JP4653547B2 - Apparatus and method for analyzing relation between operation and quality in manufacturing process, computer program, and computer-readable recording medium - Google Patents

Description

  The present invention relates to an analysis device, a method, a computer program, and a computer-readable recording medium relating to operation and product quality (hereinafter referred to as quality) in a manufacturing process, and in particular, in a general process in which quality is determined as an operation result, The present invention relates to a technique suitable for use in elucidating the cause of quality incompatibility by clarifying the relationship between the operation factor and quality, and finding out the operation conditions for obtaining the desired quality.

  Conventionally, in the process where the quality is determined as the operation result, as the operation analysis method for analyzing the influence of the operation condition on the quality, a correlation analysis method that evaluates using a correlation coefficient between a single operation factor and quality, It is well known to create and evaluate a multiple regression model with the operational factors of the input as the input and the quality as the output.

  Further, in the technique disclosed in Patent Document 1, in the steel process, the physical property value such as the carbon amount of the slab, the operation value such as the casting width, the temperature value of the cooling zone and the like are the operation factors, and the surface defects of the steel sheet are determined. A quality control diagnosis is performed by learning the relation between the quality data and the operation data by a quality prediction device using a multi-layer neural network as quality data.

  Furthermore, a method using a decision tree described in Non-Patent Document 1 is known as a model for analyzing a more complicated relationship between operation factors and quality in a format that is easy for humans to understand.

  Further, in the method disclosed in Patent Document 2, based on the operation data and the quality data, the operation factor space having the operation data as a basis vector is divided into several local regions, and the operation factor and quality in each local region are divided. Is modeled in a line format that is easy for humans to understand intuitively. Then, an activity function that expresses the contribution rate indicating how much each local line format affects the overall quality as a function of the coordinate of the operation factor space is obtained from the operation data, and the overall operation factor and quality are obtained. By deriving a mathematical model that expresses the relationship, the analysis method that presents the relationship between multivariate operating factors with complex nonlinear characteristics and quality in a form that is easy for humans to understand is realized.

JP-A-6-304723 JP 2003-141215 A J.R Quinlan, "Learning with continuous classes", Proceedings of the 5th Australian Joint Conference on Artificial Intelligence. AI '92, 1992, Pages 343-348

  In the method using the correlation coefficient and multiple regression model described above, the correlation coefficient and regression are based on the precondition that the operation and quality data to be analyzed can be expressed by a single linear model in the entire operation range. A model is derived and analyzed. Therefore, when analyzing operation and quality data obtained from a process in which a plurality of quality mismatch factors having different characteristics exist, there is a problem that the relationship between the two cannot be correctly grasped.

  In the method disclosed in Patent Document 1, a model in which the relationship between operation factors and quality is learned using a multilayer neural network is created and applied to quality control diagnosis. However, the multilayer neural network has a problem that it is extremely difficult for a human to read what logic the control diagnosis is made based on, and the operator cannot judge the rationality of the control diagnosis result.

  Furthermore, in the method using a decision tree, the operation factor space with the operation data as a basis vector is divided based on the operation conditions, and a process for deriving a linear model of the operation factor and quality in each local space is performed. Analyzing operation data for processes with multiple quality mismatch factors. At that time, since the boundary line of the local region is strictly set and different linear equations are established on both sides, there is a boundary region where the quality is determined by overlapping multiple incompatibility causes However, there was a problem that the decision tree was used for the above data.

  The technique disclosed in Patent Document 2 can solve the problems in each of the above-described techniques, and divides an operation factor space having operation data as a basis vector into several local areas, and operates in each local area. By modeling the relationship between factors and quality in a line format that is easy for humans to understand intuitively, the relationship between operations and quality that exhibit complex characteristics throughout the entire operating range is accurate and easy for humans to understand. It can be captured in a form. In addition, an activity function that indicates how much each local line format affects the overall quality characteristics under specific operating conditions is obtained from the operation data, and the relationship between the overall quality and the operation is calculated. It is expressed by a linear combination of local line formats with weights. Thus, it is possible to accurately analyze the vicinity of the boundary where the quality is determined by superimposing a plurality of incompatibility causes. However, this method does not consider the distribution of the operation data subject to analysis in the operation factor space when dividing the local region and deriving the activity function. Therefore, when applied to the analysis of actual operation data, the accuracy of the local line format deteriorates due to the bias of the data in the local area, or the division is manually changed by trial and error There was a practical problem that the cause of the quality mismatch could not be solved quickly.

  The present invention has been made in view of the above points, and when analyzing the relationship between a plurality of operating factors and quality in the manufacturing process, the operating factor space is actually an analysis target. By automatically performing appropriate space division according to the distribution state of data such as bias and sparseness of operation data, a high-quality and operation-related model is built with a relatively small number of divisions, The purpose is to make it possible to extract analysis models that are easy for humans to interpret.

