JP2019197245A - Information processing apparatus, quality related formula generation method and quality related formula generation program - Google Patents

Abstract

To improve a specific accuracy of a factor that affects a quality.SOLUTION: An information processing apparatus 10 generates a plurality of candidate formulas and sets each of the plurality of candidate formulas as an evaluation target. The information processing apparatus 10 determines a coefficient value of a coefficient of a candidate formula that is an evaluation target based on a measured value. The information processing apparatus 10 calculates a matching coefficient indicating an adaption degree of the candidate formula for item to the measured value. The information processing apparatus 10 calculates a correlation coefficient between a coefficient value for item of the candidate formula of the evaluation target and a quality value. The information processing apparatus 10 calculates a score value of the candidate formula of the evaluation target based on the matching coefficient of the candidate formula of the evaluation target and the correlation coefficient. Then the information processing apparatus 10 identifies a quality related formula including a coefficient related to qualities of the plurality of items among the plurality of candidate formulas based on each of score value of the plurality of candidate formulas.SELECTED DRAWING: Figure 1

Description

  The present invention relates to an information processing apparatus, a quality related expression generation method, and a quality related expression generation program.

  At the product manufacturing site, the quality of the product is improved by the worker, such as reducing the defect rate and reducing the variation in quality. In order to improve quality, it is important to analyze data obtained in the manufacturing process and accurately grasp phenomena occurring in the manufacturing process.

  As a data analysis technique, for example, there is a manufacturing process analysis method capable of obtaining a causal relationship model independent of an analyst in order to obtain a highly accurate and general-purpose model by multiple regression analysis. In addition, an operation status evaluation apparatus is also considered that constructs an operation evaluation function using an operation factor having a large influence on the quality of the operation status as input variable data and evaluates the operation status of the process. In addition, when analyzing the relevance between operating factors and quality, an operation and quality related analysis device that can build a high-accuracy quality and operating related model with a relatively small number of divisions is also considered when dividing the operating factor space. It has been. There is also a data analysis apparatus that can accurately examine the correlation between variables that are linked to each other and that have different sampling cycles or that span processes. There is also a product quality improvement support system that makes it easy to know which process is causing a failure and which parameter contributes to the failure even if a new part is included in the product.

JP 2008-084039 A JP 2013-140548 A JP 2006-155557 A JP 2009-187175 A Japanese Patent Laid-Open No. 10-040289

However, the conventional technology does not have sufficient accuracy for identifying the cause of defects and factors affecting quality. Therefore, it takes time to improve the quality of the product.
In one aspect, the present case aims to improve the accuracy of identifying factors affecting quality.

In one proposal, an information processing apparatus having a storage unit and a processing unit described below is provided.
A memory | storage part memorize | stores the measurement data which show the time change of the measured value which measured the physical quantity during the operation | work with respect to each of the same kind of several products, and the quality data containing the quality value showing the quality of each of several products. The processing unit generates a plurality of candidate formulas that include coefficients whose values are undetermined and that represent temporal changes in physical quantities. Next, the processing unit sets each of the plurality of generated candidate formulas as an evaluation target, and determines a coefficient value of a coefficient of the candidate formula to be evaluated for each product based on the measurement value. Next, the processing unit calculates a matching coefficient indicating the degree of matching of the candidate expression to be evaluated with respect to the measurement value, based on the coefficient value for each product of the candidate expression to be evaluated. Next, the processing unit calculates a correlation coefficient between the coefficient value for each product of the candidate formula to be evaluated and the quality value. Next, the processing unit calculates a score value of the candidate expression to be evaluated based on the matching coefficient and the correlation coefficient of the candidate expression to be evaluated. Then, the processing unit identifies a quality-related expression including a coefficient related to the quality of the plurality of products from the plurality of candidate expressions based on the score values of the plurality of candidate expressions.

  According to one aspect, it is possible to improve the accuracy of identifying a factor that affects quality.

It is a figure which shows an example of the information processing apparatus which concerns on 1st Embodiment. It is a figure which shows the system configuration example of 2nd Embodiment. It is a figure which shows the example of 1 structure of the hardware of a computer. It is a block diagram which shows an example of the function of each apparatus for specifying a quality influence cause. It is a figure which shows an example of the data stored in the manufacture data storage part. It is a figure which shows an example of the data stored in the numerical formula candidate element memory | storage part. It is a figure which shows an example of the data stored in the theoretical model memory | storage part. It is a figure which shows an example of the data stored in the response characteristic data storage part. It is a flowchart which shows an example of the procedure of a quality influence cause specific process. It is a figure which shows the example of a production | generation of the candidate model based on the set element. It is a figure which shows an example of the candidate model produced | generated using GP. It is a figure which shows an example of the generation evolution by crossing. It is a figure which shows the example of calculation of a coefficient value. It is a figure which shows the example of calculation of a matching coefficient. It is a figure which shows an example of the data stored in the analysis result memory | storage part. It is a figure which shows an example of the correlation analysis of a coefficient value and a final vacuum degree. It is a figure which shows the example of calculation of the score value of a candidate model. It is a figure explaining the difference in the score value by the difference in the calculation method. It is a figure which shows an example of the evaluation result management table in which the evaluation result of the candidate model was set. It is a figure which shows an example of a model collation process. It is a figure which shows an example of filtering of a theoretical model. It is a figure which shows an example of a character string replacement process. It is a figure which shows the 1st calculation example of Levenshtein distance. It is a figure which shows the 2nd example of calculation of Levenshtein distance. It is a figure which shows an example of a similarity management table. It is a figure which shows an example of the analysis result display screen of a quality related factor. It is a figure explaining the determination precision by a score value. It is a figure which shows the 1st example of the structure of the type | formula regarding a product. It is a figure which shows the 2nd example of the structure of the type | formula regarding a product. It is a figure which shows the 3rd example of the structure of the type | formula regarding a product. It is a figure which shows the 4th example of the structure of the type | formula regarding a product. It is a flowchart which shows an example of the procedure of the quality influence cause specific process in 3rd Embodiment. It is a figure which shows the example of calculation of a structure evaluation value. It is a figure which shows an example of a ranking management table. It is a figure which shows the example of collation with a candidate model and a theoretical model. It is a figure which shows an example of the analysis result display screen of a quality related factor. It is a figure which shows an example of the analysis result display screen of a quality related factor in case there exist multiple basic structures.

Hereinafter, the present embodiment will be described with reference to the drawings. Each embodiment can be implemented by combining a plurality of embodiments within a consistent range.
[First Embodiment]
First, the first embodiment will be described.

  FIG. 1 is a diagram illustrating an example of an information processing apparatus according to the first embodiment. In the first embodiment, the information processing apparatus 10 performs a quality-related expression generation method, thereby indicating a relationship between a factor that affects the quality of a plurality of products and product characteristics (quality-related expression). Is generated. For example, the information processing apparatus 10 executes the quality related expression generation method by executing a quality related expression generation program in which the procedure of the quality related expression generation method is described.

  The information processing apparatus 10 includes a storage unit 11 and a processing unit 12. The storage unit 11 is, for example, a memory or a storage device included in the information processing apparatus 10. The processing unit 12 is, for example, a processor or an arithmetic circuit included in the information processing apparatus 10.

  The storage unit 11 includes measurement data 11a and quality data 11b. The measurement data 11a is data indicating a time change of a measurement value obtained by measuring a physical quantity during work for each of a plurality of products of the same type. The quality data 11b is data including a quality value representing the quality of each of a plurality of products. The quality data 11b may be included in the measurement data 11a. For example, the best value among the measurement values for each product in the measurement data 11a or the final value over time may be used as the quality value in the quality data 11b.

  First, the processing unit 12 generates a plurality of candidate formulas including coefficients whose values are undetermined and representing temporal changes in physical quantities. For example, the processing unit 12 generates a plurality of candidate expressions by genetic programming. The candidate formula is a model candidate that quantitatively represents the temporal change of the physical quantity.

Next, the processing unit 12 calculates a score value for each of the plurality of generated candidate formulas based on the measurement data 11a and the quality data 11b. The procedure for calculating the score value is as follows.
The processing unit 12 sequentially selects each of the plurality of generated candidate expressions as an evaluation target. Next, the processing unit 12 determines the coefficient value of the coefficient of the candidate expression to be evaluated for each product based on the measurement value. For example, the processing unit 12 determines a coefficient value that most accurately represents a change in the measured value of the product by the least square method. The least square method is a method for determining a coefficient that minimizes the sum of squares of residuals.

  When the coefficient value for each product is determined, the processing unit 12 calculates a matching coefficient indicating the degree of matching of the candidate formula for the evaluation target with the measurement value, based on the coefficient value for each product of the candidate formula for the evaluation target. For example, the processing unit 12 calculates a residual between a regression equation obtained by setting a coefficient value for each product in the candidate formula to be evaluated and a measured value for each product, and calculates an average of absolute values of the residuals as a matching coefficient. To do. In this case, the value of the matching coefficient is smaller as the candidate formula is more suitable for the measured value.

  Next, the processing unit 12 calculates a correlation coefficient between the coefficient value for each product of the candidate formula to be evaluated and the quality value. The absolute value of the correlation coefficient increases as the correlation increases. Therefore, the processing unit 12 obtains a corrected correlation coefficient by correcting the correlation coefficient so that the value decreases as the correlation increases. For example, the processing unit 12 sets “1−absolute value of correlation coefficient” as the corrected correlation coefficient.

