JPH09330858A - Method and system for generating schedule management chart - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a management chart generation system in which the quality of product can be controlled appropriately even under a state where a statistic management state proposed by Shewhart is not reached. SOLUTION: A multinominal distribution model generating section 160, a multivariate beta distribution generating section 162, and a multivariate beta multinominal distribution generating section 164 generate a composite distribution model in which a decision is not made that the process itself is abnormal when the typical variation of variate in the process is within a specified range. Subsequently, a first management chart generating section 168 generates a management chart according to the composite distribution model thus obtained.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a control chart creating system for producing a control chart of a process using measured categorical data in a manufacturing process in which one or more kinds of categorical data are measured as inspection data. And how to create it.

[0002]

2. Description of the Related Art In recent years, when a semiconductor or the like is manufactured, a control chart is prepared to manage a device, a person (operator) arrangement or a material constituting a manufacturing process, and a product included in a lot, A method of determining whether a semi-finished product or the like is in a desirable state is used.

A binomial distribution or a polynomial distribution is generally used as a model for creating such a control chart. Moreover, when managing a process using categorical data, p control charts and multivariate control charts based on the statistical control state proposed by Shewhart have been created and used.

[0004]

The statistical management state proposed by Shewhart is interpreted as follows.
That is, "almost all of the dots plotted on the control chart are within the control limits. In the stable state, the only cause of fluctuation is accidental fluctuation, and there are causes that cannot be overlooked. It is considered not to do so (see Kaoru Ishikawa: “Control Chart”, Nikka Giren Publishing Co., Ltd., (1962)). However, in the actual manufacturing process of the product, the control chart may have to be used at a stage where the statistical control state is not reached. Particularly in the field of semiconductor manufacturing, control charts are often used at the above-mentioned stage because the product switching cycle is short.

Before reaching the state of statistical control of Shewhart, there are parameter model changes and random model changes. The parameter model changes and their causes are as follows. It is explained. That is, "the cause of a parameter model change is a numerical cause (which can be found by stratification in many cases) such as a machine, a set, or a material, and a technical awareness such as temperature and pressure. It is a cause that can be changed (often found by correlation analysis) (Ishikawa
Enka: "Control Chart", Nikkan Giren Publishing Co., Ltd., (1962)). On the other hand, the random model change and its cause are explained as follows. `` The cause of random model change is the cause of changing the characteristic value at random, and it is difficult to find the cause by stratification method, etc., and the way of grouping is changed or it jumps out of the limit. It is possible to discover the cause of the point by carefully pursuing it (see Kaoru Ishikawa: “Control Chart”, Nikkan Giren Publishing Co., Ltd., (1962)). By eliminating the causes mentioned above, the statistical management state of Shewhart is achieved. However, regarding the above two types of causes, “When controlling a process, it is easy to find a parameter-like cause and it is difficult to find a random-like cause (Ken Ishikawa:“ Control Chart Method ”, Nikka Giren Publisher, (1962)). "It is said that.

Therefore, there are many cases where a product is manufactured in a state where the cause of the variation model change cannot be completely removed.
At that time, if the state of a stable composite distribution, which is a random model change, is managed by a conventional control chart that does not allow intergroup variation, the risk rate increases. That is, when the judgment is made based on the normal management status (Shewhardt's statistical management status), it may be judged as abnormal even if the stable composite distribution is followed. At this time, even if the cause of the abnormality is pursued, it is not easy to find the cause, and there is a problem that the efficiency of failure analysis is reduced. Further, if such a state continues, there is a risk that the management of the process using the control chart may be stopped at the manufacturing site.

In particular, in the manufacturing process of semiconductors, quality control of products at the time of product startup is a problem. At this stage, there exist a mixture of a parameter model change and a random model change in the process. On the other hand, since semiconductor products are required to have a rapid rise in product yield, there are many cases where products are manufactured in a state in which the cause of variation model changes cannot be completely eliminated.