The operation and quality related analysis device in the manufacturing process of the present invention provides the quality data corresponding to the data ( hereinafter referred to as “ operation data ” ) of a plurality of operation items ( hereinafter referred to as “ operation factors ” ) in the manufacturing process . Based on the analysis of the relationship between each operating factor and quality,
A data input means for inputting quality data corresponding to operation data of the manufacturing process;
An operation space dividing means for dividing an operation factor space having an operation factor as a base vector based on a plurality of operation data of the manufacturing process input by the data input means into a plurality of local regions;
Determining a local quality model based on a linear polynomial representing a relation between an operation factor and quality based on a plurality of operation data and quality data in each local region, and determining an undetermined coefficient so that a prediction error due to the local quality model is minimized. and local quality model creation means be constructed by,
A global quality model creating means for creating a global quality model that represents the quality characteristics of the entire operating range by adding the local quality model of each local region multiplied by a weighting function for all local regions ,
When the overall quality model created by the overall quality model creating means satisfies a predetermined condition, an operation and quality related analysis device in an operation process presenting at least a local quality model for creating the overall quality model ,
The operating space dividing means is
A division target area selecting means for selecting a local area to be divided;
Local data selection means for selecting and extracting operation data distributed within the range of each local area selected by the division target area selection means;
Based on the distribution information obtained by projecting the operation data extracted by the local data selection unit onto the axis of each operation, an appropriate division that selects any one of the data grouping area division unit and the equal data number division group unit as the division unit Legal decision means;
Area subdivision means for performing subdivision of a local area based on information obtained by the data grouping area division means or the equal data number division group means,
The data grouping area dividing means includes
An initial barycentric point creating means for creating an initial barycentric point of operation data extracted by the local data selecting unit;
Center-of-gravity point-operation data distance evaluation means for calculating the distance between the operation data extracted by the local data selection means and the center of gravity point;
Based on the distance calculated by the center-of-gravity point-operation data distance evaluation means, operation data group creation means for grouping operation data that can be regarded as being close to each other;
For the group created by the operation data group creating means, the center-of-gravity point updating means for updating the center-of-gravity point using the operation data coordinates belonging to the group;
Based on the center of gravity point before and after the update and the information on the group creation result created by the operation data group creation means, it is determined whether it has converged to an appropriate grouping result, and if it has converged, the center of gravity point and the operation data group A grouping result determination unit that delivers information to the region subdivision unit;
The equal data number division group means includes:
An equal data number division position calculating means for calculating an equal data number division position for each operation axis in which the number of operation data extracted by the local data selection means is equal in each area after subdivision;
An equal data number division group creating means for calculating and grouping which region the operation data extracted by the local data selection means belongs to which region after the subdivision by the equal data number division position calculating means,
An equal data number division position obtained by the equal data number division position calculating means and the equal data number division group creating means by calculating a barycentric point of the area after subdivision by the equal data number division position calculating means, and an operation A data center division center point calculation unit is provided, which is delivered to the region subdivision unit together with the data grouping result .
The method for analyzing the relation between operation and quality in the manufacturing process according to the present invention is based on the data of a plurality of operation items ( hereinafter referred to as “ operation factors ” ) in the manufacturing process ( hereinafter referred to as “ operation data ” ) and the corresponding quality data. Based on the analysis of the relationship between each operating factor and quality,
A data input step in which the data input means inputs quality data corresponding to operation data of the manufacturing process;
An operation space dividing step of dividing the operation factor space into a plurality of local regions, the operation factor space having the operation factor as a basis vector based on the plurality of operation data of the manufacturing process input by the data input step ,
The local quality model creating means is adapted to minimize a prediction error caused by the local quality model by using a linear polynomial representing a relation between the operation factor and the quality based on the plurality of operation data and the quality data in each local region. A local quality model creation process constructed by determining undetermined coefficients in
The overall quality model creation means creates the overall quality model that represents the quality characteristics of the entire operating range by adding the local quality model of each local area multiplied by the weight function for all the local areas. A process,
When the overall quality model created by the overall quality model creating means satisfies a predetermined condition, an operation and quality related analysis method in an operation process presenting at least a local quality model for creating the overall quality model ,
The operation space dividing step is
A division target region selection step in which the division target region selection means selects a local region to be divided;
A local data selection step for selecting and extracting operation data distributed within the range of each local region selected by the division target region selection step; and
Based on the distribution information obtained by projecting the operation data extracted in the local data selection step onto the axis of each operation, the appropriate division method determination means performs either one of the data grouping region division step and the equal data number division group step. An appropriate division method determination step to be selected as a division step; and