  After calculating the matching coefficient and correlation coefficient of the candidate expression to be evaluated, the processing unit 12 calculates the score value of the candidate expression to be evaluated based on the matching coefficient and the correlation coefficient. For example, the processing unit 12 sets a product of a matching coefficient and a value corresponding to the correlation coefficient (corrected correlation coefficient) for the evaluation target candidate expression as a score value of the evaluation target candidate expression. When a plurality of coefficients are included in the candidate expression to be evaluated, the processing unit 12, for example, a value (corrected correlation coefficient) corresponding to the larger one of the absolute values of the correlation coefficients of the coefficients, and a matching coefficient Is the score value of the candidate expression to be evaluated.

  When the score values of all the generated candidate expressions are obtained, the processing unit 12 determines the quality including coefficients related to the quality of the plurality of products from the plurality of candidate expressions based on the score values of the plurality of candidate expressions. Identify related expressions. For example, the processing unit 12 specifies a candidate formula having the smallest score value as a quality-related formula. Further, the processing unit 12 may use a predetermined number of candidate formulas as the quality-related formulas from the smaller score values.

  Further, the processing unit 12 specifies a similar theoretical formula similar to the quality-related formula from a plurality of theoretical formulas representing the theoretical properties of the plurality of products. Then, the processing unit 12 outputs the physical meaning of the coefficients included in the similar theoretical formula. When the quality-related expression includes a plurality of coefficients, the processing unit 12 means the coefficients in the similar theory model corresponding to the coefficient having the largest absolute value of the correlation coefficient (the smallest value of the corrected correlation coefficient). Is output. For example, the processing unit 12 displays the meaning of the corresponding coefficient on a screen such as a monitor.

  In this way, factors that affect product quality can be identified with high accuracy. For example, when a quality-related expression is specified only by a correlation coefficient, if there is a candidate expression having a high correlation coefficient by chance, the candidate expression is specified as a quality-related expression. Since such a candidate formula only has a high correlation coefficient by chance, there is no relation between the coefficient included in the candidate formula and the quality of the product. Therefore, the information processing apparatus 10 calculates the score value by combining the correlation coefficient and the matching coefficient. A candidate formula having a small matching coefficient value (applicable to a measured value) represents a characteristic of the product. On the other hand, a candidate expression whose correlation coefficient is increased by chance does not match the measured value because the relationship with the product characteristics is low, and the matching coefficient increases. As a result, it is possible to prevent a candidate formula having a high correlation coefficient from being accidentally specified as a quality-related formula.

  By correctly specifying a quality-related expression related to the quality of a product, it is possible to specify a factor that affects quality with high accuracy based on a theoretical model similar to the quality-related expression.

  Note that the processing unit 12 can also calculate the score value by weighting the matching coefficient and the correlation coefficient (or the modified correlation coefficient). The weight value is set in the information processing apparatus 10 in advance by the user, for example. For example, when the user knows that a lot of noise is included in the measurement value, the user makes the weight for the matching coefficient smaller than the weight for the correlation coefficient. The processing unit 12 multiplies or divides each of the values according to the matching coefficient and correlation coefficient of the candidate expression to be evaluated by the weight, and uses the weight multiplication or the sum of the division results as the score value of the evaluation target candidate expression. . For example, when calculating the score value so that the candidate value having a higher degree of association with quality has a higher score value, the processing unit 12 multiplies the matching coefficient and the correlation coefficient by a weight. On the other hand, the processing unit 12 divides the matching coefficient and the correlation coefficient by the weight when calculating the score value so that the candidate value having a higher degree of association with quality has a smaller score value.

  Further, the processing unit 12 determines the ranking (ranking) of the matching coefficient and the correlation coefficient among the plurality of candidate expressions, and based on the ranking of the matching coefficient and the correlation coefficient of the candidate expression to be evaluated, You may calculate the score value of the candidate formula of evaluation object. By calculating the score value based on the rank, it is possible to prevent only one value from being greatly reflected in the score value due to the difference in the magnitude (order) from the matching coefficient or the correlation coefficient. For example, the absolute value of the correlation coefficient is in the range of 0 to 1. On the other hand, the magnitude (order) of the value of the matching coefficient varies depending on what physical quantity is measured. If the score value is calculated based on the rank, there is no difference in the magnitude (order) of the values, and the matching coefficient and the correlation coefficient can be handled equally.

  Furthermore, the processing unit 12 can specify a factor that affects quality with higher accuracy by using a basic structure of a physical quantity calculation formula based on characteristics of a plurality of products. For example, the processing unit 12 calculates the structure evaluation value of the candidate expression to be evaluated based on the similarity between the basic structure and the candidate expression to be evaluated. Then, the processing unit 12 calculates a score value of the evaluation target candidate expression based on the matching coefficient, correlation coefficient, and structure evaluation value of the evaluation target candidate expression. For example, the processing unit 12 uses a product of a value (corrected correlation coefficient) corresponding to the matching coefficient and the correlation coefficient and the structure evaluation value as the score value. The processing unit 12 can also calculate a score value based on the ranking (ranking) of each of the matching coefficient, the correlation coefficient, and the structure evaluation value among a plurality of candidate expressions.

  By reflecting the structure evaluation value corresponding to the similarity between the basic structure and the candidate expression to be evaluated in the score value, a candidate expression closer to the basic structure can obtain a better score value. As a result, even if the formula that represents the properties of a product is a complex formula that includes multiple functions, it is possible to specify an appropriate quality-related formula by specifying the basic structure of the formula in advance. It becomes. As a result, factors that affect quality can be identified with high accuracy.

[Second Embodiment]
Next, a second embodiment will be described. The second embodiment specifies factors that affect the quality of the cooling unit of the electronic equipment assembly line.

  FIG. 2 is a diagram illustrating a system configuration example according to the second embodiment. At the manufacturing site of the cooling units 1, 2,..., A refrigerant filling device 30 for charging the cooling units 1, 2,. A computer 100 is connected to the refrigerant charging device 30. The computer 100 acquires the data measured in the refrigerant filling process of the cooling units 1, 2,... From the refrigerant charging device 30, and based on the acquired data, the quality of the cooling units 1, 2,. Analyze the influencing factors.

  For example, the operator connects the refrigerant injection coupler 31 connected by a tube from the refrigerant filling device 30 to the cooling unit 1. When the operator presses the charging start switch of the refrigerant charging device 30, the refrigerant charging device 30 evacuates the refrigerant injection space in the connected cooling unit 1. The refrigerant filling device 30 injects the refrigerant into the refrigerant injection space when the degree of vacuum becomes a specified value or more. When the injection of the refrigerant is completed, the operator removes the refrigerant injection coupler 31 from the cooling unit 1. By performing such a series of operations for each cooling unit 1, 2,..., The refrigerant can be injected into each cooling unit 1, 2,.

  Among the cooling units 1, 2,..., There are those in which the degree of vacuum of the refrigerant injection space does not reach a specified value. In that case, the refrigerant filling device 30 determines that the evacuation has failed. If the evacuation fails, the operator temporarily stops the cooling unit production line, and performs evacuation again on the cooling unit that failed to be evacuated.

  Thus, the failure of evacuation becomes a stop factor of the production line and deteriorates the production efficiency. Therefore, in the second embodiment, the computer 100 is used to identify factors that affect the quality of vacuuming.

  FIG. 3 is a diagram illustrating a configuration example of hardware of a computer. The computer 100 is entirely controlled by a processor 101. A memory 102 and a plurality of peripheral devices are connected to the processor 101 via a bus 109. The processor 101 may be a multiprocessor. The processor 101 is, for example, a CPU (Central Processing Unit), an MPU (Micro Processing Unit), or a DSP (Digital Signal Processor). At least a part of the functions realized by the processor 101 executing the program may be realized by an electronic circuit such as an ASIC (Application Specific Integrated Circuit) or a PLD (Programmable Logic Device).

  The memory 102 is used as a main storage device of the computer 100. The memory 102 temporarily stores at least part of an OS (Operating System) program and application programs to be executed by the processor 101. Further, the memory 102 stores various data used for processing by the processor 101. As the memory 102, for example, a volatile semiconductor storage device such as a RAM (Random Access Memory) is used.

  Peripheral devices connected to the bus 109 include a storage device 103, a graphic processing device 104, an input interface 105, an optical drive device 106, a device connection interface 107, and a network interface 108.

  The storage device 103 writes and reads data electrically or magnetically with respect to a built-in recording medium. The storage device 103 is used as an auxiliary storage device of a computer. The storage device 103 stores an OS program, application programs, and various data. For example, an HDD (Hard Disk Drive) or an SSD (Solid State Drive) can be used as the storage device 103.

  A monitor 21 is connected to the graphic processing device 104. The graphic processing device 104 displays an image on the screen of the monitor 21 in accordance with an instruction from the processor 101. Examples of the monitor 21 include a display device using organic EL (Electro Luminescence) and a liquid crystal display device.

  A keyboard 22 and a mouse 23 are connected to the input interface 105. The input interface 105 transmits signals sent from the keyboard 22 and the mouse 23 to the processor 101. The mouse 23 is an example of a pointing device, and other pointing devices can also be used. Examples of other pointing devices include a touch panel, a tablet, a touch pad, and a trackball.

  The optical drive device 106 reads data recorded on the optical disc 24 using laser light or the like. The optical disc 24 is a portable recording medium on which data is recorded so that it can be read by reflection of light. The optical disc 24 includes a DVD (Digital Versatile Disc), a DVD-RAM, a CD-ROM (Compact Disc Read Only Memory), a CD-R (Recordable) / RW (ReWritable), and the like.