The present invention provides a control chart creating system and a creating method capable of appropriately controlling the quality of a product even when the product does not reach the statistical control state proposed by Shewhart such as the product start-up time. The purpose is to provide.

[0009]

An object of the present invention is to create a control chart for judging whether or not a process is in a stable state based on a change in quality characteristic value of a product or a semi-finished product obtained by a process. And a first distribution model generating means for generating a composite distribution model that does not judge the process itself to be abnormal when the random model change of the process is within a predetermined range. And a first control chart creating means for creating a control chart according to the composite distribution model obtained by the first distribution model producing means.

That is, according to the present invention, a stable composite distribution state is considered as a stable state from the standpoint of removing a parameter model cause and recognizing a random model cause, and a product or a semi-finished product obtained from a certain process is considered. Judging whether the group is in a stable composite distribution.

According to the present invention, since the process itself is not judged to be abnormal when the variation model-like change after removing the parameter model-like cause is within a predetermined range, the initial product mass production is not performed. It is possible to reduce the risk of erroneous determination of process abnormality in a stage or the like. As a result, the efficiency of process control can be improved.

In a preferred embodiment of the present invention, a second model for generating a model for judging that the process is in a control state when the parameter model change of the process is within a predetermined range is further provided. The distribution model generating means and the second control chart generating means for generating a control chart according to the model obtained by the model generating means are provided.

In a further preferred aspect of the present invention, according to the control chart obtained by the first control chart creating means, a variation between a predetermined group of products or semi-finished products obtained in the step is specified. It is provided with a judging means for judging whether the state of probability variation according to the probability distribution or the variation between groups does not follow a specific probability distribution.

Alternatively, according to the control chart obtained by the second control chart creating means, it is judged whether or not a predetermined group of products or semi-finished products obtained in the step is in a statistical control state. , When any one of the groups is not in the statistical control state, according to the control chart obtained by the first control chart creating means, any one of the groups changes between the groups. It is provided with a determination means for determining whether a state of probability variation according to a specific probability distribution or a state of variation between groups does not follow a specific probability distribution.

According to these preferred embodiments, the judgment means is such that the groups of products or semi-finished products are stochastically varied according to a specific probability distribution, or
It is judged whether or not the probability is unchanged, or whether or not it is in the statistical control state. As a result, the user can know in which of the above-mentioned states a certain group is, and based on that, it becomes possible to more appropriately determine the abnormality in the process.

[0016] In a further preferred aspect of the present invention, the first distribution model generation means is a multinomial distribution model generation means for generating a multinomial distribution model, and the product obtained in the step based on the multinomial distribution model generation means. Alternatively, a multivariate beta distribution model generating means for generating an inter-group variation multivariate beta distribution model considering variations between groups of semi-finished products and a multivariate beta distribution model obtained by the multivariate beta distribution model generating means Based on the multivariate beta multinomial distribution model generating means for obtaining the multivariate beta multinomial distribution model based on the
^And a variable conversion means for performing variable conversion to approximate the ^two distributions.

[0017] In a further preferred aspect of the present invention, the variable conversion means is configured to perform inverse sine conversion. Thereby, the obtained multivariate beta multinomial distribution can be approximated to a multivariate normal distribution.

[0018] In a further preferred aspect of the present invention, the first control chart creating means calculates a Mahalanobis distance from a centroid of multidimensional data of the multivariate beta multinomial distribution subjected to variable transformation. , A control chart is created by plotting the square of the obtained distance for each group.

[0019] In a further preferred aspect of the present invention, the first control chart creating means further includes a degree-of-freedom adjusting means for adjusting the degree of freedom, and a value according to χ ² of the adjusted degree of freedom. It is configured to create a control chart by plotting. According to this embodiment, the accuracy of the above-mentioned approximation can be further improved.

The object of the present invention is based on the variation of the quality characteristic value of the product or semi-finished product obtained by a certain process.
A control chart creating method for creating a control chart for determining whether or not the process is in a stable state, wherein the process itself is determined to be abnormal when the variation model change of the process is within a predetermined range. It is also achieved by a process control chart creating method configured to generate a composite distribution model that does not, create a control chart according to the obtained composite distribution model, and output the obtained control chart.