An area subdivision means has an area subdivision process for performing subdivision of a local area based on information obtained by the data grouping area division process or the equal data number division group process,
The data grouping area dividing step includes:
An initial barycentric point creation means for creating an initial barycentric point of operation data extracted by the local data selection step,
Center-of-gravity point-operation data distance evaluation means calculates a distance between the operation data extracted by the local data selection step and the center-of-gravity point;
The operation data group creation means groups operation data that can be regarded as being close to each other based on the distance calculated by the center of gravity point-operation data distance evaluation step,
Center of gravity point update means, for the group created by the operation data group creation step, the center of gravity point update step of updating the center of gravity point using the operation data coordinates belonging to the group,
The grouping result determination means determines whether or not the grouping result has converged to an appropriate grouping result based on the center of gravity points before and after the update and the group creation result information created by the operation data group creation step. A grouping result determination step of transferring information on points and operation data groups to the region subdivision step,
The equal data number division group process includes:
Equal data number division position calculating means calculates the equal data number division position for each operation axis, where the number of operation data extracted by the local data selection step is equal in each area after subdivision A division position calculating step;
The equal data number division group creation means calculates and groups which operation data extracted by the local data selection step belongs to which region after subdivision by the equal data number division position calculation step belongs Split group creation process,
The equal data number division centroid calculation means calculates the centroid of the area after the subdivision by the equal data number division position calculation step, and is obtained by the equal data number division position calculation step and the equal data number division group creation step. And an equal data number division centroid point calculation step delivered to the region subdivision step together with the obtained equal data number division position and the operation data grouping result .
The computer program of the present invention is based on quality data corresponding to data ( hereinafter referred to as “ operation data ” ) of a plurality of operation items ( hereinafter referred to as “ operation factors ” ) in the manufacturing process . In analyzing the relationship,
A data input process for entering manufacturing process operation data and corresponding quality data;
An operation space dividing process for dividing an operation factor space having an operation factor as a base vector based on a plurality of operation data input by the data input process into a plurality of local regions;
Determining a local quality model based on a linear polynomial representing a relation between an operation factor and quality based on a plurality of operation data and quality data in each local region, and determining an undetermined coefficient so that a prediction error due to the local quality model is minimized. and local quality model creation process be constructed by,
The computer executes the overall quality model creation process for creating the overall quality model representing the quality characteristics of the entire operating range by adding the local quality model of each local area multiplied by the weight function for all the local areas. ,
When the overall quality model created by the overall quality model creation process satisfies a predetermined condition, a computer program that presents at least a local quality model for creating the overall quality model ,
The operation space dividing process is
A division target area selection process for selecting a local area to be divided;
Local data selection processing for selecting and extracting operation data distributed within the range of each local region selected by the division target region selection processing;
Proper division based on distribution information obtained by projecting the operation data extracted by the local data selection process onto the axis of each operation, and selecting either one of the data grouping area division process and the equal data number division group process as the division process Legal decision processing;
Causing the computer to execute an area subdivision process for performing subdivision of a local area based on information obtained by the data grouping area division process or the equal data number division group process,
The data grouping area dividing process includes:
An initial barycentric point creation process for creating an initial barycentric point of operation data extracted by the local data selection process;
Center-of-gravity point-operation data distance evaluation processing for calculating the distance between the operation data extracted by the local data selection processing and the center of gravity point;
Based on the distance calculated by the center-of-gravity point-operation data distance evaluation processing, operation data group creation processing for grouping operation data that can be regarded as close to each other,
For the group created by the operation data group creation process, the center of gravity point update process for updating the center of gravity point using the operation data coordinates belonging to the group, and
Based on the center of gravity point before and after the update and the information of the group creation result created by the operation data group creation process, it is determined whether or not it has converged to an appropriate grouping result. Causing the computer to execute a grouping result determination process for transferring information to the area subdivision process,
The equal data number division group processing is:
An equal data number division position calculation process for calculating an equal data number division position for each operation axis, in which the number of operation data extracted by the local data selection process is equal in each region after subdivision,
An equal data number division group creation process for calculating and grouping which region the operation data extracted by the local data selection process belongs to after subdivision by the equal data number division position calculation process;
Calculate the barycentric point of the area after the subdivision by the equal data number division position calculation process, the equal data number division position obtained by the equal data number division position calculation process and the equal data number division group creation process, and the operation In addition to the data grouping result, the computer is caused to execute an equal data number division centroid calculation process handed over to the area subdivision process .
The computer-readable recording medium of the present invention is recorded with the computer program of the present invention.