  The device connection interface 107 is a communication interface for connecting peripheral devices to the computer 100. For example, the memory device 25 and the memory reader / writer 26 can be connected to the device connection interface 107. The memory device 25 is a recording medium equipped with a communication function with the device connection interface 107. The memory reader / writer 26 is a device that writes data to the memory card 27 or reads data from the memory card 27. The memory card 27 is a card type recording medium.

  The network interface 108 is connected to the network 20. The network interface 108 transmits and receives data to and from other computers or communication devices via the network 20.

  The computer 100 can realize the processing functions of the second embodiment with the above hardware configuration. Note that the apparatus shown in the first embodiment can also be realized by hardware similar to the computer 100 shown in FIG.

  The computer 100 implements the processing functions of the second embodiment by executing a program recorded on a computer-readable recording medium, for example. A program describing the processing content to be executed by the computer 100 can be recorded in various recording media. For example, a program to be executed by the computer 100 can be stored in the storage device 103. The processor 101 loads at least a part of the program in the storage apparatus 103 into the memory 102 and executes the program. A program to be executed by the computer 100 can be recorded on a portable recording medium such as the optical disc 24, the memory device 25, and the memory card 27. The program stored in the portable recording medium becomes executable after being installed in the storage apparatus 103 under the control of the processor 101, for example. The processor 101 can also read and execute a program directly from a portable recording medium.

  The hardware computer 100 analyzes manufacturing data collected by the refrigerant filling device 30 and identifies factors that may cause defective products. The information processing apparatus 10 shown in the first embodiment can also be realized by hardware similar to the computer 100.

  FIG. 4 is a block diagram illustrating an example of the function of each device for identifying the cause of quality influence. The refrigerant filling device 30 includes a manufacturing data storage unit 32 and a control unit 33. The manufacturing data storage unit 32 stores data collected in the manufacturing process of the cooling units 1, 2,. The control unit 33 controls evacuation of the cooling units 1, 2,. Further, the controller 33 periodically measures the degree of vacuum in the refrigerant injection space during evacuation, and stores the measured degree of vacuum in the manufacturing data storage unit 32. Further, in response to a data acquisition request from the computer 100, the control unit 33 transmits designated data in the manufacturing data storage unit 32 to the computer 100.

  The computer 100 includes a mathematical expression candidate element storage unit 110, a theoretical model storage unit 120, a response characteristic data acquisition unit 130, a response characteristic data storage unit 140, a candidate model construction unit 150, a data analysis unit 160, an analysis result storage unit 170, and a model. An evaluation unit 180 is included.

  The mathematical expression candidate element storage unit 110 stores elements such as an operator used to construct a mathematical expression representing a time series change in the degree of vacuum. The theoretical model storage unit 120 stores a calculation formula representing a physical phenomenon that occurs in a manufacturing process such as evacuation of the cooling units 1, 2,... As a theoretical model. The theoretical model is an example of a theoretical formula in the first embodiment.

  The response characteristic data acquisition unit 130 acquires response characteristic data indicating a time-series change of a physical quantity obtained by observing a product when a work is performed on the product to be manufactured in the course of the manufacturing process. For example, the response characteristic data acquisition unit 130 acquires, as response characteristic data, data indicating a time-series change in the degree of vacuum when the cooling units 1, 2,... The response characteristic data acquisition unit 130 stores the acquired response characteristic data in the response characteristic data storage unit 140. The response characteristic data storage unit 140 stores response characteristic data.

  The candidate model construction unit 150 combines the elements stored in the mathematical expression candidate element storage unit 110 or the elements input by the user to calculate a time-series change in the degree of vacuum represented in the response characteristic data. Build a candidate model. The candidate model is an example of the candidate formula shown in the first embodiment. For example, the candidate model construction unit 150 repeatedly constructs candidate models using a genetic algorithm (GA). Candidate model construction unit 150 can construct a complex calculation formula efficiently by using genetic programming (GP) when GA is used to construct a candidate model.

  The data analysis unit 160 performs data analysis on each of the cooling units 1, 2,. For example, the data analysis unit 160 compares the constructed candidate model with the response characteristic data of each of the cooling units 1, 2,..., And determines an appropriate value of the coefficient value included in the candidate model as the cooling unit 1, 2,... Further, the data analysis unit 160 calculates a matching coefficient indicating the degree of coincidence between the candidate model whose coefficient value is determined and the response characteristic data. The data analysis unit 160 stores the data analysis result in the analysis result storage unit 170. The analysis result storage unit 170 stores an analysis result for each candidate model.

  The model evaluation unit 180 calculates a score value indicating the degree to which the physical quantity corresponding to the coefficient included in the candidate model has an influence on the quality of the product (final vacuum degree after execution of evacuation). For example, the model evaluation unit 180 calculates a score value based on the average of the matching coefficient values for each cooling unit 1, 2,... And the coefficient values included in the candidate model. When the candidate model construction unit 150 constructs a candidate model by GA or GP, the model evaluation unit 180 transmits a candidate model having an excellent score value to the candidate model construction unit 150 among the evaluated candidate models. In the following example, the score value is better as the value is smaller. Thereby, the candidate model construction unit 150 can construct an appropriate candidate model in accordance with the GA or GP algorithm, such as constructing a candidate model for the next generation based on a candidate model having an excellent score value. Further, the model evaluation unit 180 determines the physical meaning of the coefficient of the candidate model whose score value is less than the threshold based on the theoretical model. And the model evaluation part 180 displays the physical meaning of the coefficient of the candidate model whose score value is less than a threshold value on the monitor 21 as a factor affecting quality.

  Note that the lines connecting the elements shown in FIG. 4 indicate a part of the communication paths, and communication paths other than the illustrated communication paths can be set. Also, the function of each element shown in FIG. 4 can be realized by causing the computer 100 to execute a program module corresponding to the element, for example.

  Next, with reference to FIGS. 5 to 8, data used for quality influence cause identification processing will be described in detail. Of the data used for the quality influence cause identification process, the data stored in the manufacturing data storage unit 32, the formula candidate element storage unit 110, and the theoretical model storage unit 120 are not subjected to the quality influence cause identification process. Be prepared.

  FIG. 5 is a diagram illustrating an example of data stored in the manufacturing data storage unit. In the manufacturing data storage unit 32, for example, a manufacturing data management table 32a is stored. In the manufacturing data management table 32a, quality data and manufacturing data are set in association with the unit numbers of the cooling units 1, 2,.

  The quality data is data indicating a criterion for determining the quality of the corresponding cooling unit. For example, the final degree of vacuum is set in the manufacturing data management table 32a as quality data. The degree of vacuum is represented by the atmospheric pressure in the space to be evacuated, and the degree of vacuum is higher as the value is smaller.

  In the production data, the quality determination result and the degree of vacuum for each evacuation elapsed time are set. As a determination result, when the final vacuum satisfies the specified value (the final vacuum is less than the threshold value), a value “OK” indicating good quality is set, and the final vacuum does not satisfy the specified value ( When the final vacuum value is equal to or greater than a threshold value, a value “NG” indicating a quality defect is set.

  FIG. 6 is a diagram illustrating an example of data stored in the formula candidate element storage unit. The formula candidate element storage unit 110 stores formula candidate element lists 111, 112,... For each category of the technical field, for example. In each of the formula candidate element lists 111, 112,..., A list of elements (formula candidate elements) used for calculating the physical quantity in the corresponding category is registered. Formula candidate elements include operators, functions, and variables. The operator is, for example, an arithmetic operator. The function is, for example, a trigonometric function, an exponential function, or a logarithmic function. Variables include real numbers and coefficients in addition to variables such as x and y.

  As described above, by listing functions used in a corresponding field in advance for each category, an appropriate candidate model can be efficiently created. The theoretical calculation formula of the physical quantity for each category is registered in the theoretical model storage unit 120 in advance.

  FIG. 7 is a diagram illustrating an example of data stored in the theoretical model storage unit. The theoretical model storage unit 120 stores a theoretical model management table 121, for example. In each record of the theoretical model management table 121, the category, the theoretical model, the meaning of the theoretical model, and the meaning of the coefficient are set. A category is a technical field to which a corresponding theoretical model is applied. The theoretical model is a calculation formula for calculating a physical quantity in a corresponding category. The meaning of the theoretical model is the meaning of the physical quantity calculated by the theoretical model. The meaning of the coefficient is the physical meaning of the coefficient included in the theoretical model. For example, a theoretical model “P (x) = a / x” whose category is “evacuation” is an equation for calculating an exhaust velocity, and a coefficient “a” is an exhaust resistance.

  After the data shown in FIGS. 5 to 7 are prepared, the response characteristic data acquisition unit 130 acquires the manufacturing data from the manufacturing data storage unit 32 as a pre-process of the quality influence cause specifying process. The response characteristic data acquisition unit 130 generates response characteristic data for each of the cooling units 1, 2,... Based on the acquired manufacturing data, and stores the response characteristic data in the response characteristic data storage unit 140.

  FIG. 8 is a diagram illustrating an example of data stored in the response characteristic data storage unit. The response characteristic data storage unit 140 stores response characteristic data 141, 142,... For each cooling unit 1, 2,. In each of the response characteristic data 141, 142,..., The degree of vacuum is set for each elapsed time from the start of evacuation. The vacuum degree of the last record (maximum elapsed time) in the response characteristic data 141, 142,... Is the final vacuum degree of the corresponding cooling unit.

  After the response characteristic data 141, 142,... Are generated, the computer 100 starts the quality influence cause specifying process in response to a start instruction of the quality influence cause specifying process from the user. Hereinafter, the quality influence cause specifying process will be described in detail.