[0021]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the accompanying drawings. FIG. 1 is a block diagram showing the configuration of a control chart creating system according to an embodiment of the present invention. As shown in FIG. 1, the control chart creation system 10 includes a data input device 11 including a keyboard and a mouse, a control unit 12 that controls input / output of the system, and a data storage unit 1 including a database.
4, a data processing unit 16 that executes a process for creating a control chart used for process control, and an output device 18 including a CRT, a printer, and the like. In the present embodiment, the control chart creating system is configured to obtain the control chart based on the data obtained by the inspection of the semi-finished product obtained when the previous process is completed in the semiconductor manufacturing process. There is.

The semiconductor manufacturing process includes a step of forming a rod-shaped single crystal, a step of cutting a rod of a single crystal and polishing the surface of the cut piece to form a mirror-like wafer, a circuit on the mirror-like wafer. It includes a step of forming a pattern, a step of cutting a mirror-finished wafer into chip sizes, a step of wiring the cut chips, and a step of packaging. In the present embodiment,
The pre-process means forming a circuit pattern on the mirror-finished wafer.

The control unit 12 accepts the data given to the data input device 11 by the operation of the operator, and in response to the accepted data, reads the data stored in the data storage unit 14 or reads the read data. Is sent to the data processing unit 16 and predetermined processing is performed.
To run. Further, it is connected to an inspection device (not shown) for inspecting various steps of a semiconductor manufacturing device (not shown),
The data given from the inspection device is accepted and the data is stored in the database of the data storage unit 14.

The data processing unit 16 responds to a command from the control unit 12 to create a predetermined control chart. This data processing unit includes a multinomial distribution generation unit 160 that generates a multinomial distribution model according to the number of categories, a multivariate beta distribution generation unit 162 that generates an intergroup variation multivariate beta distribution model based on the multinomial distribution model, Data from the multivariate beta multinomial distribution model generation unit 164 that obtains the multivariate beta multinomial distribution model based on the obtained multivariate beta distribution model, the variable conversion unit 166 that performs the variable conversion on the multivariate beta multinomial distribution, and the variable conversion unit 166 In accordance with the above, the first control chart creating unit 168 and the multinomial distribution generating unit 160 for creating the first control chart
A second control chart creating unit 17 that creates a second control chart by a conventional method according to the multinomial distribution model obtained in
0, and a determination unit 172 that determines a process defect, a product defect, or a semi-finished product defect based on the control charts obtained by the first control chart creation unit 168 and the second control chart creation unit 170. ing.

In this embodiment, after the pre-process is completed, the obtained semi-finished products are inspected to classify them into non-defective products and other P-type defective products. That is, the semi-finished products obtained by this inspection are classified into any of the P + 1 categories.

Therefore, in this embodiment,
With an inspection device (not shown), for each semi-finished product lot,
Categorical data, which is inspection data classified into P + 1 categories, is obtained, and the obtained inspection data is given to the control chart creating system 10, and the data storage unit 1 thereof is provided.
4 is stored. More specifically, in this embodiment, of the k groups (lots), the i-th (1 ≦ i ≦
From the group (lot) of k), n samples are extracted and classified into P categories, and the j-th (1
Let r _ij be the number of samples that belong to the category (j-th classification) of ≦ j ≦ P). Therefore, the categorical data is the number of samples r _ij (1 ≦ i ≦ k, 1 ≦ j
≦ P).

Further, conventionally, a binomial distribution or a polynomial distribution has been used as a model for describing categorical data. In the present embodiment, the multinomial distribution model generation unit 161 causes the control unit 12 to generate a multinomial distribution model based on the inspection data read from the data storage unit 14.