According to the present invention, it is possible to analyze a complicated relationship between a plurality of operating factors and product quality in a manufacturing process with high accuracy and in a format that is easy for humans to understand. In particular, when analyzing the relationship between multiple operating factors and quality, when dividing the operating factor space into local regions, it is appropriate depending on the distribution of data such as the bias or sparseness of the actual operating data being analyzed. By automatically performing space division, it is possible to quickly build a high-quality and operation-related model with a relatively small number of divisions. Therefore, when quality mismatch occurs using the analysis results, the cause is quickly found, and countermeasures such as changing the appropriate operation range to obtain a high-quality product are promptly executed. Generation of non-defective products can be suppressed.

  DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, with reference to the drawings, a preferred embodiment of an operation and quality relation analysis device, method, computer program, and computer-readable recording medium in the manufacturing process of the present invention will be described.

  FIG. 1 is a block diagram showing a configuration of an operation and quality relation analysis apparatus in the manufacturing process of the present embodiment. Moreover, the processing flow which considered each block in FIG. 1 as a process is an example which shows the relational analysis method of the operation and quality in the manufacturing process of this Embodiment. In the figure, reference numeral 101 denotes a data input unit, and operation data of a manufacturing process and quality data corresponding to the operation are input to a related analysis device. The data input unit 101 includes a keyboard, an OCR that reads a data sheet, or a LAN in a factory.

  For example, in the steel process, the operation data is a fluctuation amount of the molten metal surface in a continuous casting process, a heating furnace temperature in a hot rolling process, and the like, and is given as a continuous value. When a plurality of p operation factors u1, u2,..., Up are given for N products, the input operation data is a matrix of N rows and p columns.

  The quality data is, for example, the number of surface defects per steel plate coil manufactured by a steel process, and is given as a continuous value. When N cases of quality data are given corresponding to the operation data, the input quality data is an N-dimensional vector.

  Given input operation data that is an N-by-p matrix and quality data that is an N-dimensional vector, the operation data is distributed in a p-dimensional operation factor space based on u1 to up by linear algebra theory. It can be regarded as N points. At this time, if the quality is represented by the symbol y, the operation data and the quality are associated with each other, and therefore, it can be considered that the relationship is generally represented by the following expression (1) via the mapping function f (•).

  The above mapping function f (•) is generally a nonlinear / multivariate complex function in the entire operation region, and it is difficult to find an appropriate functional expression over the entire operation region. Therefore, in the present invention, the operation area is divided into several local areas, a quality model represented by a function that is relatively simple and easy to understand in each local area is constructed, and these are combined to operate data in the entire manufacturing process. By constructing a relationship between quality and quality, that is, a quality model, an apparatus that quickly creates an analysis model that is easy for humans to understand is realized.

  Reference numeral 102 denotes an initial division creation unit. When an analysis of the relationship between operation and quality is performed, if an approximate division of the appropriate operation area is known in advance, an initial division is performed at this point, and subsequent processing starts from this initial division. To do. If the approximate proper division is not known, the process after the division target area selection unit 103 may be executed with the entire operation area as the initial division. Specifically, for a plurality of given operation data, the minimum value (the following expression (2)) and the maximum value (the following expression (3)) are calculated for each base u1 to up of the operation factor space. There is a method in which a p-dimensional hypercube having apexes of the minimum value and the maximum value (the following expression (4)) is used as an initial division corresponding to the entire operation area.

  As another method of dividing the operation factor space, a method of dividing a p-dimensional space by a general plane or curved surface can be considered. However, in this division method, when the number of operating factors affecting quality is 4 or more and the dimension of the operating factor space is 4 or more, the division is performed on a general plane or curved surface that is not parallel to the base axis. However, it is not easy to present it in a form that is easy for humans to understand. Therefore, in order to obtain an analysis result that can be easily understood by humans, it is effective to make the dividing plane a plane parallel to any one of the base axes u1 to up of the operation factor space. By dividing in this way, the divided local region also becomes a p-dimensional hypercube. For example, when the local region L is divided so that the following expression (5) becomes a vertex, as described in (6) below It is easy to present a range where the local quality model is established as a range of specific operating conditions. FIG. 2 is a diagram for explaining a case where the division is performed with a line parallel to u2, taking an operation factor space based on two operation factors u1 and u2 as an example.

  Reference numeral 103 denotes a division target area selection unit. A process of selecting a local region to be further divided (subdivided) from the local regions created by the initial division creating unit 102 is performed. As a method for selecting a local region to be subdivided, for example, a local quality model is created for each local region, and a model error calculated from the predicted quality and quality results by the local model is evaluated. There is a method of selecting to subdivide the region. FIG. 3 is a diagram illustrating a process of selecting a division target region and subdividing the region, taking a two-dimensional operation factor space as an example. A rectangle in the two-dimensional plane of u1 and u2 including all operation data is set as a space initial division, and a division axis parallel to the u2 axis is set by a space division operation described later. Next, based on the local quality model errors of the subdivided areas 2-1 and 2-2, the area 2-2 is selected as a division target area, and the subdivision and area selection are repeated in the same manner.

  A local data selection unit 104 has a function of selecting and extracting operation data belonging to an area determined as a local area to be subdivided by the division target area selection unit 103. That is, when the local region is the above-described p-dimensional hypercube, the coordinate value of the vertex of the hypercube and the coordinate value of the operation data are used to determine whether each operation data point is located inside the hypercube. It may be determined and selected. In the subsequent processing, the region is subdivided based on the distribution state of the data selected here.

