JP2014238666A - Prediction expression generation method, prediction expression generation device and prediction expression generation program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate a prediction expression presenting simple dependency of a manufacturing condition parameter and a manufacturing result.SOLUTION: A prediction expression generation device applies a data order in a predetermined order according to the size of an index, to a plurality of pieces of past result data acquired in a past and comprising a manufacturing condition and a predetermined index related to a manufacturing result using the manufacturing condition; and is a predetermined prediction expression calculating a score by applying the data of the manufacturing condition. When a score order is applied in a predetermined order according to the size of the score calculated by the prediction expression, to each of the plurality of pieces of past result data, the prediction expression generation device generates a prediction expression so that the score order of each of the plurality of pieces of past result data is identical to the data order.

Description

  The present invention relates to a prediction formula creation method for predicting a manufacturing result from manufacturing conditions.

  In general, a means for classifying performance data into a plurality of groups based on the manufacturing result is defined for the manufacturing condition and the manufacturing result, and further, a mathematical formula (discriminant) capable of such classification is determined from the manufacturing condition. The “discriminant analysis” found is widely used. For example, a certain threshold is set for the defect rate, and cases (actual data) are classified into a “low defect rate class” in which the defect rate is lower than the threshold and a “high defect rate class” in which the defect rate is higher than the threshold. is there.

  As an example in which such discriminant analysis is used, manufacturing result information is “defective rate”, manufacturing condition information is “composition composition”, and principal component analysis and discriminant analysis are used to produce a low defective rate. A method for determining the condition, that is, the blending ratio has been proposed (Patent Document 1).

  In such discriminant analysis, for example, when X1, X2,... Are used as manufacturing condition parameters, constant coefficients A1, A2,... Are used, and the discriminant Y = A1 * X1 + A2 * X2 +.・ ・ Is defined. When the actual manufacturing result using the actual manufacturing condition parameter is classified into class 1, the value of the discriminant Y calculated for the actual manufacturing condition parameter value is the actual manufacturing result. Coefficients A1, A2,... That are classified in the same way as (also called training data) are obtained. For example, if the value of Y exceeds a certain threshold value α, that is, if Y> α, the class A is classified into class 1, the coefficients A1, A2,. Desired.

  And the value of Y calculated by giving the manufacturing condition parameter to be analyzed to the discriminant using the obtained coefficients A1, A2,... Grouping is performed.

JP 2011-70503 A

  However, in such discriminant analysis, the Y value obtained by the discriminant is for determining which class it belongs to, and therefore, from the Y value, for example, the “defective rate” belongs Class, in other words, you can know if the “defective rate” is high or low. However, it is difficult to predict the manufacturing result index indicating how high or how low the “defective rate” is, that is, the degree of “defective rate”.

  Therefore, an object of the present invention is to generate a prediction expression that represents a monotonous dependency between a manufacturing condition parameter and a manufacturing result.

  In order to achieve the above-described object, the prediction formula generation device according to the present invention includes a plurality of past performance data acquired in the past consisting of manufacturing conditions and a predetermined index related to manufacturing results using the manufacturing conditions. A ranking provision unit that assigns a data ranking in a predetermined order according to the size of the index; and a prediction formula generation unit that generates a predetermined prediction formula for calculating a score given the data of the manufacturing condition, the prediction formula The generation unit assigns the score ranking of each of the past performance data to the past performance data when the score ranking is given in the predetermined order according to the score calculated by the prediction formula. The prediction formula is generated so as to be the same as the data ranking.