The multinomial distribution model generator 160 is a joint random variable P _{M of} the random variables (r ₁ , ..., r _{P + 1} ) according to the multinomial distribution (P + 1 term distribution in this embodiment).
Is calculated based on the following equation (1).

[0029]

[Equation 1]

In the present embodiment, n in equation (1) is used.
Is the number of semi-finished samples taken from one lot, r _i (1 ≦ i ≦ P + 1) is the number of semi-finished products included in a j-th category (j-th classification), π _j (1 ≦
j ≦ P + 1) is a parameter.

The parameters of the joint random variable P _M obtained by the multinomial distribution model generation unit 160 are given to the second control chart generation unit 170 and the multivariate beta distribution generation unit 162.

In the present invention, the composite distribution model based on the composite distribution of the multinomial distribution and the beta distribution means that the distributions within the group (reference numerals 201-1 to 201-k) are used as shown in FIG. The attached distribution refers to a model in which the parameters of the conditional distribution follow a constant distribution (see reference numeral 203) for each group. In the present embodiment, as an example of the model, it is considered that the number r _{ij of} samples belonging to a specific category follows the multivariate beta distribution.
In order for the number of samples to follow the multivariate beta distribution,
It is necessary that data is collected in a predetermined data format, that a work standard exists, and that the process is executed in compliance with the work standard to some extent. Of these conditions, the data in the predetermined format corresponds to the categorical data given to the system in the present embodiment. Therefore, in the present embodiment, there is a work standard in the semiconductor manufacturing process, and , I think that the process is executed so as to comply with the work standard.

The multivariate beta distribution generator 162 for obtaining the intergroup variation multivariate beta distribution is a multinomial distribution model generator 160.
The parameters (π ₁ , ..., π _P ) given by are accepted, and the multivariate beta distribution (in the present embodiment,
The joint probability density function f _MB of the random variable according to the P-variate beta distribution) is calculated (see the equation (2) below).

[0034]

[Equation 2]

This is because when n samples extracted from the population can be distributed to a plurality of types (for example, P + 1 types) that are repulsive, the categorical data of one group is conditional multinomial distribution. According to (for example, P + 1 term distribution), the population component ratio of the conditional multinomial distribution for each group (for example, (π ₁ , ..., π _P )) becomes a multivariate beta distribution (for example, P variable beta distribution). Therefore, it can be assumed to fluctuate. Considering this way, further, the distribution according to the categorical data of (for example, the number of constituents P + 1) can be represented by the multivariate beta multinomial distribution (for example, the P-variate beta P + 1 term distribution) as a whole.

Therefore, in this embodiment, the multivariate beta multinomial distribution generator 164 uses the P-variate beta P + 1.
The joint random variable P _MBM of the random variables (r ₁ , ..., R _{P + 1} ) according to the term distribution is calculated based on the following formula (3).

[0037]

(Equation 3)

The parameters of the joint random variable P _MBM thus obtained are given to the variable conversion unit 166. The variable conversion unit 166 is provided to approximate the multivariate beta multinomial distribution to a multivariate normal distribution and obtain a state in which a multivariate control chart can be created.

Here, the principle of the calculation executed by the variable conversion unit 166 and the first control chart creation unit 168 will be described.

By approximating the distribution of variation between groups to the composite distribution to a normal distribution and approximating the conditional distribution corresponding to the variation within the group to a normal distribution of equal variance, the entire composite distribution can be approximated to a composite normal distribution. it can. This will be described in more detail below. In addition, in order to simplify the explanation,
A case where the variable is 1 will be described.

The beta binomial distribution BB (n, α1, α2) has a structure in which intergroup variation is a beta distribution and conditional distribution corresponding to intragroup variation is a binomial distribution. In the binomial distribution,
It is well known that normal approximation can be performed under the condition of N π ≧ 5, where N is the size of the group and π is the population defective rate. However, in the binomial distribution of the beta, since the population defective rate π is distributed, even if the normality of the conditional binomial distribution is guaranteed, the homoscedasticity is not guaranteed.