  An initial barycentric point creation unit 105 creates an initial value of barycentric coordinates in order to create an operation data group for calculating information necessary for subdividing the region in consideration of the operation data distribution. The number of initial center-of-gravity points is set in advance, but this may be input from the outside when performing analysis. In addition, as a method of creating the initial value of the center-of-gravity coordinates, for example, using a random number generator or the like, an arbitrary number of points located inside the p-dimensional hypercube corresponding to the local region are generated by the number of initial centers of gravity, and the initial center of gravity and There is a way to do it. When the number of centroids is k, the centroid coordinates are expressed as the following equation (7).

  A centroid point-operation data distance evaluation unit 106 calculates the operation data selected by the local data selection unit 104 and the centroid point distance d. The distance is calculated by calculating the distances from all the gravity center points for each operation data point. For example, as shown in the following equation (8), for the operation data points assigned number i, the distances from k centroid points are calculated. As a distance calculation method, for example, there is a method using the Euclidean distance defined by the following equation (9). As another distance calculation method, for example, the Mahalanobis distance described in page 84 of Miyamoto Sadaaki, “Introduction to Cluster Analysis”, Morikita Publishing (1999) may be used, and distance evaluation between two variables may be used. Any calculation method proposed as a method may be used.

  Reference numeral 107 denotes an operation data group creation unit, which selects a group center of gravity closest to each operation data based on the distance calculated by the center-of-gravity point-operation data distance evaluation unit 106, and a group to which the operation data belongs. Give a number. When a group number is assigned to all the operation data, operation data to which the same group number is assigned is extracted, and a process of collecting these as one operation data group is performed.

  Reference numeral 108 denotes a center-of-gravity point update unit. For each group created in the operation data group creation unit 107, the average value of the operation data coordinates belonging to the group is obtained using the following equation (10), and the process is performed to update the coordinates as new centroid coordinates in this group.

  Reference numeral 109 denotes a grouping result determination unit. When the group created by the operation data group creation unit 107 is the group created first using the initial barycentric coordinates, the processes after the barycentric point-operation data distance evaluation unit 106 are repeatedly executed. . In addition, when the group created in the operation data group creation unit 107 is calculated from the centroid point that has already undergone the update process, the operation data group created in the previous iteration process is compared with this group, When the group classification results are different, the processing after the gravity center point-operation data distance evaluation unit 106 is repeatedly executed. If the group classification result is exactly the same as the previous one, it is determined that the center of gravity has converged to the optimum center of gravity, and the next area subdivision unit 110 is executed.

  The processing executed from the initial barycentric point creation unit 105 to the grouping result determination unit 109 is referred to as “data grouping area division” in the present invention. FIG. 4 schematically illustrates the processing performed in the “data grouping area division” using a two-dimensional operation factor space composed of two operation factors as an example. In this figure, the number of initial barycentric points is set to 2, and the initial barycentric coordinates are determined from real values generated by a random number generator. The distance from the center of gravity is evaluated for all operation data, and the data is classified as belonging to the nearest center of gravity. Next, the center of gravity is updated, and the distance evaluation with the operation data and the grouping are repeated until the data classification result does not change.

  An area subdivision unit 110 performs subdivision of the local area based on the operation data group created by the processing up to the grouping result determination unit 109. As a specific subdivision method, for example, a circumscribed hypercube surrounding each data group is created, a plane including the ridgeline is created, and an appropriate one is adopted as the boundary surface. It is done. In this case, it is assumed that the operation data is strictly separated at the boundary of each local region, and that the local quality model that expresses the quality characteristic also has different quality models on both sides of the boundary surface.

  However, in an actual manufacturing process, it is considered that a plurality of quality incompatibility factors dominate the overall quality characteristics while changing the degree of influence depending on the operation range. In order to appropriately model this phenomenon, operation data in the vicinity of the boundary belongs to each adjacent local region, and an expression that assumes that the quality characteristics are also affected by each local quality model is suitable.

  Therefore, as the present embodiment, here, a partitioning technique for modeling a state in which operation data belongs to a plurality of local regions is applied by applying the concept of the membership function proposed from the study of fuzzy theory. Such a partitioning method is sometimes referred to as soft partitioning as a concept of hard partitioning in which data is strictly partitioned at boundaries, and this name will be used hereinafter in the present invention.

  As a specific method of soft partitioning, a membership function is created using the operation data group and centroid point obtained in the above processing, and the operation factor space is divided into local regions using this membership function. There is.

  In explaining the detailed division procedure, first, the concept of region division by membership function will be described with reference to FIGS. FIG. 5 is an example in which a region is hard-divided so as to separate two operation data points P and Q existing on the one-dimensional operation factor space x. The point P is separated from the region A, and the point Q is separated from the region B by the dividing boundary S indicated by a one-dot chain line in the figure.