  Then, the prediction formula generation method according to the present invention provides a plurality of past performance data acquired in the past consisting of a manufacturing condition and a predetermined index related to a manufacturing result using the manufacturing condition, in accordance with the size of the index. A ranking ordering step for assigning data rankings in order, and a prediction formula generation step for generating a predetermined prediction formula for calculating the score given the data of the manufacturing conditions, in the prediction formula generation step, the past results When the score ranking is given to each data according to the score calculated by the prediction formula in the predetermined order, the score ranking of each of the past performance data is the same as the data ranking given in the ranking granting step. A prediction formula is generated so that

  Further, according to the present invention, the prediction formula generation program to be executed by the computer is a plurality of past performance data acquired in the past consisting of manufacturing conditions and a predetermined index related to manufacturing results using the manufacturing conditions. The computer functions as a rank assigning unit that assigns data ranks in a predetermined order according to the size of the index, and a prediction formula generation unit that generates a predetermined prediction formula that calculates the score given the data of the manufacturing conditions, The prediction formula generation unit assigns the score ranking of each of the past performance data to each of the past performance data when the score ranking is assigned in the predetermined order according to the magnitude of the score calculated by the prediction formula. The prediction formula is generated so as to be the same as the data rank assigned in the section.

  Further, in the above-described state estimation device, the prediction formula is a linear polynomial composed of a plurality of manufacturing conditions and coefficients, and the prediction formula generation unit is under a constraint condition that a sum of squares of the coefficients is 1. Based on the first score when the production condition of past performance data of a certain data rank is given to the prediction formula, the production condition of the past performance data of the previous data rank of the certain data rank is given to the prediction formula. When the difference value obtained by subtracting the second score is 0 or more, the difference value is replaced with 0 as a new difference value, and the difference value obtained by subtracting the second score from the first score is greater than 0. In the case of being small, the difference value is replaced with a value corresponding to the difference value as a new difference value, and the absolute value of the sum of the new difference values corresponding to all past performance data is equal to or less than a predetermined threshold value. It is preferable to determine the coefficient .

  According to the prediction formula generation device, the prediction formula generation method, and the prediction formula generation program having such a configuration, a prediction formula that can calculate a large value score if a predetermined index related to an actual manufacturing result increases. Can be generated. Therefore, by using the prediction formula, it is possible to predict how much the index, for example, the “defective rate” is. In addition, as a predetermined | prescribed parameter | index regarding a manufacturing result, there exist an index | index showing product quality, such as a parameter | index showing production efficiency, such as a yield and a defective rate, a component ratio of the finished product, for example.

  With the prediction formula generation device, the prediction formula generation method, and the prediction formula generation program having such a configuration, it is possible to generate a prediction formula that represents a monotonous dependency between the manufacturing condition parameter and the manufacturing result.

It is a figure which shows the usage example of a prediction formula production | generation apparatus. It is a block diagram which shows the structure of a prediction formula production | generation apparatus. It is a flowchart of the prediction formula production | generation process of the prediction formula production | generation apparatus of FIG. It is a figure which shows the structure and content example of track record data. It is a figure for demonstrating the actual quality index Q and the score Y by a prediction formula. It is a figure which shows the structure and content example of track record data. It is a figure for demonstrating the actual quality index Q and the score Y by a prediction formula. It is a figure which shows the structure and content example of track record data. It is a figure for demonstrating the actual quality index Q and the score Y by a prediction formula.

<Embodiment>
In discriminant analysis, the value of Y according to the discriminant is not an indication (predicted value) indicating the manufacturing result index (eg, “defective rate”) itself. Therefore, from the overall average, it can be said that there is a monotonous dependency such as the score of cases with a low defect rate is higher than the average with a high defect rate, but for individual cases , The magnitude of the Y value and the defect rate do not necessarily have a monotonous relationship, for example, “the larger the score, the smaller the defect rate”.

  In addition, such “average monotonic dependence” may give results that are contrary to actual phenomena or intuition, depending on variations in data or variables used for analysis. Such analysis is often performed using data obtained in actual operation, and is easily subject to "bias" due to production conditions (variety, equipment, raw material conditions) and measurement conditions at that time.