Further, the beta distribution according to the mother defective rate has two shape parameters α1 and α2, and various shapes are obtained by combining them. However, as in the present embodiment, there is a work standard in the actual manufacturing process of semiconductor devices and the like, so that it is sufficiently expected that the distribution shape will be a single peak.

Therefore, in connection with the present embodiment, a range will be considered in the case where α1> 1 and α2> 1 in which the beta distribution is unimodal. In the range of α1> 1 and α2> 1, the beta distribution is unimodal, but even in this case, it may have distortion. Therefore, as a beta binomial distribution, approximation to the normal distribution is not always sufficient. is not. Therefore, the inverse sine transform, which is the dispersion stabilizing transform of the binomial distribution with respect to the beta binomial distribution, is calculated according to the equation (4).

[0044]

(Equation 4)

By performing such an inverse transformation, the conditional binomial distribution can be approximated to a normal distribution having homodispersity, and the distortion of the beta distribution can be improved. In this way, it is possible to improve the approximation to the normal distribution by applying the inverse sine transform to the beta binomial distribution.

Next, the approximation of the multivariate beta multinomial distribution to the multivariate normal distribution will be described. By obtaining this multivariate normal distribution, it becomes possible to create a multivariate control chart. Of the P + 1 random variables (r ₁ , ..., R _{P + 1} ) that follow the multivariate beta multinomial distribution, P random variables (r ₁ ,
, R _p ) and perform the inverse sine transformation based on them. Of these, the number of observations of the j-th classification of the i-th group is r _ij . A vector of values obtained by performing a numerical conversion on these r _{ij according} to the equation (4) (in reality, j = 1, 2, ... P + 1 in the equation (4)) is R _i (R = {R _i1 ,
R _i2 , ..., R _{i (P + 1)} }), and the population mean vector of the distribution is μ _RMBM , and the _population variance covariance matrix Σ _RMBM is given, the multivariate beta polynomial The distribution can be approximated to a multidimensional normal distribution by the inverse sine transform. At this time, as shown in the equation (5), the Mahalanobis distance D _RMBM from the center of gravity of the multidimensional data approximately follows the χ (chi) square distribution of the degree of freedom P.

[0047]

(Equation 5)

However, even if the multivariate beta distribution is unimodal, it takes various shapes depending on the parameters. Therefore, when certain parameters are combined, the approximation to the normal distribution becomes insufficient, and the Mahalanobis distance is reduced. It may not be approximated to the χ (chi) square distribution of the degree of freedom P. For this reason, the Mahalanobis distance D calculated by equation (5)
_The variable conversion shown in the equations (6) and (7) is applied to the _RMBM .

[0049]

(Equation 6)

[0050]

(Equation 7)

Here, φ is the degree of freedom.

The value Δ ² after this variable conversion approximately follows the χ (chi) square distribution of the degree of freedom φ. By adjusting the degree of freedom φ in this way, the accuracy of approximation can be further improved. The variable conversion value Δ ² is used as the value to be plotted on the control chart.

Now, the parameter α _j (j = 1, 2, ... P + 1) of the multivariate beta multinomial distribution and the population mean vector μ
Relationship between _RMBM and population variance-covariance matrix sigma _RMBM is represented by equation (8) to (11).

[0054]

(Equation 8)

Here, E (R _i ) is an element of the population mean vector and represents the average of the variable R _i , and V (R _i ) is the variable R _i.
, Cov (R _i , R _i ) is the covariance of the variables R _i and R _j .

_Further , the relation between the parameters of the multivariate beta multinomial distribution and the _population mean vector μ _RMBM / _population variance covariance matrix Σ _RMBM after variable conversion is expressed by the following equations (12) to (17). . In the equation (12), G = [dr _i /
r _j ] (where d is a partial differential symbol).

[0057]

[Equation 9]

Based on the above-described principle, in the present embodiment, the variable conversion unit 166 divides the number of observations r _i by the size of the group, that is, the number n of samples, and calculates the inverse sine of the equation (4). Perform the conversion.