  On the other hand, in the soft division shown in FIG. 6, the membership function ΦA representing the ratio belonging to the region A and the membership function ΦB regarding the region B are determined for the data, and the point P is ΦA = 1 and ΦB = 0. The point Q is ΦA = 0.3 and ΦB = 0.7. Here, the membership function has a value in the range of 0 to 1, and Φi = 1 completely belongs to the region i, and Φi = 0 does not belong to the region i at all.

  In the present embodiment, when there are a plurality of membership functions, the sum of the values of the membership functions at an arbitrary point x in the space is always set to 1. Therefore, in the example of FIG. 6, all the points P belong to the region A, while the point Q indicates that the proportion belonging to the region A is 0.3 and the belonging proportion to the region B is 0.7.

  In this way, the data located in the vicinity of the boundary belongs to each of the local regions on both sides, and the attribution ratio is quantitatively expressed by the membership function is the basic concept of soft partitioning. . FIG. 7 shows, as a two-dimensional example, an example of a membership function that softly divides an operation factor space composed of u1 and u2 into three regions.

  Next, a specific procedure for obtaining the membership function Φ will be described. First, the membership function corresponding to the kth local region in the division of the operation factor space into M pieces must be a function that takes a range of 0 to 1 depending on the position u of the operation factor space. Therefore, in order to clarify that the membership function is a function of u, it is expressed as the following expression (11).

  Next, the membership function in the present embodiment requires a normal condition in which the sum of each function value is 1 at an arbitrary position in the operation factor space, and this is expressed as the following equation (12). .

  In general, any function that takes a range from 0 to 1 according to the position u_ of the operation factor space and satisfies Expression (12) can be adopted as the membership function. For example, a p-dimensional normal distribution function shown in the following equation (13) is used as a function that can directly reflect the barycentric point of the data group and smoothly connect the boundary between adjacent regions. There is a method of deriving the membership function 14).

Here, c ^k _j represents the center of gravity of the local region, and σ ^k _j represents the standard deviation of the normal distribution function. FIG. 8 shows an example in which a membership function is derived when a data group approximated by four normal distribution functions exists in a one-dimensional operation factor space. In this example, the membership function is calculated using equation (14) based on a normal distribution function having centroids at u of 0.1, 0.2, 0.4, and 0.8. The membership function thus obtained has a maximum value at the center of gravity, and shows a characteristic of overlapping with an adjacent function in the boundary region.

Therefore, if the normal distribution function μ defined by the equation (13) can be obtained, the membership function can be easily calculated by the equation (14). Here, for the barycentric point c ^k _j in the normal distribution function, the barycentric point reflecting the data distribution is calculated by the initial barycentric point creating unit 105 and the barycentric point updating unit 108. The area subdivision unit 110 needs to determine another parameter, the standard deviation σ ^k _j, from the data. As a specific method for determining the standard deviation, for example, there is an EM algorithm described in Chapter 4 of “Introduction to Cluster Analysis” written by Morimoto Publishing, 1999. The EM algorithm is a method proposed by the research of mathematical statistics, and is an algorithm for estimating the value of a parameter included in a function assuming given form of a certain probability distribution function from given data. In particular, in the case of a mixed density function in which a plurality of Gauss functions of Equation (13) exist, the parameter calculation procedure is known. According to the EM algorithm, the parameter σ of the Gaussian function is determined according to the degree of soot data concentration. FIG. 9 illustrates the concept of σ calculation by the EM algorithm, taking as an example the case where there are two data groups in a one-dimensional space. Of the two data groups, group B has data points concentrated near the center as compared to group A. According to the EM algorithm, group B has a small standard deviation reflecting this distribution. It is a normal distribution function.

  As described above, the region subdivision unit 110 calculates the normal distribution function based on the data grouping result obtained by the processing up to the grouping result determination unit 109 and the barycentric point, and derives the membership function based on the normal distribution function. Thus, it is possible to realize soft division that reflects the data distribution and in which the data belongs to the regions on both sides in the vicinity of the boundary of the local region.

Reference numeral 111 denotes a local quality model creation unit, which creates a local quality model that expresses the relationship between the operation factor and the quality using mathematical formulas for each local region obtained as a result of the processing up to the region subdivision unit 110. Here, as the local quality model, any modeling method capable of expressing the relationship between the quality index ^ y _i that is numerical data and the operation factor u _i can be adopted. For example, a local quality model based on a linear polynomial expressed by Expression (15) can be used as a technique in which the modeling result is easily read by humans and has sufficient accuracy.

  Next, a method for calculating the undetermined coefficient in Expression (15) when soft division is performed in the processing up to the area subdivision section 110 will be described. When the operation data is matrix data of p rows and N columns and the quality data is N-dimensional vector data, each local quality model is represented by a matrix expression of the following equation (16).