  For example, if data on relatively easy-to-create varieties and data on difficult-to-make varieties are mixed, class discrimination is performed using manufacturing condition parameters that are characteristic for manufacturing easy-to-make varieties. In some cases, there is no practical meaning, and it is useful to analyze data after extracting only the same varieties that are difficult to make.

  As an alternative, a method for predicting the manufacturing result index itself, for example, a method for predicting the defect rate itself from the manufacturing condition parameter may be considered. In other words, it is a method of finding a mathematical formula of <defective rate> = F (<manufacturing condition parameter>). In this case, if predictable, monotonic dependence on a case-by-case basis is guaranteed, and the above problems can be avoided to some extent. It is difficult to reproduce (predict) with.

  The prediction formula generation apparatus of the embodiment is not a formula for predicting the manufacturing index (defective rate) itself from the example, but a prediction formula in which the magnitude of the Y value and the manufacturing index (defective rate) have a monotonous relationship. , More easily generated.

Embodiments according to the present invention will be described below with reference to the drawings.
<Configuration>
FIG. 1 is a diagram illustrating a prediction formula generation device 1 and a usage example of the prediction formula generation device 1. The prediction formula generation device 1 includes a database (auxiliary storage unit) 16 that stores past performance data, and an arithmetic processing unit 11 that generates a prediction formula from the performance data. Details of the prediction formula generation apparatus 1 will be described later with reference to FIG. The user uses the prediction formula generated by the prediction formula generation device 1 and the prediction formula displayed on the screen of the output unit 13 and the input unit 12 (described later) included in the prediction formula generation device 1 or other personal computers. With reference to (graph etc.), selection of past performance data used for generation of the prediction formula is performed in the dialogue processing 2, and a desired prediction formula is found. The screen 21 is an example of a screen used by the user in the dialogue process 2.

FIG. 2 is a block diagram illustrating a configuration of the prediction formula generation device 1. The prediction formula generation apparatus 1 generates the following linear polynomial prediction formula (1) for calculating a quality index (yield) as a manufacturing result.
Y = a * P1 + b * P2 + c * P3 + d (1)
P1, P2, and P3 are manufacturing condition parameters, and indicate manufacturing variables such as pressure and temperature in the manufacturing process. a, b, and c are coefficients, and d is an intercept.

  The prediction formula generation device 1 obtains coefficients a, b, and c such that the quality index and the Y value (hereinafter referred to as “score Y”) have a monotone dependency.

  In FIG. 2, the prediction formula generation device 1 includes an arithmetic processing unit 11, an input unit 12, an output unit 13, an internal storage unit 14, an auxiliary storage unit 16, and a bus 18.

  The arithmetic processing unit 11 includes, for example, a microprocessor, and functionally includes a control unit 111, a rank assignment unit 112, an initial value calculation unit 113, and a prediction formula generation unit 114.

  The control unit 111 controls the rank assignment unit 112, the initial value calculation unit 113, and the prediction formula generation unit 114 to perform a calculation for generating a prediction formula. Also, the input unit 12 and the output unit 13 according to the control program. The internal storage unit 14 and the auxiliary storage unit 16 are controlled.

  The rank assignment unit 112 assigns ranks to past performance data used to generate a prediction formula. In the embodiment, ranks are given to the performance data in ascending order of “yield” which is a quality index (manufacturing result).

  The initial value calculation unit 113 calculates the initial value of the coefficient of the prediction formula.

  The prediction formula generation unit 114 starts a search from the initial value calculated by the initial value calculation unit 113 and generates a prediction formula. Details of these will be described in the section <Prediction Formula Generation Method>.

  The input unit 12 is a device that inputs various commands such as a calculation start instruction of the prediction formula generation device 1 and various data such as system parameters to the state estimation device 1, and is, for example, a keyboard or a mouse. The output unit 13 is a device that outputs a command and data input from the input unit 12, a calculation result of the state estimation device 1, and the like. For example, a CRT (Cathode Ray Tube) display, an LCD (Liquid Crystal Display), an organic EL (Electro Luminescence) A display device such as a display or a plasma display, or a printing device such as a printer.