Next, the first control chart creating unit 168
According to the equation (5), the Mahalanobis distance of the numerical value after the inverse sine transformation is calculated. At this time, the parameters of the multivariate beta polynomial distribution are actually estimated from the past data using the method of moments, and the population mean vector μ _RMBM and _population variance calculated based on the equations (13) to (18) are calculated. The covariance matrix Σ _RMBM is used. Furthermore, equation (6) and
Δ approximated to χ (chi) square distribution according to equation (7)
Ask for ² . A control chart can be obtained by plotting the obtained Δ ² . Note that E (D _RMBM ² ) and V (D _RMBM ² ) used in equations (6) and (7) are
The average and variance of D _RMBM ² obtained from the actual data based on the equation (5) are used.

Further, the first control chart creating section 168 produces a control chart in which these values are plotted based on the obtained value Δ ² . The control chart thus obtained is displayed on the screen of the CRT that constitutes the output device 18, or printed on a printer sheet. FIG. 3 shows an example of the control chart thus obtained.

In this control chart, statistical control states are defined to mean stable beta multinomial states. Also, the P-variate vector P + 1 of the i-th group (i-th group)
If the parameters of the term distribution are α _{i · 1} , ..., α _{i · P + 1} and the parameters in the control state are α _1c , ..., α _{P + 1c} , the control chart is Will be tested.

H0: α _{i · 1} = α _1c , α _{i · 2} = α _2c , ...
,, α _{i · P + 1} = α _{P + 1c} H1: ~ H0 (at least one of the above equations is not satisfied), where "~" indicates negation.

Further, under the above-mentioned statistical management state, the distribution of the statistical amount is approximately a χ (chi) square distribution of the degree of freedom φ.

As shown in FIG. 3, the control chart 300 is provided with two control limit lines 301 and 302. These control limit lines are calculated by the second control chart creation unit 170.

One control limit line 301 is the upper control limit line (UCL) and corresponds to the value of [χ ² (φ; 0.0027)]. The other control limit line 302 is the central line (CL), which is a median line. In the first control chart creating unit 162, the median line is also used to determine the run.

On the other hand, as described above, the parameters of the joint random variable P _M obtained by the multinomial distribution model generating unit 160 are given to the second control chart generating unit 170. The second control chart creation unit 170 creates a p control chart or a multivariate control chart based on the given parameters according to a conventional method. FIG. 4 shows the second control chart creation unit 17
0 shows an example of a control chart obtained using the conventional method.

The determination unit 172 is the first control chart creation unit 16
8 and the control chart obtained by the second control chart creating unit 170, whether each group (lot) is in the control state,
Alternatively, it is determined whether it is in an unmanaged state. In this embodiment, when the statistic of the group is between the upper limit and the lower limit of the control chart (normal control chart) created by the second control chart creating section 170, the determining section 172 determines whether the group statistic Judging to be in the statistical management state proposed by Hart. This means that there is no intergroup variation in status. On the other hand, although the normal control chart is not in a stable state (statistical control state proposed by Shewhart), the statistic of the group is the control chart created by the first control chart creating unit 168 (intergroup control). When it is between the upper limit (upper control limit line) and the lower limit (center line) in the control chart in consideration of fluctuation, it is determined that the control state is in a broad sense. This means a state in which there is variation between groups (variation between groups), but there is a probability variation according to a specific probability distribution, that is, a state according to a specific distribution. Further, in the normal control chart, the control chart is not in a stable state (statistical control state), and the statistic of the group is a control chart created by the first control chart creating unit 168 (a management considering the intergroup variation). When it is not between the upper limit (upper limit control line) and the lower limit (center line) in the figure), it is determined that the state is unmanaged. This is because there is intergroup variability,
This means a state that does not follow a specific probability distribution.