In order to obtain the undetermined coefficient w _ij in consideration of the membership function, the undetermined coefficient may be determined so that the weighted error evaluation function by the membership function expressed by the following equation (20) is minimized. This means that weighting is performed so that the error in the region where the value of the membership function is small is evaluated to be small.

  The undetermined coefficient that minimizes the expression (20) is equal to the coefficient satisfying the following expression (21), and can be calculated by the matrix calculation of the following expression (22).

  Reference numeral 112 denotes an overall quality model creation unit. Using the local quality model that uses the membership function created by the area subdivision unit 110 as a weight function, a linear combination formula of the following formula (24) is created to create a mathematical model that represents the quality characteristics of the entire operating range. .

The overall quality model obtained in this way has a configuration in which each local quality model is smoothly connected via a membership function. If you want to extract the governing factors that have the greatest impact on quality under a specific operating condition, evaluate the membership function value under that operating condition and determine the local quality model for the area that has the largest membership function value. Analyzing it, the operating factor with the largest undetermined coefficient can be considered as the controlling factor. FIG. 10 shows an example of the overall quality model when the two-dimensional operation factor space is softly divided into three regions. The operation factor space is expressed as a region 3-1 (0.5, 0.75), a region 3-2 (0.25, 0.25), and a region 3-3, where the center-of-gravity coordinates are expressed by (u1, u2). Software division is performed by a membership function based on a normal distribution function having a center of gravity at (0.75, 0.25), and a local quality model is expressed in the following line format in each region.
Region 3-1: y = 7.65-1.56u1-5.57u2
Region 3-2: y = 13.7-12.5u1-12.0u2
Region 3-3: y = 9.27-12.3u1-1.50u2

  The overall quality model is obtained by linearly combining the local quality models using the membership function as a weight function as shown in Equation (24), and modeling that shows smooth characteristics even in the boundary region from the graph of the figure. It has been realized.

  Reference numeral 113 denotes a minimum error model selection unit. When the operation factor space is divided by the region subdivision unit 110, if there are a plurality of division degrees of freedom, a plurality of division patterns are created, and a membership function and a local quality model are calculated for each, and then the overall quality is calculated. Configure the model. For each overall model, the model error is evaluated by the following equation (25), and the model with the smallest error is adopted.

  Reference numeral 114 denotes a convergence determination unit that compares the error of the minimum error model obtained by the minimum error model selection unit 113 with an evaluation reference value (error determination factor) set in advance and can explain the data with sufficient accuracy. Determine whether the mathematical model has been built. Examples of error determination methods include a method of comparing the absolute value of an error with an error determination factor, a method of comparing an error change amount with respect to a division increment with an error determination factor, and an evaluation function that takes into account the number of divisions and a model error. For example, a method of canceling the division when the evaluation function increases with respect to the increase of the division is used. In any method, when it is evaluated that the convergence is insufficient, the process after the division target area selecting unit 103 is repeatedly executed.

  Reference numeral 115 denotes an analysis result display unit, which displays the area division pattern of the finally obtained quality and operation formula model, the local quality model formula in each local area, and the membership function distribution according to the operation range. It is possible to present operational factors that have a high impact on different qualities and operational change ranges for improving quality.

  In the configuration of the analysis apparatus described above, the data distribution adaptive space division means is realized by the area subdivision section 110 from the division target area selection section 103, and a highly accurate analysis model is created with a small number of area divisions. It is possible.

  Next, it is explained that depending on the distribution state of the operation data, more appropriate space division can be performed by using the data distribution adaptive space dividing means as an embodiment to which the preprocessing shown in FIG. 12 is applied. To do.

  FIG. 13 shows, as an example of operation data related to the manufacture of steel sheets, data on the coiling temperature in the hot rolling process for a plurality of coils, and illustrates the frequency distribution of the coiling temperature average value of each coil as a histogram. It is. The coiling temperature is an important operating condition in order to obtain desired values for the material properties of thin sheet products such as tensile strength and elongation rate. Operations are often carried out. For this reason, there are many cases where the temperature measurement data including coils having different material characteristic values presents a multi-peak histogram having a plurality of peaks as shown in FIG. When such multi-peak histogram operation data is divided into regions, it is appropriate to subdivide into small regions corresponding to each peak. In this case, the grouping result from the initial barycentric point creation unit 105 in FIG. By performing data grouping area division up to the determination unit 109, proper division can be performed.

  On the other hand, the operation data includes many operation factors that exhibit a single peak histogram in which a single peak as shown in FIG. 14 exists. For example, the misalignment between the center position of the width direction of the plate and the center of the sheet-passing line during the rolling process or sheet conveyance, the so-called off-center amount, operates so that the steel plate is positioned at the line center regardless of the size and material of the steel plate. Therefore, even in a histogram of data including steel sheets of various material characteristic values and sizes, a single peak single peak histogram is obtained. In the case of such operation data, in the area division by the above-described data grouping, the division position is influenced by a slight data bias caused by non-essential factors such as data noise, and appropriate division cannot be obtained. There's a problem. Therefore, for such unimodal histogram operation data, appropriate data considering the data bias by dividing the number of data so that the number of data in the subdivision area after division is almost equal. Division can be performed.

