembly yield confidence interval for each of the plurality of check locations based on the assembly yield for each of the plurality of check locations calculated for each bootstrap sample by the third yield calculation section. A confidence interval calculator,
The assembly yield prediction device according to appendix 7, including:

(Appendix 9)
An error occurring in the multivariate distribution parameter of the partial dimension due to the number of samples of the actual measurement value is estimated, and the estimated error, the sensitivity information, and a change in each partial dimension in the same part are checked. A confidence interval for the assembly yield of the product is calculated based on the multivariate distribution parameter of the check spot size including correlation information generated between the dimensions of the plurality of check spots due to affecting the size of the spot. The assembly yield prediction apparatus according to appendix 6, further comprising a second confidence interval calculation unit.

(Appendix 10)
The second confidence interval calculation unit includes:
A second sample generation unit that generates a bootstrap sample for the multivariate distribution parameter of the partial dimension based on the number of samples and the multivariate distribution parameter of the partial dimension by a parametric bootstrap method;
For each of the bootstrap samples generated by the second sample generation unit, based on the sensitivity information, the change in the size of each part in the same part affects the size of the plurality of check points. A multivariate distribution parameter of a check spot size including correlation information generated between dimensions of a plurality of check spots is calculated, and a set of dimension data of the plurality of check spots is calculated based on the calculated multivariate distribution parameter of the check spot dimension. A plurality of Monte Carlo samples each including a plurality of Monte Carlo simulations, the dimensions of the plurality of check locations included in the generated plurality of Monte Carlo samples are compared with the size tolerances of the plurality of check locations, respectively. Based on the result of the comparison, the assembly yield of the product is calculated. And the yield calculation unit,
A product yield confidence interval calculation unit that calculates an assembly yield confidence interval of the product based on the assembly yield of the product calculated for each bootstrap sample by the fourth yield calculation unit;
The assembly yield prediction apparatus according to appendix 9, including:

(Appendix 11)
The second confidence interval calculation unit includes:
A second sample generation unit that generates a bootstrap sample for the multivariate distribution parameter of the partial dimension based on the number of samples and the multivariate distribution parameter of the partial dimension by a parametric bootstrap method;
For each of the bootstrap samples generated by the second sample generation unit, based on the sensitivity information, the change in the size of each part in the same part affects the size of the plurality of check points. A multivariate distribution parameter of a check spot size including correlation information generated between the dimensions of a plurality of check spots is calculated, and the calculated multivariate distribution parameter of the check spot dimension and the dimension tolerance of the plurality of check spots are normalized. A plurality of eigenvectors and eigenvalues corresponding to each vector are calculated by singular value decomposition from the normalized multivariate distribution parameters of the check spot dimensions, and the cumulative contribution defined by the eigenvalues of the plurality of eigenvectors is calculated. In a space spanned by eigenvectors whose rate exceeds a predetermined threshold, the plurality of A plurality of Monte Carlo samples each including a set of dimension data of check locations are generated by Monte Carlo simulation, and the sizes of the plurality of check locations included in the generated plurality of Monte Carlo samples and the plurality of normalized checks A fourth yield calculation unit that compares the dimensional tolerances of each part and calculates the assembly yield of the product based on the result of the comparison;
A product yield confidence interval calculation unit that calculates an assembly yield confidence interval of the product based on the assembly yield of the product calculated for each bootstrap sample by the fourth yield calculation unit;
The assembly yield prediction apparatus according to appendix 9, including:

(Appendix 12)
To a computer that predicts the assembly yield of products assembled by multiple parts,
Obtain multivariate distribution parameters of partial dimensions including correlation information between multiple partial dimensions in each part,
Each part in the same part based on the acquired multivariate distribution parameter of the part dimension and the sensitivity information indicating the degree of influence of the change in the part dimension of each part on the dimensions of the plurality of check points in the product Calculating a multivariate distribution parameter of a check spot size including correlation information generated between the dimensions of the plurality of check spots due to a change in dimension affecting the dimensions of the plurality of check spots;
Predicting the assembly yield of the product based on the calculated multivariate distribution parameters of the check spot dimensions;
Assembly yield prediction program that executes processing.