FIG. 9 is a flowchart illustrating an example of the procedure of the quality influence cause identification process. In the following, the process illustrated in FIG. 9 will be described in order of step number.
[Step S101] The candidate model construction unit 150 accepts an input for designating an element (such as an operator) used to construct a candidate model. For example, the user performs an input for designating what the variable of the candidate model is, what operator is used, and what function is used. The user can also specify one of the formula candidate element lists in the formula candidate element storage unit 110 instead of inputting individual elements. When the formula candidate element list is designated, the candidate model construction unit 150 uses the operators, functions, and variables shown in the designated formula candidate element list as elements used for construction of the candidate model.

  In addition, the user can input an end condition for constructing the candidate model. For example, the user inputs a score value threshold as an end condition. Candidate model construction part 150 memorizes the inputted threshold as an end condition, when the threshold of score value is inputted. In addition, when the threshold value used as the end condition is not input, the candidate model construction unit 150 sets, for example, a preset threshold value as the end condition.

  [Step S102] The candidate model construction unit 150 constructs a candidate model by combining mathematical expression candidate elements by GP. For example, when constructing a first generation candidate model of GP, the candidate model construction unit 150 constructs a predetermined number (for example, 10) of candidate models by randomly combining mathematical expression candidate elements. In addition, when building candidate models for the second generation and subsequent generations of the GP, the candidate model building unit 150 selects two candidate models from the already built candidate models with the better score value (for example, the lower value). . Then, the candidate model construction unit 150 constructs a next-generation candidate model by performing an operation such as crossover with the selected candidate model as a parent.

  [Step S103] The data analysis unit 160 calculates the value of the coefficient included in the constructed candidate model for each of the response characteristic data 141, 142,. For example, the data analysis unit 160 calculates the coefficient value of the candidate model that matches the response characteristic data by regression analysis. Thereby, the calculation formula (regression formula) of the candidate model is determined.

  [Step S104] The data analysis unit 160 calculates a matching coefficient for each cooling unit for the constructed candidate model. For example, the matching coefficient becomes smaller as the residual between the response characteristic data of the cooling unit and the curve of the candidate model in which the coefficient is set is smaller.

  [Step S105] The data analysis unit 160 performs a correlation analysis with the product quality (final vacuum degree) for each coefficient in the candidate model. By the correlation analysis, a correlation coefficient is calculated for each coefficient of the constructed candidate model. The correlation coefficient is a real number ranging from −1 to +1. The correlation coefficient indicates that the larger the absolute value, the higher the degree of correlation between the coefficient and the final vacuum degree. The data analysis unit 160 calculates, for example, “1-absolute value of correlation coefficient” and sets the calculation result as a corrected correlation coefficient. As a result, a corrected correlation coefficient having a smaller value as the degree of correlation is higher is obtained.

  [Step S106] The model evaluation unit 180 calculates the score value of the candidate model based on the corrected correlation coefficient for each coefficient in the candidate model and the matching coefficient indicating the difference between the candidate model and the response characteristic data. .

  [Step S107] The model evaluator 180 determines whether or not the candidate model construction end condition is satisfied. For example, the model evaluation unit 180 determines that the end condition is satisfied when there is at least one candidate model whose score value is less than the threshold value. If the end condition is satisfied, the model evaluation unit 180 proceeds with the process to step S108. On the other hand, if the end condition is not satisfied, the model evaluation unit 180 proceeds with the process to step S102. Note that, when the termination condition is not satisfied, the model evaluation unit 180 transmits, for example, two candidate models having the highest score value among the candidate models of the latest generation to the candidate model construction unit 150.

  [Step S108] The model evaluation unit 180 collates a predetermined number of candidate models with the smaller score values with the theoretical model. The model evaluation unit 180 calculates the structural similarity between the candidate model and the theoretical model, for example. Then, the model evaluation unit 180 determines the meaning of the coefficient of the candidate model based on the meaning of the coefficient of the theoretical model similar to the candidate model.

  [Step S109] The model evaluation unit 180 outputs a result of specifying the cause of quality influence. For example, the model evaluation unit 180 displays on the monitor 21 the meanings of the coefficients of a predetermined number of candidate models from the smaller score values as factors that affect product quality.

The process for identifying the cause of quality influence is performed in such a procedure. Hereinafter, the quality influence cause identifying process will be described in detail.
FIG. 10 is a diagram illustrating a generation example of a candidate model based on set elements. For example, the candidate model construction unit 150 acquires the element group 41 by element designation input. The element group 41 includes a variable “t”, an operator, and a function as elements constituting the candidate model. Next, candidate model construction part 150 generates calculation formula 42 which combined the constituent element of a candidate model using GP. For example, a calculation formula 42 such as “1 / t” is generated.

  The candidate model construction unit 150 assigns, for example, a coefficient indicating a gain and an offset to the generated calculation formula 42 and sets the obtained calculation formula as the candidate model 43. The coefficient indicating the gain is a coefficient indicating a value to be multiplied by the entire calculation formula generated by the GP, for example. The coefficient indicating the offset is a coefficient indicating the value to be added to the variable. When the calculation formula obtained by GP is “1 / t”, the candidate model 43 is “a / (t + b)”. In the candidate model 43, “a” is a coefficient indicating gain, and “b” is a coefficient indicating offset.

In the example of FIG. 10, an example of the candidate model 43 having a simple structure is shown, but a candidate model having a complicated structure can be generated by using the GP.
FIG. 11 is a diagram illustrating an example of a candidate model generated using GP. In the example of FIG. 11, the candidate model 44 of the calculation formula “{sin (a + (x × y) + b) + In (c × (y × y))} + exp (z)” is represented by a tree structure. In the tree structure candidate model 44, an element designated as an element becomes a tree structure node.

Candidate model construction unit 150 constructs a next-generation candidate model, for example, by performing operations such as crossing or mutation of a part (subtree) of a plurality of tree structures.
FIG. 12 is a diagram illustrating an example of generational evolution due to crossover. Candidate model construction section 150 specifies subtrees 45a and 46a from candidate models 45 and 46, respectively, with two candidate models 45 and 46 of the current generation as parents. The partial trees 45a and 46a have, for example, a tree structure below a node selected at random from nodes other than the root node. Candidate model construction unit 150 generates two next-generation candidate models 47 and 48 in which partial trees 45a and 46a identified from candidate models 45 and 46 are replaced. The candidate model 47 has a structure in which the partial tree 45a is deleted from the candidate model 45, and the partial tree 47a having the same structure as the partial tree 46a in the candidate model 46 is connected to the position where the partial tree 45a is located. The candidate model 48 has a structure in which the partial tree 46a is deleted from the candidate model 46, and a partial tree 48a having the same structure as the partial tree 45a in the candidate model 45 is connected to the position where the partial tree 46a exists.

  The candidate model construction unit 150 generates a predetermined number of next-generation candidate models by performing generation evolution by crossing the candidate models 45 and 46 a plurality of times. For example, if the candidate model construction unit 150 performs generation evolution by crossover five times, ten next-generation candidate models are generated.

  The candidate model construction unit 150 can also simplify the generated candidate model. For example, if there is a part of addition or subtraction such that a plurality of coefficients are “a + b” in the candidate model, the candidate model construction unit 150 collects the parts into one coefficient. For example, “a + b → a”.

  The candidate model construction unit 150 may collect a plurality of terms in the candidate model. For example, when a plurality of terms “sin (x) × In (y) + sin (x) × log (z)” in the candidate model are included, the candidate model construction unit 150 designates this part as “sin (x) { In (y) + log (z)} ”.

  Furthermore, the candidate model construction unit 150 can also check for the existence of an irrational function of the candidate model. An irrational function is a function whose structure is not allowed mathematically. For example, the candidate model construction unit 150 checks for the existence of an irrational function such as zero percent, out of region, or no variable. The zero division function is a function that divides by “0” (a fraction whose denominator is “0”), for example, “sin (x) / 0”. A function outside the region is a function in which a variable that is outside the mathematical definition is set, such as “log (−x): x> 0” (a logarithm can be defined when the true number x is an integer). is there. A function without a variable is a function that does not include a variable, such as “cos (a)” (a is a coefficient). A function without variables can be replaced with one coefficient, for example.

When the candidate model is constructed, the data analysis unit 160 calculates the coefficient value of the candidate model.
FIG. 13 is a diagram illustrating an example of calculating coefficient values. The data analysis unit 160 creates graphs 51, 52,... In which the points indicating the degree of vacuum p for each elapsed time t are plotted for each of the response characteristic data 141, 142,. Then, the data analysis unit 160 reduces the distance from each plotted point to the curve (candidate model curve 43a) indicating the candidate model 43 in which the coefficient value is set for each of the graphs 51, 52,. The coefficient value in the candidate model 43 is calculated. For example, the data analysis unit 160 calculates the coefficient value by the least square method. Thereby, the coefficient value for each cooling unit is calculated for one candidate model 43.

  In the example of FIG. 13, the candidate model construction unit 150 calculates the coefficient value while ignoring the degree of vacuum during a period in which the degree of vacuum hardly changes. After calculating the coefficient value, the candidate model construction unit 150 calculates a matching coefficient.

  FIG. 14 is a diagram illustrating a calculation example of the matching coefficient. The data analysis unit 160 calculates a residual between the points plotted on the graph 51 generated for one cooling unit and the candidate model curve 43a. The residual is the distance in the direction of the degree of vacuum p from the plotted point to the candidate model curve 43a. The data analysis unit 160 uses the average of the absolute values of the residuals for each plotted point as a matching coefficient for the corresponding cooling unit. The data analysis unit 160 calculates such a matching coefficient for each cooling unit 1, 2,.