The judging section 172 judges whether each group (lot) is in the statistical management status, the management status in a broad sense, or the non-management status, and prepares a comprehensive judgment table based on this judgment. And output this to a CRT, plotter, etc. 1
Give 8

FIG. 5 is a diagram showing an example of the comprehensive judgment table obtained by the judgment unit 17. In FIG. 5, for example,
The first group (lot) (No. 501) is not included in the statistical control state, that is, the statistic is not between the upper limit and the lower limit in the normal control chart, but in the broad control state. It is included, that is, it means that the statistic is between the upper limit and the lower limit in the control chart in which the variation between groups is taken into consideration. Further, the second group (lot) (number 502) and the third group (lot) (number 503) are included in the statistical management state, and the Mth group (lot) is the statistical amount. Between the upper and lower limits in the normal control chart, respectively, and
It means that it is not between the upper limit and the lower limit in the control chart in which the variation between groups is taken into consideration.

In this way, the judgment section 172 obtains the comprehensive judgment table, which is displayed on the screen of the CRT,
Alternatively, it is printed on printer paper by a plotter. Based on this comprehensive judgment table, the manager
You can judge defects.

According to the present embodiment, in process control in a state where the cause of the variation model-like change cannot be completely eliminated,
It is possible to reduce the possibility of accidentally determining an abnormality.

Further, according to the present embodiment, it is possible to obtain the control chart by the conventional method and the control chart in which the variation between groups (variation between groups) is taken into consideration, and therefore, the statistics proposed by Shewhart In addition to the statistical management state, the stable composite distribution state can be determined even when the statistical management state does not apply. This makes it possible to determine the control status of the process more precisely. That is, it is possible to improve the efficiency of process control in the initial stage of mass production by classifying into two states the states in which there is inter-group variation, which is the non-control state in the conventional control chart. The present invention is not limited to the above embodiments, and various modifications can be made within the scope of the invention described in the claims, and those are also included in the scope of the present invention. Needless to say.

For example, in the above embodiment, the Mahalanobis distance χ is adjusted by adjusting the degree of freedom φ.
^Although the accuracy of approximation to the ^two distributions has been improved, such adjustment of the degree of freedom φ is not always necessary. In this case, the Mahalanobis distance D squared (D
² ) may be obtained and the obtained D ² may be plotted to obtain a control chart.

Further, in the above-mentioned embodiment, the data obtained by inspecting the obtained semi-finished product after the pre-process of the semiconductor manufacturing process is finished is used, but the present invention is not limited to this. Alternatively, the data obtained by inspecting the semi-finished product obtained when the other steps are completed or the final product may be used. Further, it is needless to say that the data is not limited to the data in the semiconductor manufacturing process.

Furthermore, although lots are associated with groups in the above-described embodiment, the present invention is not limited to this, and the target (eg, chip, wafer, due date) or the like that the user wants to analyze and compare is not limited to this. Clearly, groups can be matched.

In the present specification, the term "means" does not necessarily mean physical means, but also includes the case where the function of each means is realized by software.
Further, the function of one means may be realized by two or more physical means, or the functions of two or more means may be realized by one physical means.

[0077]

According to the present invention, it is possible to appropriately control the quality of a product even when the product does not reach the statistical control state proposed by Shewhart such as the product start-up time. And it becomes possible to provide the creation method.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of a control chart creating system according to an embodiment of the present invention.

FIG. 2 is a diagram for explaining the concept of a composite distribution model.

FIG. 3 is a control chart obtained according to an embodiment of the present invention.

FIG. 4 is a control chart obtained by a conventional method.

FIG. 5 is a diagram showing an example of a determination result obtained by the determination unit of the present embodiment.