  The internal storage unit 14 is a so-called working memory that reads a prediction formula generation program and a control program executed by the arithmetic processing unit 11 from the auxiliary storage unit 16 and temporarily stores each data during execution of the prediction formula generation program. For example, a RAM (Random Access Memory) that is a volatile storage element is provided.

  The auxiliary storage unit 16 is a device that stores data and programs such as a non-volatile storage element such as a ROM (Read Only Memory) and an EEPROM (Electrically Erasable Programmable Read Only Memory), a hard disk, and the like, and a performance data storage unit 161, In addition to including the evaluation formula storage unit 162 and the prediction formula storage unit 163, each program (not shown) such as a control program for operating the prediction formula generation program and the prediction formula generation apparatus 1, and the execution of each program Necessary data (not shown) and the like are stored.

  The actual data storage unit 161 stores actual data for generating a prediction formula, for example, manufacturing condition parameters and manufacturing results (quality indexes) in association with those conditions in association with each other.

  The evaluation formula storage unit 162 has a function of storing an evaluation formula. Data and evaluation formulas stored in the record data storage unit 161 will be described in the section <Prediction Formula Generation Method>.

  The prediction formula storage unit 163 has a function of storing a prediction formula.

  The arithmetic processing unit 11, the input unit 12, the output unit 13, the internal storage unit 14, and the auxiliary storage unit 16 are connected to a bus 18 so that data can be exchanged with each other.

  Note that the prediction formula generation apparatus 1 may further include an external storage unit 15 and a communication interface unit (not shown) indicated by a broken line in FIG. 1 as necessary.

  The external storage unit 15 stores data with a recording medium such as a flexible disk, a CD-ROM (Compact Disc Read Only Memory), a CD-R (Compact Disc Recordable), and a DVD-R (Digital Versatile Disc Recordable). An apparatus that performs reading and / or writing, such as a flexible disk drive, a CD-ROM drive, a CD-R drive, and a DVD-R drive. The communication interface unit is connected to the communication network and is a device for transmitting and receiving communication signals to and from other client devices via the communication network.

If each program is not stored, it may be configured to be installed in the auxiliary storage unit 16 via the external storage unit 15 from a recording medium on which these programs are recorded, and a server computer that manages these programs You may comprise so that each program may be downloaded via a communication network and a communication interface part (not shown). Further, the data to be input to the prediction formula generation apparatus 1 in the calculation of the prediction formula may be configured to be input to the prediction formula generation apparatus 1 via the external storage unit 15 by a recording medium storing the data. .
<Prediction formula generation method>
First, the ranking assigning unit 112 creates the result data 1610 shown in FIG. 4 from the result data stored in the result data storage unit 161. FIG. 4 is a diagram illustrating an example of the configuration and contents of the record data 1610.

  The actual data 1610 includes items of “data rank”, manufacturing condition parameters “P1”, “P2”, “P3”, and a quality index “Q” as a manufacturing result, and one record is registered for each actual data. ing.

  The rank assigning unit 112 creates a record data 1610 by assigning ranks to the record data stored in the record data storage unit 161. That is, the actual data stored in the actual data storage unit 161 does not include the item “data rank”, and the manufacturing condition parameters “P1”, “P2”, “P3”, and the quality index “Q”. This data includes the items. The rank assigning unit 112 rearranges the result data so that the value of the quality index “Q” is in ascending order, assigns “data rank”, and creates the result data 1610 of FIG. For example, in the performance data 1610 of FIG. 4, there are 10 performance data, and “1” is assigned as “data ranking” to the performance data of “−0.7” having the smallest quality index “Q”. . In the embodiment, the value of the quality index “Q” is given in a predetermined order, that is, ascending order, but may be in descending order.