Candidate model construction unit 150 stores the calculation result of the coefficient value and the matching coefficient in analysis result storage unit 170.
FIG. 15 is a diagram illustrating an example of data stored in the analysis result storage unit. In the analysis result storage unit 170, for example, analysis result management tables 171, 172,... For each candidate model are stored.

  In the analysis result management tables 171, 172,..., Records indicating analysis results based on the response characteristic data 141, 142,. In each record, the final vacuum, the coefficient value of each coefficient included in the candidate model, and the matching coefficient are set in association with the unit numbers of the cooling units 1, 2,. As a result of the analysis by the data analysis unit 160 as described above, coefficient values and matching coefficients for each cooling unit 1, 2,... Are obtained for each of the constructed candidate models. The average of the matching coefficients calculated for each cooling unit 1, 2,... For one candidate model becomes the matching coefficient of the candidate model.

  Here, when the candidate model accurately represents the product quality, the coefficient value included in the candidate model is considered to have a physical meaning that affects a physical phenomenon related to the product quality. That is, the candidate model is generated by the GP regardless of the natural law, but if the candidate model accurately represents the quality of the product quality, the candidate model is a physical property related to the product quality. It represents a phenomenon. In that case, the structure of the formula that constitutes the candidate model represents the characteristics of the physical phenomenon, and the coefficients included in the candidate model also represent the characteristics of the physical phenomenon.

  Therefore, the model evaluation unit 180 evaluates the degree of representing the characteristics of the physical phenomenon that affects the product quality based on the coefficient value and the matching coefficient for the coefficient included in the candidate model. For example, the model evaluation unit 180 performs a correlation analysis between the coefficient value of the coefficient included in the candidate model and the final degree of vacuum.

  FIG. 16 is a diagram illustrating an example of correlation analysis between a coefficient value and a final vacuum degree. When the candidate model includes a plurality of coefficients, the model evaluation unit 180 performs correlation analysis for each coefficient and calculates a correlation coefficient. In the example of FIG. 16, correlation coefficients are calculated for two coefficients a and b included in the candidate model “a / (t + b)”. The correlation coefficient between the coefficient a and the final vacuum degree is “0.86”, and the correlation coefficient between the coefficient b and the final vacuum degree is “0.25”. Since the correlation coefficient is higher as the absolute value is larger, the coefficient a has a higher correlation with the final degree of vacuum than the coefficient b.

  Based on the calculated correlation coefficient, the model evaluation unit 180 calculates a corrected correlation coefficient that becomes smaller as the correlation is higher. The corrected correlation coefficient is expressed by “corrected correlation coefficient = 1−absolute value of correlation coefficient of coefficient”. The model evaluation unit 180 sets a corrected correlation coefficient in the evaluation result management table 181.

  In the evaluation result management table 181, for example, a matching coefficient, a corrected correlation coefficient for each coefficient, and a score value are registered in association with the candidate model. The matching coefficient registered in the evaluation result management table 181 is, for example, an average value of matching coefficients calculated for each cooling unit 1, 2,. Since the score value is not calculated at the stage shown in FIG. 16, the score value column of the candidate model “a / (t + b)” is blank.

  The model evaluation unit 180 stores the evaluation result management table 181 in the memory 102, for example. Then, the model evaluation unit 180 calculates the score value of the candidate model based on the matching coefficient set in the evaluation result management table 181 and the modified correlation coefficient for each coefficient of the candidate model.

  FIG. 17 is a diagram illustrating a calculation example of the score value of the candidate model. When a plurality of coefficients are included in one candidate model, the model evaluation unit 180 selects a coefficient having a smaller value of the modified correlation coefficient, and uses the selected coefficient as a quality-related feature. Next, the model evaluation unit 180 calculates the product of the modified correlation coefficient of the quality-related feature and the matching coefficient. The model evaluation unit 180 sets the product calculation result in the evaluation result management table 181 as a score value.

  Thereby, the score value becomes smaller as the value of the modified correlation coefficient of the quality-related feature becomes smaller, and becomes smaller as the value of the matching coefficient becomes smaller. Even when the sum of the corrected correlation coefficient of the quality-related feature and the matching coefficient is used as the score value, the score value becomes smaller as the value of the corrected correlation coefficient of the quality-related feature is smaller. The smaller the value, the smaller the value. However, in order to find a coefficient that achieves both a small matching coefficient and a small corrected correlation coefficient, it is better to use the product of the corrected correlation coefficient of the quality-related feature and the matching coefficient as a score value.

  FIG. 18 is a diagram for explaining a difference in score value due to a difference in calculation method. FIG. 18 shows an evaluation result coordinate system 60 representing the evaluation result. The horizontal axis of the evaluation result coordinate system 60 is a matching coefficient, and the vertical axis is a corrected correlation coefficient. The evaluation result is located somewhere in the evaluation result area 61 of the first quadrant. When calculating the score value, when the evaluation result is at the position (target position 64) where the matching coefficient is the minimum “0” and the corrected correlation coefficient is the minimum “0”, the score value is minimum (excellent). It is appropriate to use a simple calculation formula.

  In FIG. 18, two evaluation results 62 and 63 are shown. One evaluation result 62 has a matching coefficient of “99.9” and a corrected correlation coefficient of “0.1”. The other evaluation result 63 has a matching coefficient of “99.1” and a corrected correlation coefficient of “0.9”.

  If the sum of two coefficients is taken as a score value calculation method, the result is a score value “100” and no difference is produced. However, it is the evaluation result 62 that is closer to the target position 64, as can be seen when the evaluation results 62 and 63 are arranged in the evaluation result coordinate system 60. By adopting the product of two coefficients as a score value calculation method, the evaluation result 62 has a smaller score value than the evaluation result 63 (becomes an excellent score value). Therefore, the model evaluation unit 180 uses the product of the matching coefficient and the modified correlation coefficient as the score value.

  Each time a repetitive candidate model is constructed by GP, the model evaluation unit 180 calculates a corrected correlation coefficient and a score value for each constructed candidate model. Then, the model evaluation unit 180 sets the calculation result in the evaluation result management table 181. This process is repeated until a candidate model construction end condition is satisfied.

  FIG. 19 is a diagram illustrating an example of an evaluation result management table in which evaluation results of candidate models are set. As shown in FIG. 19, a score value is calculated for each candidate model. In the case of a candidate model including a plurality of coefficients, the coefficient having the smallest value of the modified correlation coefficient among the coefficients of the candidate model is the quality-related feature used for calculating the score value. Among the candidate models shown in the evaluation result management table 181, the smaller the score value, the higher the quality-related features included in the candidate model are related to the product quality.

When the candidate model termination condition is satisfied, the model evaluation unit 180 collates the candidate model with the theoretical model, thereby examining the meaning of the quality-related feature having high relevance to the product quality.
FIG. 20 is a diagram illustrating an example of the model matching process. For example, it is assumed that the mathematical formula of the candidate model 71 having the smallest score value (good evaluation) is “a / (t + b)”. Further, it is assumed that the quality-related feature in the candidate model 71 is a coefficient a.

  The model evaluation unit 180 compares the mathematical formula of the candidate model 71 with the mathematical formula of each theoretical model registered in the theoretical model management table 121, and extracts a similar theoretical model. In the example of FIG. 20, the theoretical model “P (x) = a / x” has a high similarity to the candidate model 71.

  In this case, the model evaluation unit 180 indicates the meaning “exhaust resistance” of the coefficient “a” corresponding to the quality-related feature in the theoretical model “P (x) = a / x” having a high similarity. Extract from Then, the model evaluation unit 180 displays on the monitor 21 that the exhaust resistance has an influence on the product quality.

Hereinafter, the model matching process will be described in detail.
The model evaluation unit 180 first filters the theoretical model in the model matching process. Filtering is a process of excluding a theoretical model that is clearly not similar to a candidate model from the calculation target of similarity.

  FIG. 21 is a diagram illustrating an example of filtering of the theoretical model. In the example of FIG. 21, it is assumed that the mathematical formula of the candidate model 72 with the highest evaluation is “a × sin (b × x + c)”. At this time, the model evaluation unit 180 first analyzes the configuration of each theoretical model. Then, theoretical model configuration information 73 is generated. For example, the model evaluation unit 180 analyzes the type of function, the number of variables, and the order of each theoretical model, and sets the determination result in the theoretical model configuration information 73. Similarly, the model evaluation unit 180 also analyzes the type of function, the number of variables, and the order of the candidate model 72.

  Then, the model evaluation unit 180 deletes from the theoretical model configuration information 73 the candidate model 72 and the theoretical model in which any of the function type, the number of variables, and the order does not match. Note that the model evaluation unit 180 may regard functions such as sin and cos that have only a phase difference as the same function. In the example of FIG. 21, the function of the candidate model 72 is “sin”. On the other hand, the theoretical model “a / x” shown in the theoretical model configuration information 73 does not include the function “sin”. Therefore, the model evaluation unit 180 deletes the theoretical model “a / x” from the theoretical model configuration information 73 and excludes it from the similarity calculation target. The function of the theoretical model “aexp (−bx)” (multiplication symbol is omitted) is “exp”, which is different from the function “sin” of the candidate model 72. Therefore, the model evaluation unit 180 deletes the theoretical model “aexp (−bx)” from the theoretical model configuration information 73 and excludes it from the similarity calculation target.