(Appendix 13)
In addition to the computer,
Based on the multivariate distribution parameter of the check spot dimensions, a plurality of Monte Carlo samples each including a set of dimension data of the plurality of check spots is generated by Monte Carlo simulation,
The dimensions of the plurality of check locations included in the generated plurality of Monte Carlo samples are respectively compared with the size tolerance ranges of the plurality of check locations, and the assembly yield of the product is calculated based on the comparison result. ,
The assembly yield prediction program according to appendix 12, which causes processing to be executed.

(Appendix 14)
In addition to the computer,
Normalizing the multivariate distribution parameters of the check spot dimensions and the dimensional tolerances of the plurality of check spots;
From the normalized multivariate distribution parameter of the check spot size, a plurality of eigenvectors and eigenvalues corresponding to each vector are calculated by singular value decomposition,
Among the plurality of eigenvectors, in a space spanned by eigenvectors whose cumulative contribution rate defined by the eigenvalue exceeds a predetermined threshold, a plurality of Monte Carlo samples each including a set of dimension data of the plurality of check locations are obtained by Monte Carlo simulation. Generate
The dimensions of the plurality of check points included in the generated plurality of Monte Carlo samples are respectively compared with the normalized size tolerances of the plurality of check points, and the assembly step of the product is based on the comparison result. Calculate the
The assembly yield prediction program according to appendix 12, which causes processing to be executed.

(Appendix 15)
In the computer,
Based on the measured value of each manufactured part, to obtain the multivariate distribution parameter of the partial dimensions,
The assembly yield prediction program according to any one of appendix 12 to appendix 14, wherein the program is executed.

(Appendix 16)
In addition to the computer,
An error occurring in the multivariate distribution parameter of the partial dimension due to the number of samples of the actual measurement value is estimated, and a confidence interval of the assembly yield of each of the plurality of check points is determined based on the estimated error and the sensitivity information. calculate,
The assembly yield prediction program according to appendix 15, which causes the process to be executed.

(Appendix 17)
In the computer,
Based on the number of samples and the multivariate distribution parameter of the partial dimension, a bootstrap sample for the multivariate distribution parameter of the partial dimension is generated by a parametric bootstrap method,
For each of the generated bootstrap samples, based on the sensitivity information, the change in the size of each part in the same part affects the size of the plurality of check locations. Multivariate distribution parameters of the check location dimensions including correlation information generated in the check location dimensions, and based on the calculated multivariate distribution parameters of the check location dimensions and the dimensional tolerances of the plurality of check locations, Calculate assembly yield,
Based on the assembly yield of each of the plurality of check locations calculated for each bootstrap sample, calculate a confidence interval for the assembly yield of each of the plurality of check locations;
The assembly yield prediction program according to appendix 16, wherein the process is executed.

(Appendix 18)
In addition to the computer,
An error occurring in the multivariate distribution parameter of the partial dimension due to the number of samples of the actual measurement value is estimated, and the estimated error, the sensitivity information, and a change in each partial dimension in the same part are checked. A confidence interval for the assembly yield of the product is calculated based on the multivariate distribution parameter of the check spot size including correlation information generated between the dimensions of the plurality of check spots due to affecting the size of the spot. ,
The assembly yield prediction program according to appendix 15, which causes the process to be executed.