[Explanation of symbols]

 10 control chart creation system 11 data input device 12 control unit 14 data storage unit 16 data processing unit 18 output device 160 multinomial distribution model generation unit 162 multivariate beta distribution generation unit 164 multivariate beta multinomial distribution generation unit 166 variable conversion unit 168th 1 control chart creation unit 170 2nd control chart creation unit

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Claims (12)

[Claims] 1. A control chart creating system for producing a control chart for judging whether or not a process is in a stable state based on a change in a quality characteristic value of a product or a semi-finished product obtained by a process, wherein: When the variation model change of the process is within a predetermined range,
First distribution model generation means for generating a composite distribution model that does not judge the process itself to be abnormal, and first creation of a control chart according to the composite distribution model obtained by the first distribution model generation means A process control chart creation system, comprising: 2. A second distribution model generating means for generating a model for judging that the process is in a controlled state when the parameter model change of the process is within a predetermined range, and The process control chart creation system according to claim 1, further comprising: second control chart creation means for creating a control chart according to the model obtained by the model generation means. 3. According to the control chart obtained by the first control chart creating means, the variation between the predetermined groups of the product or the semi-finished product obtained in the step varies according to a specific probability distribution. 2. The process control chart creation system according to claim 1, further comprising: a determination unit that determines whether the current state or a variation between groups does not follow a specific probability distribution. 4. According to the control chart obtained by said second control chart creating means, it is judged whether or not a predetermined group of products or semi-finished products obtained in said step is in a statistical control state. , When any one of the groups is not in the statistical control state, according to the control chart obtained by the first control chart creating means, any one of the groups changes between the groups. 7. A determination means is provided for determining whether a state of probability variation according to a specific probability distribution or a state of variation between groups does not follow a specific probability distribution. The process control chart creation system described in 2. 5. The first distribution model generating means generates a polynomial distribution model, a polynomial distribution model generating means, and a group of products or semi-finished products obtained in the step based on the polynomial distribution model generating means. A multivariate beta multinomial distribution model based on a multivariate beta distribution model generation means for generating a group-variable multivariate beta distribution model considering fluctuations and a multivariate beta distribution model obtained by the multivariate beta distribution model generation means A multivariate beta multinomial distribution model generating means for obtaining the above and a variable transforming means for performing a variable transform for approximating the multivariate beta polynomial distribution to a χ ² distribution having a predetermined degree of freedom. The process control chart creation system according to any one of 1 to 4. 6. The process control chart creation system according to claim 5, wherein the variable conversion means executes inverse sine conversion. 7. The first control chart creating means calculates a Mahalanobis distance from a centroid of multidimensional data of the multivariate beta polynomial distribution subjected to variable conversion, and for each group,
7. The process control chart creation system according to claim 5, wherein the control chart is created by plotting the obtained square of the distance. 8. The first control chart creating means further comprises:
8. The process control chart creation according to claim 7, further comprising: a degree-of-freedom adjusting unit for adjusting the degree of freedom, and creating a control chart by plotting a value according to χ ² of the adjusted degree of freedom. system. 9. A control chart creating method for producing a control chart for judging whether or not a process is in a stable state based on a change in a quality characteristic value of a product or a semi-finished product obtained by a process, comprising: When the variation model change of the process is within a predetermined range,
It is configured to generate a composite distribution model that does not judge that the process itself is abnormal, create a control chart according to the obtained composite distribution model, and output the obtained control chart. A method for creating process control charts. 10. A third model obtained by generating a second model for judging that the process is in a control state when the parameter model change of the process is within a predetermined range. 10. The process control chart creating method according to claim 9, wherein the method is configured to create a second control chart according to the model and output the obtained second control chart. 11. Further, according to the first control chart, a state in which a variation in a predetermined group of products or semi-finished products obtained in the step is a probability variation according to a specific probability distribution, and 10. The process control chart creating method according to claim 9, wherein the process control chart creating method is configured to determine which of the states does not follow a specific probability distribution and output the determination result. 12. Further, according to the second control chart, it is judged whether or not a predetermined group of products or semi-finished products obtained in the step is in a statistical control state, and When any of the groups is not in the statistical management state, according to the first control chart, any one of the groups has a probability that the variation between the groups varies according to a specific probability distribution. 11. The process control chart creation according to claim 10, wherein it is configured to determine which of the states where the variation between groups does not follow a specific probability distribution and output the determination result. Method.