By such a filtering process, the theoretical model to be used for calculating the similarity is narrowed down. Next, the model evaluation unit 180 performs character string replacement between the candidate model and the theoretical model.
FIG. 22 is a diagram illustrating an example of the character string replacement process. In the model evaluation unit 180, for example, a replacement rule 74 is defined in advance. In the replacement rule 74, a replacement destination character string is set in association with the replacement source element. In the example of FIG. 22, the replacement rule 74 is defined so that the replacement source element is replaced with one character.

  The model evaluation unit 180 replaces the character string according to the replacement rule 74 for each of the candidate model and the theoretical model. For example, the model evaluation unit 180 replaces the function “sin” of the candidate model “asin (bx + a)” (the multiplication symbol is omitted) with “f”. In addition, the model evaluation unit 180 replaces the coefficient “a, b” of the candidate model “asin (bx + a)” with “a”.

  Similarly, the model evaluation unit 180 replaces the character string of the theoretical model according to the replacement rule 74. For example, the variable “t” in the theoretical character string “asin (ωt + θ)” (the multiplication symbol is omitted) is replaced with “x”.

  Next, the model evaluation unit 180 compares the degree of similarity between the character string of the candidate model after replacement and the character string of the theoretical model after replacement by the Levenshtein distance method. The Levenshtein distance can be calculated using, for example, a two-dimensional matrix.

FIG. 23 is a diagram illustrating a first calculation example of the Levenshtein distance. Figure 23 is a candidate model after substitution "a × f (a × x + a) ", Request Levenshtein distance between the theoretical model after substitution ^{"a 2 × f 2 (x)} × g 2 (x) " An example is shown. The first row and the first column of the Levenshtein distance calculation matrix 75a correspond to empty characters. In each line, after the empty character, the character of the candidate model after replacement is associated in order from the top. In each column, after the null character, the character of the theoretical model after replacement is associated in order from the top. The distance between one character of the candidate model after replacement and one character of the theoretical model after replacement is set to a square corresponding to those characters.

The distance between the empty character of one character string and the nth character (n is an integer of 1 or more) of the other character string is n. For the other cells, the smallest value of the following three numbers is set.
・ Number of square above own square +1
・ Number of left cell of own cell +1
・ Number of upper left cell of own cell + a (a is “0” when the vertical and horizontal characters of the own cell are equal, and “1” when different)
The number “8” in the lower right corner of the matrix 75a created in this way is the Levenshtein distance (minimum number of edits) between the candidate model after replacement and the theoretical model after replacement.

  FIG. 24 is a diagram illustrating a second calculation example of the Levenshtein distance. FIG. 24 shows an example of obtaining the Levenshtein distance between the candidate model “a × f (a × x + a)” after replacement and the theoretical model “a × f (x)” after replacement. The number in the lower right corner of the Levenshtein distance calculation matrix 75b shown in FIG. 24 is “4”, and the Levenshtein distance is “4”.

  The model evaluation unit 180 uses the calculated Levenstein distance as the similarity. When the similarity of each logical model is calculated, the model evaluation unit 180 compares the similarities of the respective theoretical models and ranks them in descending order of similarity. Then, the model evaluation unit 180 creates a similarity management table indicating the rank order of similarity of the theoretical model.

For example, the model evaluation unit 180 calculates the similarity with the theoretical model for each of a predetermined number of candidate models from the highest score value, and creates a similarity management table.
FIG. 25 is a diagram illustrating an example of the similarity management table. As shown in FIG. 25, similarity management tables 76a, 76b,... For each candidate model are created. In the similarity management tables 76a, 76b,..., The meaning of the theoretical model, the replaced theoretical model, the similarity, and the rank are set in association with the theoretical model. The model evaluation unit 180 stores the created similarity management tables 76a, 76b,.

  The model evaluation unit 180 identifies a coefficient corresponding to a quality-related feature of a theoretical model having a high degree of similarity with a candidate model having a low score value (high evaluation), and the coefficient affects the quality of the product. A quality-related factor with a high probability. The model evaluation unit 180 displays the analysis result of the quality-related factor on the monitor 21.

  FIG. 26 is a diagram illustrating an example of a quality-related factor analysis result display screen. The analysis result display screen 77 includes, for example, quality related factor information 77a. In the quality-related factor information 77a, quality-related factors obtained from similar theoretical models are shown for each candidate model.

  For example, in the quality-related factor information 77a, candidate models with lower score values (higher evaluations) are shown higher. Furthermore, in the quality-related factor information 77a, for example, a list of theoretical models having a similarity equal to or higher than a predetermined value is shown in association with each candidate model. In the list of theoretical models, the theoretical models with higher similarity are shown at the top.

  In the quality-related factor information 77a, the meaning of the theoretical model, the meaning of the quality-related factor, the candidate model, the quality-related feature, the modified correlation coefficient, and the score value are shown in association with each theoretical model. The meaning of the theoretical model is the physical meaning of the theoretical model and is information acquired from the theoretical model management table 121. The meaning of the quality-related factor is the physical meaning of the coefficient corresponding to the coefficient of the quality-related feature among the coefficients included in the theoretical model. For example, when a coefficient indicating a gain in the candidate model is a quality-related feature, a coefficient corresponding to the gain in the theoretical model (a coefficient to be multiplied by a variable or a function) is a quality-related factor. When the coefficient indicating the offset in the candidate model is a quality-related feature, the coefficient corresponding to the offset in the theoretical model (coefficient added to or subtracted from the variable) is the quality-related factor. The candidate model, quality-related feature, modified correlation coefficient, and score value associated with each theoretical model are information indicating the basis for determining that the coefficient of the theoretical model is a quality-related factor.

  The user can recognize what physical quantity is related to the quality of the product by referring to the analysis result display screen 77. In the example of FIG. 26, it can be understood that the exhaust resistance related to the exhaust speed affects the quality of the product. Thereby, it can be expected that the final vacuum degree of the product is NG (defective) due to the exhaust resistance. Therefore, for example, the user specifies the variation of the unit piping component that becomes the exhaust resistance, and investigates the piping component. Then, the user can suppress the occurrence of products whose final vacuum does not reach the target value by taking measures to improve the variation in the pipe bending shape and diameter.

  Moreover, in the second embodiment, since the score value is calculated by combining the correlation coefficient and the matching coefficient, the candidate model including the coefficient corresponding to the factor affecting the quality can be determined with high accuracy. it can.

FIG. 27 is a diagram illustrating determination accuracy based on score values. FIG. 27 is a diagram illustrating an example of analysis results of three candidate models 78a to 78c.
Candidate model 78a is represented by a six-dimensional equation. Such a higher-order candidate model 78a can be matched with the response characteristic data with high accuracy. As a result, the matching coefficient becomes a good value (small value). On the other hand, the correlation coefficient between the quality-related features of the candidate model 78a and the product quality is small, and the value of the corrected correlation coefficient (1-the absolute value of the correlation coefficient) is large. Even if the candidate model 78a accurately represents the response characteristic data, if the correlation between the included coefficient and the product quality is low, it cannot be said that the coefficient represents a factor affecting the quality.

  The candidate model 78b matches the response characteristic data to some extent, and a good matching coefficient is obtained. Further, the correlation coefficient between the quality-related features of the candidate model 78b and the product quality is larger than that of the candidate model 78a, and the value of the corrected correlation coefficient is small. That is, in the candidate model 78b, the matching coefficient and the correlation coefficient are both good values.

  In the candidate model 78c, the correlation coefficient between the quality-related feature and the product quality is accidentally high, and the value of the corrected correlation coefficient is small. When the correlation coefficient is increased by chance, the value of the correlation coefficient does not represent a causal relationship between the quality-related feature and the product quality. The candidate model 78c has a higher matching coefficient value than the other candidate models 78a and 78b.

  By using the product of the corrected correlation coefficient and the matching coefficient of each of these three candidate models 78a, 78b, 78c as the score value, the correlation model and the matching coefficient of the candidate model 78b having a reasonably good value are obtained. The score value is the highest. That is, the coefficient of the candidate model 78a obtained by accurately tracing the response characteristic data using the higher-order equation does not represent a factor that affects the quality, and thus the score value is poor (large value). In addition, the candidate model 78c in which the correlations coincided by chance is prevented from erroneously having a good score value due to a poor (large) value of the matching coefficient.

  Thus, by calculating the score value by combining the correlation coefficient and the matching coefficient, it is possible to appropriately extract a candidate model including a coefficient representing a factor that affects quality. As a result, it is possible to correctly determine factors that affect product quality based on the corresponding candidate model.

[Third Embodiment]
Next, a third embodiment will be described. In the third embodiment, the score value is calculated in consideration of the structure of the formula that is known in advance based on the properties of the product.

  When the product includes a plurality of elements, the calculation formula representing the property of the product is complicated, and in the second embodiment, which element among the plurality of elements causes the product defect. You may not know. Therefore, in the third embodiment, by defining the basic structure of the formula according to the product properties in advance, even if the product includes a plurality of elements, factors that affect the product quality can be obtained. Ensure that it can be identified accurately.

Hereinafter, with reference to FIG. 28 to FIG. 31, the structure of the formula corresponding to the property of the product will be described.
FIG. 28 is a diagram illustrating a first example of a structure of an expression related to a product. In the example of FIG. 28, the calculation formula of the tip coordinate of the hand part of the industrial robot 81 (manipulator) is shown. The robot 81 has a plurality of joints, and the hand tip coordinates are obtained by multiplying the function f corresponding to the number of joints. If the robot 81 is a 6-axis articulated robot, hand tip coordinates can be obtained by multiplying the function f six times. That is, the hand tip coordinates are represented by an expression having a basic structure of “f × f × f × f × f × f”.