(Appendix 19)
In the computer,
Based on the number of samples and the multivariate distribution parameter of the partial dimension, a bootstrap sample for the multivariate distribution parameter of the partial dimension is generated by a parametric bootstrap method,
For each of the generated bootstrap samples, based on the sensitivity information, the change in the size of each part in the same part affects the size of the plurality of check locations. A plurality of Monte Carlo samples each including a set of dimension data of the plurality of check locations based on the calculated multivariate distribution parameter of the check location dimensions including the correlation information generated in Is generated by Monte Carlo simulation, and the dimensions of the plurality of check locations included in the generated plurality of Monte Carlo samples are respectively compared with the dimension tolerance ranges of the plurality of check locations, and based on the result of the comparison, Calculate the product assembly yield,
Calculating a confidence interval for the assembly yield of the product based on the assembly yield of the product calculated for each bootstrap sample;
The assembly yield prediction program according to appendix 18, wherein the process is executed.

(Appendix 20)
A computer that predicts the assembly yield of a product assembled by multiple parts,
Obtain multivariate distribution parameters of partial dimensions including correlation information between multiple partial dimensions in each part,
Each part in the same part based on the acquired multivariate distribution parameter of the part dimension and the sensitivity information indicating the degree of influence of the change in the part dimension of each part on the dimensions of the plurality of check points in the product Calculating a multivariate distribution parameter of a check spot size including correlation information generated between the dimensions of the plurality of check spots due to a change in dimension affecting the dimensions of the plurality of check spots;
An assembly yield prediction method for predicting an assembly yield of the product based on the calculated multivariate distribution parameter of the check spot size.

1 Assembly yield prediction device 2 Processing unit (CPU, computer)
3 Storage unit (memory)
10 Multivariate distribution parameter determination unit (acquisition unit)
20 Yield calculation processing unit 21 Check point calculation unit 211 Multivariate distribution calculation unit (multivariate distribution calculation unit)
212 Check point yield calculator (second yield calculator)
22, 22 'Monte Carlo processing unit (prediction unit)
221 and 221 ′ Monte Carlo sample generator (first sample generator)
222, 222 'Product yield calculator (first yield calculator)
223 normalization unit 224 eigenvector / eigenvalue calculation unit 30 multivariate distribution parameter estimation unit (acquisition unit)
40 confidence interval calculator (first confidence interval calculator, second confidence interval calculator)
41 Bootstrap yield calculation unit 411 Bootstrap sample generation unit (second sample generation unit)
412 Yield calculation processing unit (third yield calculation unit, fourth yield calculation unit)
42 Check location yield confidence interval calculation unit (Check location yield confidence interval calculation unit)
43 Product yield confidence interval calculator (Product yield confidence interval calculator)
51 Partial variation information (Product manufacturing variation)
52 Design value of part 53 Sensitivity information (influence) of parts
54 Check point design value 55 Check point tolerance (Check point dimension tolerance)
56,63 Partial multivariate distribution parameters (partial size multivariate distribution parameters)
57, 67, 67 'Check point multivariate distribution parameters (check point size multivariate distribution parameters)
58, 69 Check location yield (assembling yield of check location)
59, 59 ', 59 ", 76 Checked Monte Carlo samples 60, 68 Product yield (product assembly yield)
61 Parts sample measurement information (actual measurement)
62 Number of specimens (number of samples)
64 Bootstrap sample 65 Bootstrap sample product yield (product assembly yield)
66 Bootstrap sample check point yield 70 Check point yield confidence interval 71 Product yield confidence interval 72 Check point tolerance (after normalization)
73 Average of multivariate distribution of check points after normalization 74 Variance covariance matrix of multivariate distribution of check points after normalization 75 Eigenvectors and eigenvalues

Claims (12)