  Here, a graph showing the quality index “Q” in the order of “data rank” is shown in FIG. The graph of the quality index “Q” is a solid line graph. In the graph of FIG. 5, the horizontal axis represents “data ranking” and the vertical axis represents the quality index “Q”.

  Next, the initial value calculation unit 113 obtains the coefficients a, b, c, and the intercept d of the prediction formula (1) that minimize the square error with the actual quality index “Q”. For example, the intercept d is “−0.49”, the coefficient a is “0.58”, the coefficient b is “0.056”, and the coefficient c is “0.82”. The coefficient and the intercept value are set as initial values.

  The score Y calculated by using each of the actual data with the coefficient and intercept of the prediction formula (1) as initial values is shown in a broken line graph of the graph of FIG. The vertical axis of the graph in FIG.

  As shown in FIG. 5, the score Y using the initial value roughly increases as the actual quality index “Q” increases. However, the score Y of the data ranks “2” and “3” becomes small despite the fact that the data rank is large, that is, the actual quality index “Q” is large. Yes. In other words, the rank of the actual quality index “Q” and the rank of the score Y are reversed. The same applies to data ranks “5” and “6” and data ranks “8” and “9”.

  Next, the prediction formula generation unit 114 obtains coefficients a, b, and c that do not reverse the order of the actual quality index “Q” and the order of the score Y, that is, maintain the order relationship. Since the value of the intercept d does not affect the order relationship, the intercept d uses an initial value.

The prediction formula generation unit 114 defines the following evaluation formula (2) as the “order constraint violation amount”.
Y _j : IF (Y _j −Y _j−1 > 0, 0, (γ + Q _j −Q _j−1 ) * (Y _j−1 −Y _j ))
j = 2, 3, 4,..., N
γ> 0 (2)
Y indicates the score Y of the prediction formula (1), Q indicates the value of the actual quality index “Q”, and j indicates the data rank. N is the number of performance data. For example, γ is 1.

The meaning of the evaluation formula (2) is that when the value of (Y _j −Y _j−1 ) is greater than zero, the violation amount is zero, and in other cases, that is, (Y _j −Y _j−1 ) When the value is less than or equal to zero, the violation amount is ((γ + Q _j −Q _j−1 ) * (Y _j−1 −Y _j )). That is, when the ranking of Q and the ranking of score Y are reversed as in the data ranking “2” and “3” in the score Y graph of FIG. If the ranking of the score Y is not reversed as in the data rankings “1” and “2”, the violation amount is zero.

  Then, the amount of violation in each case where j is 2 to N is obtained, and the total of the amounts of violation is set as the order constraint violation amount S.

Further, the constraint condition of the evaluation formula (2) is that the coefficients a, b, and c are a ² + b ² + c ² = 1. This is to prevent all the coefficients from becoming zero. When this constraint is not imposed, according to the evaluation formula (2), if all Y _j are 0, the violation amount is also 0. This constraint prevents that. Note that the evaluation formula is not limited to the formula (2) as long as the constraint that the smaller the inversion amount is, the smaller the violation amount is satisfied.

  The prediction formula generation unit 114 searches for the coefficients a, b, and c such that the order constraint violation amount S is zero in the above constraint conditions. In practice, a coefficient is searched for such that the absolute value of the order constraint violation amount S is equal to or less than a predetermined threshold value.

For example, calculation is performed by giving actual data to the prediction formula (1) using the coefficient a “0.17”, the coefficient b “−0.49”, and the coefficient c “0.86” obtained by the prediction formula generation unit 114. The score Y is shown as a dashed-dotted line graph in FIG. In this example, the score Y for each performance data keeps the rank given to the performance data, and it is possible to predict the degree of the quality index “Q” by using this prediction formula.
<How to read the graph>
The three graphs shown in FIG. 5, that is, the graph of the actual quality index “Q” (solid line), the score Y graph (broken line) using the initial value prediction formula, and the score using the generated prediction formula Looking at the Y graph (dashed line), it can be seen that the score Y graph (broken line) using the prediction formula of the initial value is “oscillating” around the quality index, and the average deviation is small. On the other hand, the score Y value of the score Y graph (one-dot chain line) using the generated prediction formula is different from the value itself, but the value of the quality index “Q” of the actual quality index “Q” graph (solid line). It can be seen that the order relationship is maintained.