  FIG. 29 is a diagram illustrating a second example of the structure of formulas related to products. In the example of FIG. 29, a calculation formula for the optical output of a lithium niobate (LN) modulator 82 is shown. The optical output of the LN modulator 82 shown in FIG. 29 is represented by the equation “(f + f) × f” in the basic structure.

  FIG. 30 is a diagram illustrating a third example of the structure of formulas related to products. In the example of FIG. 30, the calculation formula of the voltage V of the electric circuit 83 is represented. In the electric circuit 83, three resistors R1 to R3 are connected in parallel, and the voltage V is expressed by an expression “f + f + f” in the basic structure.

  FIG. 31 is a diagram illustrating a fourth example of the structure of formulas related to products. In the example of FIG. 31, the calculation formula of the pressure loss of the fluid which flows into the piping 84 bent in the crank shape is represented. Since the pipe 84 shown in FIG. 31 has two bent portions, the pressure loss is represented by the formula “f × f” in the basic structure.

  Thus, the structure of the calculation formula for the physical quantity to be calculated can be predicted in advance according to the property of the product. Therefore, in the third embodiment, the data analysis unit 160 calculates the similarity between the candidate model and the calculation formula predicted for the product, and uses the similarity as the structure evaluation value. Then, the model evaluation unit 180 calculates a score value based on the correlation coefficient, the matching coefficient, and the structure evaluation value.

Hereinafter, the third embodiment will be described in detail.
FIG. 32 is a flowchart illustrating an example of a procedure of quality influence cause identification processing according to the third embodiment. In the following, the process illustrated in FIG. 32 will be described in order of step number.

  [Step S201] The candidate model construction unit 150 receives an element designation input used for construction of a candidate model. For example, the user performs an input for designating what the variable of the candidate model is, what operator is used, and what function is used. The user can also specify one of the formula candidate element lists in the formula candidate element storage unit 110 instead of inputting individual elements. When the formula candidate element list is designated, the candidate model construction unit 150 uses the operators, functions, and variables shown in the designated formula candidate element list as elements used for construction of the candidate model.

  The user also inputs the basic structure of the calculation formula corresponding to the target product. For example, if the product is a six-axis robot 81, the user inputs “f × f × f × f × f × f” as the basic structure.

  Further, the user inputs a weight for each index (matching coefficient, correlation coefficient, structure evaluation value) serving as a reference for calculating the score value. The user increases the weight value for the more important index.

  Further, the user inputs an end condition for constructing the candidate model. For example, the user inputs a score value threshold as an end condition. The user may input a structural evaluation threshold value, a matching coefficient threshold value, and a correlation coefficient threshold value as termination conditions. In this case, for example, when the candidate model construction unit 150 detects a candidate model having a structure evaluation value (similarity) equal to or lower than a threshold, a matching coefficient equal to or less than a threshold, and a correlation coefficient equal to or greater than the threshold, To do.

  Candidate model construction section 150 holds the input threshold value as an end condition when the threshold value of the score value is input. In addition, when the threshold value used as the end condition is not input, the candidate model construction unit 150 sets, for example, a preset threshold value as the end condition.

  [Step S202] The candidate model construction unit 150 constructs a candidate model by combining mathematical expression candidate elements by GP. Note that in the third embodiment, the candidate model construction unit 150 sets coefficients of gain and offset for each function when the candidate model includes a plurality of functions. Candidate model construction unit 150 also sets a coefficient to be multiplied with the variable. For example, the candidate model construction unit 150 constructs a candidate model of “acos (bt + c) + [dsin (et + f) + g sin (et + f)] × fhsin (et + f)”. This candidate model includes coefficients “a, b, c, d, e, f”.

  [Step S203] The data analysis unit 160 calculates the value of the coefficient included in the constructed candidate model for each response characteristic data acquired from the product to be analyzed. Thereby, the calculation formula of a candidate model is decided.

  [Step S204] The data analysis unit 160 calculates the structure evaluation value of the constructed candidate model. For example, the data analysis unit 160 calculates the similarity between the constructed candidate model and an expression indicating the basic structure of the product, and uses the similarity as a structure evaluation value.

  At this time, the data analysis unit 160 may compare the calculated structure evaluation value with a threshold value of the structure evaluation value. In that case, if the structure evaluation value is less than the threshold value, the data analysis unit 160 proceeds to step S205. If the structure evaluation value is equal to or greater than the threshold value, the data analysis unit 160 skips steps S205 to S207 and performs processing. Proceed to step S208.

  [Step S205] The data analysis unit 160 calculates a matching coefficient for each product for the constructed candidate model. For example, the matching coefficient becomes smaller as the residual between the response characteristic data of the product and the curve of the candidate model in which the coefficient is set is smaller.

  At this time, the data analysis unit 160 may compare the calculated matching coefficient with a threshold value of the matching coefficient. In that case, if the matching coefficient is less than the threshold value, the data analysis unit 160 proceeds to step S206. If the matching coefficient is equal to or greater than the threshold value, the data analysis unit 160 skips the processes in steps S206 to S207 and performs the process in step S208. Proceed to

  [Step S206] The data analysis unit 160 performs a correlation analysis with the product quality for each coefficient in the candidate model. By the correlation analysis, a correlation coefficient is calculated for each coefficient of the constructed candidate model.

  At this time, the data analysis unit 160 may compare the calculated correlation coefficient with a threshold value of the correlation coefficient. In this case, if the correlation coefficient is greater than the threshold, the data analysis unit 160 proceeds to step S207. If the correlation coefficient is equal to or less than the threshold, the data analysis unit 160 skips step S207 and proceeds to step S208. .

[Step S207] The model evaluation unit 180 calculates a score value of the candidate model based on the correlation coefficient for each coefficient in the candidate model, the matching coefficient, and the structure evaluation value.
[Step S208] The model evaluator 180 determines whether or not the candidate model construction end condition is satisfied. For example, if there is at least one candidate model whose structure evaluation value is less than the threshold, matching coefficient is less than the threshold, correlation coefficient is greater than the threshold, and score value is less than the threshold, the model evaluation unit 180 sets the end condition as Judging to meet. If the end condition is satisfied, the model evaluation unit 180 advances the process to step S209. On the other hand, if the end condition is not satisfied, the model evaluation unit 180 proceeds with the process to step S202. Note that, when the termination condition is not satisfied, the model evaluation unit 180 transmits, for example, two candidate models having the highest score value among the candidate models of the latest generation to the candidate model construction unit 150.

  [Step S209] The model evaluation unit 180 collates a predetermined number of candidate models with a smaller score value with a theoretical model. The model evaluation unit 180 calculates the structural similarity between the candidate model and the theoretical model, for example. Then, the model evaluation unit 180 determines the meaning of the coefficient of the candidate model based on the meaning of the coefficient of the theoretical model similar to the candidate model.

  [Step S210] The model evaluation unit 180 outputs a result of specifying the cause of quality influence. For example, the model evaluation unit 180 displays on the monitor 21 the meanings of the coefficients of a predetermined number of candidate models from the smaller score values as factors that affect product quality.

The process for identifying the cause of quality influence is performed in such a procedure. Thus, the third embodiment is greatly different from the second embodiment in that the score value is calculated using the structure evaluation value.
FIG. 33 is a diagram illustrating a calculation example of the structure evaluation value. The data analysis unit 160 generates the structure of the calculation formula of the candidate model 91 (candidate model structure 91a) by simplifying the candidate model 91. For example, the data analysis unit 160 simplifies the candidate model by, for example, a character string replacement process shown in FIG.

  The data analysis unit 160 calculates a structure evaluation value based on the similarity between the basic structure 90 and the candidate model structure 91a. For example, the data analysis unit 160 uses the Levenshtein distance method to calculate the minimum number of edits (Levenstein distance) for converting the candidate model structure 91a into the basic structure 90. The data analysis unit 160 sets, for example, a value obtained by dividing the minimum number of edits by the number of characters of the basic structure as the structure evaluation value.

  For example, when the calculated structure evaluation value is less than the structure evaluation value threshold, the data analysis unit 160 determines that the candidate model 91 is compatible with the basic structure 90. Further, the data analysis unit 160 determines that the candidate model 91 is incompatible with the basic structure 90 when the calculated structure evaluation value is equal to or greater than the structure evaluation value threshold. In the case of incompatibility, the data analysis unit 160 sets a structure incompatibility flag in the record of the candidate model 91 in the evaluation result management table 181 (see FIG. 19), for example. If the structure of the candidate model 91 becomes incompatible, the data analysis unit 160 can improve the efficiency of the process by omitting the calculation of the matching coefficient of the candidate model 91 and the correlation analysis process.

  In the third embodiment, the model evaluation unit 180 calculates the score value of the candidate model based on the rank (ranking) for each index (structure evaluation value, matching coefficient, correlation coefficient) between candidate models. . Ranking is performed for each index of the candidate model and set in the ranking management table.

  FIG. 34 is a diagram illustrating an example of a ranking management table. In the ranking management table 92, rankings of structure evaluation values, matching coefficients, and correlation coefficients are set in association with individual numbers of candidate models.

  The ranking of the structure evaluation value is the order of each candidate model when a plurality of candidate models are sorted in ascending order by the structure evaluation value. Therefore, the candidate model having the smallest structure evaluation value is ranked first in the structure evaluation value ranking.

  The ranking of matching coefficients is the order of candidate models when a plurality of candidate models are sorted in ascending order by matching coefficients. Therefore, the candidate model with the smallest matching coefficient is ranked first in the matching coefficient ranking.

  The correlation coefficient ranking is the order of each candidate model when a plurality of candidate models are sorted in descending order by correlation coefficient. Therefore, the candidate model having the largest correlation coefficient is ranked first in the correlation coefficient ranking.