An assembly yield prediction apparatus for predicting an assembly yield of a product assembled by a plurality of parts,
An acquisition unit for acquiring multivariate distribution parameters of partial dimensions including correlation information between a plurality of partial dimensions in each part;
The same component based on the multivariate distribution of the partial dimensions acquired by the acquisition unit and the sensitivity information indicating the degree of influence of the change in the partial dimensions of the components on the dimensions of the plurality of check points in the product A multivariate for calculating a multivariate distribution parameter of a check spot size including correlation information generated between the dimensions of the plurality of check spots due to a change in the size of each of the parts in FIG. A distribution calculator;
A prediction unit that predicts an assembly yield of the product based on a multivariate distribution parameter of the check spot size calculated by the multivariate distribution calculation unit;
An assembly yield prediction apparatus having: The prediction unit
A plurality of Monte Carlo samples each including a set of dimension data of the plurality of check locations based on the multivariate distribution parameter of the check location dimensions; a first sample generation unit that generates by Monte Carlo simulation;
The dimensions of the plurality of check locations included in the plurality of Monte Carlo samples generated by the first sample generation unit are respectively compared with the dimension tolerance ranges of the plurality of check locations, and the product based on the comparison result A first yield calculation unit for calculating the assembly yield of
The assembly yield prediction apparatus according to claim 1, comprising: The prediction unit
A normalization unit that normalizes the multivariate distribution parameter of the check spot dimension and the dimension tolerance of the plurality of check spots;
An eigenvector / eigenvalue calculation unit that calculates a plurality of eigenvectors and eigenvalues corresponding to each vector by singular value decomposition from the multivariate distribution parameter of the check spot size normalized by the normalization unit;
Among the plurality of eigenvectors, in a space spanned by eigenvectors whose cumulative contribution rate defined by the eigenvalue exceeds a predetermined threshold, a plurality of Monte Carlo samples each including a set of dimension data of the plurality of check locations are obtained by Monte Carlo simulation. A first sample generation unit to generate;
The dimensions of the plurality of check points included in the plurality of Monte Carlo samples generated by the first sample generation unit are respectively compared with the dimension allowable ranges of the plurality of check points normalized by the normalization unit. A first yield calculation unit for calculating an assembly yield of the product based on the result of the comparison;
The assembly yield prediction apparatus according to claim 1, comprising:   Second yield calculation for calculating an assembly yield of each of the plurality of check locations based on the multivariate distribution parameter of the check location dimensions calculated by the multivariate distribution calculation unit and the size tolerance of the plurality of check locations. The assembly yield prediction apparatus according to claim 1, further comprising a unit.   The assembly yield prediction apparatus according to any one of claims 1 to 4, wherein the acquisition unit acquires a multivariate distribution parameter of the partial dimensions based on an actual measurement value of each manufactured part.   An error occurring in the multivariate distribution parameter of the partial dimension due to the number of samples of the actual measurement value is estimated, and a confidence interval of the assembly yield of each of the plurality of check points is determined based on the estimated error and the sensitivity information. The assembly yield prediction apparatus according to claim 5, further comprising a first confidence interval calculation unit for calculating. The first confidence interval calculation unit includes:
A second sample generation unit that generates a bootstrap sample for the multivariate distribution parameter of the partial dimension based on the number of samples and the multivariate distribution parameter of the partial dimension by a parametric bootstrap method;
For each of the bootstrap samples generated by the second sample generation unit, based on the sensitivity information, the change in the size of each part in the same part affects the size of the plurality of check points. A multivariate distribution parameter of a check spot size including correlation information generated between the dimensions of a plurality of check spots is calculated, and based on the calculated multivariate distribution parameter of the check spot dimension and the dimension tolerance of the plurality of check spots. A third yield calculator that calculates an assembly yield of each of the plurality of check points;
Check location yield for calculating an assembly yield confidence interval for each of the plurality of check locations based on the assembly yield for each of the plurality of check locations calculated for each bootstrap sample by the third yield calculation section. A confidence interval calculator,
The assembly yield prediction apparatus according to claim 6, comprising:   An error occurring in the multivariate distribution parameter of the partial dimension due to the number of samples of the actual measurement value is estimated, and the estimated error, the sensitivity information, and a change in each partial dimension in the same part are checked. A confidence interval for the assembly yield of the product is calculated based on the multivariate distribution parameter of the check spot size including correlation information generated between the dimensions of the plurality of check spots due to affecting the size of the spot. The assembly yield prediction apparatus according to claim 5, further comprising a second confidence interval calculation unit. The second confidence interval calculation unit includes:
A second sample generation unit that generates a bootstrap sample for the multivariate distribution parameter of the partial dimension based on the number of samples and the multivariate distribution parameter of the partial dimension by a parametric bootstrap method;
For each of the bootstrap samples generated by the second sample generation unit, based on the sensitivity information, the change in the size of each part in the same part affects the size of the plurality of check points. A multivariate distribution parameter of a check spot size including correlation information generated between dimensions of a plurality of check spots is calculated, and a set of dimension data of the plurality of check spots is calculated based on the calculated multivariate distribution parameter of the check spot dimension. A plurality of Monte Carlo samples each including a plurality of Monte Carlo simulations, the dimensions of the plurality of check locations included in the generated plurality of Monte Carlo samples are compared with the size tolerances of the plurality of check locations, respectively. Based on the result of the comparison, the assembly yield of the product is calculated. And the yield calculation unit,
A product yield confidence interval calculation unit that calculates an assembly yield confidence interval of the product based on the assembly yield of the product calculated for each bootstrap sample by the fourth yield calculation unit;
The assembly yield prediction apparatus according to claim 8, comprising: The second confidence interval calculation unit includes:
A second sample generation unit that generates a bootstrap sample for the multivariate distribution parameter of the partial dimension based on the number of samples and the multivariate distribution parameter of the partial dimension by a parametric bootstrap method;
For each of the bootstrap samples generated by the second sample generation unit, based on the sensitivity information, the change in the size of each part in the same part affects the size of the plurality of check points. A multivariate distribution parameter of a check spot size including correlation information generated between the dimensions of a plurality of check spots is calculated, and the calculated multivariate distribution parameter of the check spot dimension and the dimension tolerance of the plurality of check spots are normalized. A plurality of eigenvectors and eigenvalues corresponding to each vector are calculated by singular value decomposition from the normalized multivariate distribution parameters of the check spot dimensions, and the cumulative contribution defined by the eigenvalues of the plurality of eigenvectors is calculated. In a space spanned by eigenvectors whose rate exceeds a predetermined threshold, the plurality of A plurality of Monte Carlo samples each including a set of dimension data of check locations are generated by Monte Carlo simulation, and the sizes of the plurality of check locations included in the generated plurality of Monte Carlo samples and the plurality of normalized checks A fourth yield calculation unit that compares the dimensional tolerances of each part and calculates the assembly yield of the product based on the result of the comparison;
A product yield confidence interval calculation unit that calculates an assembly yield confidence interval of the product based on the assembly yield of the product calculated for each bootstrap sample by the fourth yield calculation unit;
The assembly yield prediction apparatus according to claim 8, comprising: To a computer that predicts the assembly yield of products assembled by multiple parts,
Obtain multivariate distribution parameters of partial dimensions including correlation information between multiple partial dimensions in each part,
Each part in the same part based on the acquired multivariate distribution parameter of the part dimension and the sensitivity information indicating the degree of influence of the change in the part dimension of each part on the dimensions of the plurality of check points in the product Calculating a multivariate distribution parameter of a check spot size including correlation information generated between the dimensions of the plurality of check spots due to a change in dimension affecting the dimensions of the plurality of check spots;
Predicting the assembly yield of the product based on the calculated multivariate distribution parameters of the check spot dimensions;
Assembly yield prediction program that executes processing. A computer that predicts the assembly yield of a product assembled by multiple parts,
Obtain multivariate distribution parameters of partial dimensions including correlation information between multiple partial dimensions in each part,
Each part in the same part based on the acquired multivariate distribution parameter of the part dimension and the sensitivity information indicating the degree of influence of the change in the part dimension of each part on the dimensions of the plurality of check points in the product Calculating a multivariate distribution parameter of a check spot size including correlation information generated between the dimensions of the plurality of check spots due to a change in dimension affecting the dimensions of the plurality of check spots;
An assembly yield prediction method for predicting an assembly yield of the product based on the calculated multivariate distribution parameter of the check spot size.

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