  FIG. 5 shows a graph when the prediction formula (1) that can calculate the score Y that does not change the order relationship with the actual quality index “Q” can be obtained.

  However, in reality, there are cases where the prediction formula (1) that maintains the order relationship between the score Y and the actual value of the quality index “Q” cannot be generated.

  Such an example is shown in FIG. 6 and FIG. FIG. 6 is a diagram illustrating an example of the configuration and contents of the record data 1610-2. The actual data 1610-2 is substantially the same as the actual data 1610 in FIG. 4, but the “data rank” is “5” and the manufacturing condition parameters “P2” and “P3” are different.

  FIG. 7 shows a graph (one-dot chain line) of the score Y using the prediction formula (1) generated as described above using the result data 1610-2. The solid line graph in FIG. 7 is a graph of the actual quality index “Q”. The coefficients of the prediction formula (1) at this time are the coefficient a “0.018”, the coefficient b “−0.59”, and the coefficient c “0.81”.

  Referring to FIG. 7, the score Y of the data ranking “5” and “6” is reversed from the actual quality index “Q”, and the score Y of the data ranking “5” is particularly large. .

  Accordingly, FIGS. 8 and 9 show a case where the prediction data (1) is generated using the performance data excluding the performance data with the data rank “5” as an exception.

  In actual manufacturing, there is a manufacturing variation even under the same conditions. Therefore, it is often necessary to remove “exceptional” data in data analysis. However, it is necessary to interpret whether it is an exception in accordance with the manufacturing process phenomenon. FIG. 7 shows that the magnitude of the score Y of the case of the data rank “5” is exceptional as compared with the score Y of the other cases. However, whether or not to remove the actual data as an exception needs to be examined and judged by the manufacturing process phenomenon.

  FIG. 8 is a diagram illustrating an example of the configuration and contents of the record data 1610-3. The data structure is the same as that of the actual data 1610 in FIG. 6, except for the actual data whose “data rank” is “5”.

  FIG. 9 shows a graph of a score Y (one-dot chain line) using the prediction formula (1) generated as described above using the result data 1610-3. The solid line graph of FIG. 9 is a graph of the actual quality index “Q”, and the broken line graph is a score Y graph using the prediction formula of the initial value. The coefficients of the prediction formula at this time are the coefficient a “0.16”, the coefficient b “−0.49”, and the coefficient c “0.86”.

  As shown in FIG. 9, the value of the score Y of the score Y graph (one-dot chain line) using the generated prediction formula (1) is different, but the graph of the actual quality index “Q” (solid line). It can be seen that the order relationship with the value of the quality index “Q” is maintained. That is, by excluding actual data that seems to be an exception, it is possible to obtain a prediction formula that can calculate a score Y that does not change the order relationship with the actual quality index “Q”.

  As shown in FIG. 1, the prediction formula generation device 1 generates the prediction formula (1), and by referring to the score Y graph and the result data, the user increases or decreases the score Y. It becomes possible to find the cause. Then, by eliminating the exceptional performance data, it is possible to obtain the prediction formula (1) that can calculate the score Y that does not change the order relationship with the actual quality index “Q”.

  In addition, from the values of the coefficients a, b, c in the prediction formula (1) and the values of the manufacturing condition parameters “P1”, “P2”, “P3” of the actual data, any manufacturing parameter value is decreased or increased. Then, it becomes possible to estimate whether the score Y as a result index can be increased. For example, in FIG. 7, the score Y of the data rank “5” is particularly large and the value of the production condition parameter “P3” of the data rank “5” is the highest, “0.5”. Can be guessed.