The model evaluation unit 180 weights the ranking of each index and calculates a score value. For example, the model evaluation unit 180 divides each index by the weight of the index for each candidate model, and sets the sum of the division results as the score value of each candidate model. The score value is expressed as follows.
Score value = (structure evaluation value ranking / structure evaluation value weight Wf) + (matching coefficient ranking / matching coefficient weight Wr) + (correlation coefficient ranking / correlation coefficient weight Wc)
The model evaluation unit 180 sets the calculated score value in the ranking management table 92. The model evaluation unit 180 stores the created ranking management table 92 in the memory 102.

  The model evaluation unit 180 compares the score values of the constructed candidate models, and extracts the candidate model having the highest score value as the optimum model. Then, the model evaluation unit 180 compares the candidate model extracted as the optimal model with the theoretical model, and determines the meaning of the coefficient that affects the quality.

  FIG. 35 is a diagram illustrating a collation example between a candidate model and a theoretical model. In the example of FIG. 35, the meaning of the theoretical model, the coefficient included in the theoretical model, and the meaning of each coefficient are set in the theoretical model management table 121a in association with the theoretical model.

  For example, the model evaluation unit 180 simplifies the candidate model 91 extracted as the optimum model and the theoretical model, and calculates the similarity using the Levenshtein distance method. Then, the theoretical models are sorted by similarity (minimum number of edits). Next, the model evaluation unit 180 specifies a coefficient corresponding to a coefficient indicating a quality-related feature in the candidate model among coefficients in the theoretical model having a high similarity. Then, the model evaluation unit 180 displays the meaning of the identified coefficient on the monitor as an analysis result.

  FIG. 36 is a diagram illustrating an example of a quality-related factor analysis result display screen. On the analysis result display screen 93, formulas of theoretical models are displayed in descending order (in descending order of score values). Each theoretical model is associated with its meaning and the included coefficient. Each coefficient is associated with its meaning, matching coefficient, correlation coefficient, and structure evaluation value. Among the coefficients included in the theoretical model, information on the coefficient indicating the quality-related feature is highlighted.

In this way, by setting the basic structure according to the property of the product in advance, it is possible to extract a candidate model that matches the basic structure.
A plurality of basic structures may be defined for one type of product. For example, the physical properties of a product are complex, and there are a plurality of basic structures that may represent the properties, and it may be difficult to limit to one basic structure. In that case, the model evaluation unit 180 calculates the score value of each candidate model for each basic structure. Then, the model evaluation unit 180 displays similar theoretical models and the meanings of the coefficients in the theoretical models in order from the candidate model having the highest score value calculated for each basic structure.

  FIG. 37 is a diagram showing an example of a quality-related factor analysis result display screen when there are a plurality of basic structures. The example of FIG. 37 is a case where the score value for each candidate model is calculated based on the two basic structures 90a and 90b. The model evaluation unit 180 sorts records corresponding to pairs of theoretical models and basic structures similar to the candidate model in ascending order according to score values, and displays them on the analysis result display screen 94.

  On the analysis result display screen 94, the basic structure matching part is displayed in association with the theoretical model. In the basic structure matching part, the basic structure from which the score value is calculated is displayed, and the coefficients that are the quality-related features in the basic structure are highlighted.

In this way, the optimum model can be determined in consideration of the structure of the product, and factors that affect the quality of the product can be accurately identified.
[Other Embodiments]
In the second and third embodiments, the candidate model is constructed by GP, but the candidate model may be constructed by other methods. In addition, for example, the candidate model construction end condition may be that the constructed candidate model exceeds the maximum amount or that the generation of the candidate model constructed by the GP has reached a predetermined generation.

  In the second embodiment, the product of the matching coefficient and the modified correlation coefficient is used as the score value. However, in the second embodiment, the matching coefficient and the correlation coefficient are the same as in the third embodiment. The score value may be calculated based on the ranking.

Further, methods other than the Levenshtein distance method may be used for calculating the similarity between the candidate model and the theoretical model and for calculating the similarity between the candidate model and the basic structure.
As mentioned above, although embodiment was illustrated, the structure of each part shown by embodiment can be substituted by the other thing which has the same function. Moreover, other arbitrary structures and processes may be added. Further, any two or more configurations (features) of the above-described embodiments may be combined.

DESCRIPTION OF SYMBOLS 10 Information processing apparatus 11 Memory | storage part 11a Measurement data 12b Quality data 12 Processing part

Claims (11)

A storage unit for storing measurement data indicating a time change of a measurement value obtained by measuring a physical quantity during work for each of a plurality of products of the same type, and quality data including a quality value indicating the quality of each of the plurality of products,
A plurality of candidate formulas including a coefficient whose value is undetermined and representing a temporal change of the physical quantity are generated, each of the generated candidate formulas is set as an evaluation target, and the coefficient of the candidate formula of the evaluation target based on the measurement value A coefficient value is determined for each product, and based on the coefficient value for each product of the evaluation target candidate formula, a matching coefficient indicating the degree of fit of the evaluation target candidate formula with respect to the measurement value is calculated, and the evaluation target A correlation coefficient between the coefficient value of each candidate formula product and the quality value is calculated, and based on the matching coefficient and the correlation coefficient of the evaluation target candidate formula, the score value of the evaluation target candidate formula And a processing unit that identifies a quality-related expression including a coefficient related to the quality of the plurality of products from the plurality of candidate expressions, based on the score value of each of the plurality of candidate expressions,
An information processing apparatus. The processing unit calculates a residual between a regression equation obtained by setting a coefficient value for each product in the candidate formula to be evaluated and the measured value for each product, and calculates an average of absolute values of residuals as the matching Coefficient
The information processing apparatus according to claim 1. The processing unit generates the plurality of candidate expressions by genetic programming.
The information processing apparatus according to claim 1 or 2. The processing unit further specifies a similar theoretical formula similar to the quality-related formula from a plurality of theoretical formulas representing the theoretical properties of the plurality of products, and determines the physical properties of the coefficients included in the similar theoretical formula. Output meaning,
The information processing apparatus according to claim 1. The processing unit sets, as the score value of the evaluation target candidate expression, a product of the matching coefficient and a value corresponding to the correlation coefficient for the evaluation target candidate expression.
The information processing apparatus according to claim 1. When the candidate expression to be evaluated includes a plurality of coefficients, the processing unit has a value corresponding to the correlation coefficient having a larger absolute value of the correlation coefficients of the plurality of coefficients, A product with a matching coefficient is used as the score value of the candidate expression to be evaluated,
The information processing apparatus according to claim 5. The processing unit multiplies or divides a value corresponding to each of the matching coefficient and the correlation coefficient of the evaluation target candidate expression, and calculates a sum of weight multiplication or division results of the evaluation target candidate expression. The score value,
The information processing apparatus according to claim 1. The processing unit determines the rank of the matching coefficient and the correlation coefficient among the plurality of candidate expressions, and is based on the rank of the matching coefficient and the correlation coefficient of the candidate expression to be evaluated Calculating the score value of the candidate expression to be evaluated,
The information processing apparatus according to claim 1. The processing unit calculates a structure evaluation value of the evaluation target candidate expression based on a similarity between the basic structure of the physical quantity calculation expression based on the characteristics of the plurality of products and the evaluation target candidate expression. Calculating the score value of the evaluation target candidate formula based on the matching coefficient of the evaluation target candidate formula, the correlation coefficient, and the structure evaluation value;
The information processing apparatus according to claim 1. Computer
Stored in the storage unit is measurement data indicating a time change of a measurement value obtained by measuring a physical quantity during work for each of a plurality of products of the same type, and quality data including a quality value indicating the quality of each of the plurality of products,
A plurality of candidate formulas including coefficients whose values are undetermined and representing temporal changes of the physical quantity;
Each of the plurality of generated candidate formulas is to be evaluated, the coefficient value of the candidate formula of the evaluation target is determined for each product based on the measurement value, and based on the coefficient value of each product of the candidate formula of the evaluation target Calculating a matching coefficient indicating the degree of adaptation of the candidate formula of the evaluation target to the measurement value, calculating a correlation coefficient between the quality value and the coefficient value of each product of the candidate formula of the evaluation target, Based on the matching coefficient of the target candidate formula and the correlation coefficient, the score value of the candidate formula of the evaluation target is calculated,
Based on the score value of each of the plurality of candidate formulas, a quality related formula including a coefficient related to the quality of the plurality of products is specified from the plurality of candidate formulas.
Quality related expression generation method. On the computer,
Stored in the storage unit is measurement data indicating a time change of a measurement value obtained by measuring a physical quantity during work for each of a plurality of products of the same type, and quality data including a quality value indicating the quality of each of the plurality of products,
A plurality of candidate formulas including coefficients whose values are undetermined and representing temporal changes of the physical quantity;
Each of the plurality of generated candidate formulas is to be evaluated, the coefficient value of the candidate formula of the evaluation target is determined for each product based on the measurement value, and based on the coefficient value of each product of the candidate formula of the evaluation target Calculating a matching coefficient indicating the degree of adaptation of the candidate formula of the evaluation target to the measurement value, calculating a correlation coefficient between the quality value and the coefficient value of each product of the candidate formula of the evaluation target, Based on the matching coefficient of the target candidate formula and the correlation coefficient, the score value of the candidate formula of the evaluation target is calculated,
Based on the score value of each of the plurality of candidate formulas, a quality related formula including a coefficient related to the quality of the plurality of products is specified from the plurality of candidate formulas.
Quality-related expression generation program that executes processing.

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