  Actually, the manufacturing condition parameters “P1”, “P2”, and “P3” have a range depending on the product type, equipment, raw material conditions, etc., and cannot be arbitrarily changed, but it is considered to try a more advantageous combination. It is done. Alternatively, when there is a degree of freedom with respect to the values of the manufacturing condition parameters “P1”, “P2”, and “P3”, for example, “P1” and “P2” cannot be freely changed, but “P3” can be slightly changed. In such a case, a combination of P1, P2, and P3 such that the score Y is larger than a predetermined threshold, for example, 0.2, in comparison with the actual value Q may be considered as the “standard condition”. That is, by using the prediction formula generation device 1, the manufacturing condition parameters can be examined in detail by freely extracting the performance data to be examined and generating the prediction formula (1).

As a premise, so-called “explanatory variables” such as “P1”, “P2”, and “P3” are assumed to be independent. It is well known that when there is a correlation between them, the reliability of the obtained coefficient and the degree of influence cannot be ensured. Along with the examination from the statistical viewpoint of examining these correlations, for example, after examining whether the process is independent (whether it is involved in which process or equipment, there is a mutual influence in the phenomenon) It is assumed that “Explanation Variable” is selected.
<Operation>
Next, the prediction formula generation process of the prediction formula generation device 1 will be described.

  FIG. 3 is a flowchart of the prediction formula generation process of the prediction formula generation apparatus 1.

  Prior to starting the prediction formula generation process, the evaluation formula (2) and the prediction formula (1) are stored in the evaluation formula storage unit 162 and the prediction formula storage unit 163, respectively, and the actual data is stored in the actual data storage unit 161. It shall be.

  First, the user inputs a command or the like for instructing the start of the prediction formula generation process via the input unit 12. At this time, the result data that is the basis for generating the prediction formula is designated. For example, performance data of 10 cases is specified.

  The control unit 111 of the arithmetic processing unit 11 that has detected that a command instructing the start of the prediction formula generation process is input via the input unit 12 reads out the actual data designated by the user from the actual data storage unit 161. , And pass to the ranking assigning unit 112.

  The rank assigning unit 112 that has received the result data from the control unit 111 assigns a rank to the result data in ascending order of the quality index “Q” and creates the result data 1610 (step S10). FIG. 4).

  Next, the control unit 111 passes the result data 1610 created by the ranking assigning unit 112 to the initial value calculation unit 113 and requests calculation of the initial values of the coefficients a, b, c, and the intercept d.

  Upon receiving the request, the initial value calculation unit 113 reads the prediction formula (1) from the prediction formula storage unit 163, and performs the least square as described above to obtain the initial value (step S11).

  Next, the control unit 111 requests the prediction formula generation unit 114 to generate a prediction formula.

  Upon receiving the request, the prediction formula generation unit 114 reads one record from the record data 1610, and adds the manufacturing condition parameter “P1” to the prediction formula (1) with the coefficients a, b, c, and the intercept d as initial values. Data (values) set as “P2”, “P3”, and quality index “Q” are given, and score Y is calculated (step S12).

  Next, the prediction formula generation unit 114 calculates the order constraint violation amount S for the score Y calculated in step S12, using the evaluation formula (2) described above (step S13). The evaluation formula (2) is read from the evaluation formula storage unit 162.

  When the absolute value of the calculated order constraint violation amount S is equal to or larger than a predetermined threshold (step S14: No), the prediction formula generation unit 114 changes the coefficients a, b, and c by a predetermined method, Processing from step S12 is performed.

  In step S14, when the absolute value of the order constraint violation amount S is smaller than a predetermined threshold (step S14: No), the prediction equation (1) using the coefficients a, b, and c at that time is expressed. The final prediction formula (1) is used (step S16). Then, the prediction formula generation unit 114 passes the score Y value at that time to the control unit 111, and the control unit 111 causes the output unit 13 to display a graph of the passed score Y.

  Note that the process surrounded by the broken-line rectangle in the flowchart of FIG. 3, that is, the process of steps S12 to S15 is a so-called optimization calculation, and a conventional method may be used as the method.

In the embodiment, the prediction formula is a linear polynomial like the prediction formula (1), but the present invention is not limited to this. For example, the following formula (3) may be used.
Y = a * P1 * P1 + b * logP2 + c * P3 + d (3)
P1 is a scale of square with respect to the increase, and P2 is a logarithmic scale, which represents a case where the quality index Y is affected. When a minute condition change in the vicinity of a steady operation condition is targeted, a linear polynomial is often sufficient, but an arbitrary function system based on influence sensitivity may be used.

DESCRIPTION OF SYMBOLS 1 Prediction formula production | generation apparatus 11 Arithmetic processing part 12 Input part 13 Output part 16 Auxiliary memory | storage part 111 Control part 112 Order assignment | providing part 113 Initial value calculation part 114 Prediction formula production | generation part 161 Performance data memory | storage part 162 Evaluation formula memory | storage part 163 Prediction formula memory | storage Part

Claims (4)

A rank assigning unit for assigning a data rank in a predetermined order according to the size of the index to a plurality of past performance data acquired in the past consisting of a manufacturing condition and a predetermined index related to a manufacturing result using the manufacturing condition;
A predictive expression generation unit that generates a predetermined predictive formula for calculating the score given the data of the manufacturing conditions;
The prediction formula generation unit assigns the score ranking of each of the past performance data to each of the past performance data when the score ranking is assigned in the predetermined order according to the magnitude of the score calculated by the prediction formula. The prediction formula generation apparatus, wherein the prediction formula is generated so as to be the same as the data rank assigned by the unit. The prediction formula is a linear polynomial composed of a plurality of manufacturing conditions and coefficients,
The prediction formula generation unit is configured to calculate a certain score from a first score when a manufacturing condition of past performance data having a certain data rank is given to the prediction formula under a constraint condition that a sum of squares of coefficients is 1. When the difference value obtained by subtracting the second score when the production condition of the past performance data of the data rank immediately before the data rank is given to the prediction formula is 0 or more, the difference value is set as a new difference value. When the difference value obtained by subtracting the second score from the first score is smaller than 0, the difference value is replaced with a value corresponding to the difference value as a new difference value, and all past result data The prediction formula generation device according to claim 1, wherein the coefficient is determined so that an absolute value of a sum of the new difference values corresponding thereto is not more than a predetermined threshold value. A rank assigning step for assigning a data rank in a predetermined order according to the size of the index to a plurality of past performance data acquired in the past consisting of a manufacturing condition and a predetermined index related to a manufacturing result using the manufacturing condition;
A predictive formula generating step for generating a predetermined predictive formula for calculating the score given the data of the manufacturing conditions,
In the prediction formula generation step, when the score ranking is given to each of the past performance data according to the score calculated by the prediction formula, the score ranking of each of the past performance data is given the ranking. A prediction formula generation method characterized by generating a prediction formula so as to be the same as the data rank assigned in the process. A prediction formula generation program for causing a computer to execute,
A rank assigning unit for assigning a data rank in a predetermined order according to the size of the index to a plurality of past performance data acquired in the past consisting of a manufacturing condition and a predetermined index related to a manufacturing result using the manufacturing condition;
The computer functions as a predictive expression generation unit that generates a predetermined predictive expression for calculating the score given the data of the manufacturing conditions,
The prediction formula generation unit assigns the score ranking of each of the past performance data to each of the past performance data when the score ranking is assigned in the predetermined order according to the magnitude of the score calculated by the prediction formula. A prediction formula generation program characterized by generating a prediction formula so as to be the same as the data rank assigned in the section.

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