  The equal data number division can be realized by the following procedure, for example. First, with respect to data selected by the local data selection unit 104, attention is paid to one operation factor, and sort processing is performed based on the magnitude of the value of the operation data. Next, after counting the number of selected data, find the integer closest to the value divided by the number of subdivisions of the area to be divided (2 if subdividing the area into two), and after subdivision The number of data per area is calculated. Next, the sorted operation data is regarded as an array, and array elements stored in array positions that are integer multiples of the number of data per subdivision area are extracted, and this value is used as the coordinates of the partition position. .

  In FIG. 12, reference numeral 117 denotes an equal data number division position calculation unit, which determines a division position in the division target area based on the above-described procedure.

  Reference numeral 118 denotes an equal data number division group creation unit. For each piece of data selected by the local data selection unit 104, it is determined from the coordinate value which of the subdivision regions divided by the division position determined by the equal data number division position calculation unit 117 belongs from the coordinate value. And data grouping.

  Reference numeral 119 denotes an equal data number division centroid calculation unit. Based on the data grouping result determined by the equal data number division group creation unit 118, the coordinates of the barycentric point of the operation data belonging to each subdivision area are calculated. As a specific method of calculating the center of gravity, for example, the average value of the operation data may be obtained using Expression (10). Furthermore, by passing the data grouping result obtained by the above processing and the centroid calculation result to the region subdivision unit 110, information necessary for performing the region soft division processing by the normal membership function is obtained. introduce.

  Reference numeral 116 denotes an appropriate division method determination unit. There are a plurality of operation data affecting the quality of the thin plate product, and these are approximately the multi-peak histogram distribution of FIG. 13 or the single-peak histogram distribution of FIG. In order to analyze the relationship between mixed operation data and quality, when subdividing an area, either one of data grouping area dividing means and equal data number dividing means is selected according to the histogram distribution of the operation data. It is necessary to select as an appropriate dividing means. The proper division method determination unit 116 projects the data in the division target region onto the axis of each operation to obtain a histogram, determines whether the histogram is unimodal or multimodal from the distribution form, and uses the operation data of the unimodal histogram. If there is an equal data number dividing means, if it is operation data of a multi-peak histogram, a data grouping area dividing means is selected.

  As specific means for determining whether the histogram is a single peak histogram or a multi-peak histogram, for example, there is a procedure described below. Focusing on one operating factor among the data selected by the local data selection unit 104, a histogram relating to the operating factor is created. At this time, as the number of sections of the histogram, for the purpose of determining the approximate shape of the histogram, it is not necessary to divide it more finely than necessary, and the number of sections may be about 10. Next, in the histogram sections, the section having the largest frequency and the section having the second largest frequency are extracted, and the median value of each section is calculated. The absolute value of the difference between this maximum frequency category median and the second highest frequency category median and the ratio of the total range of operation data are evaluated, and the threshold value specified by the analyst (for example, the threshold value 0 with the total operation range set to 1) .5) If the ratio is equal to or greater than the above, it is determined that the multi-peak histogram has two or more peaks and the subdivision means based on data grouping is appropriate. When the ratio is less than the threshold value, it is a unimodal histogram, and an equal data number dividing means is selected for this operation factor. The means for determining whether the histogram is a single peak or a multi-peak histogram is not limited to the above means, and embodiments in which the histogram is determined by other means are also included in the scope of the present invention.

  According to the operation and quality relation analysis apparatus according to the present embodiment described above, when the operation factor space is divided into local regions in analyzing the relationship between the plurality of operation factors and the quality, By automatically performing appropriate space division according to the distribution state of data such as the bias and sparseness of the operation data, it is possible to quickly build high-quality and operation-related models with a relatively small number of divisions. be able to. In addition, by creating a quality model for each divided local region and configuring a membership function that smoothly connects the boundaries of each local region, a process that has multiple causes of quality inconsistencies with different characteristics can be obtained. The obtained data can be appropriately analyzed in consideration of the influence of the superimposed region.

(Example)
In the following, quality data is an index obtained by normalizing the number of surface defects of a plated steel sheet for automobiles with the coil weight, using the four items of the sheet feed speed, load amount, plate temperature, and additive element component amount in the steel process as operating factors. The embodiment will be described.

  The analysis target was data for 420 coils collected via the process computer, and the operation data was obtained by averaging the time series data at the operation timing corresponding to each coil as a representative value. In the analysis, the operation results were normalized to a value of 0 to 1 in the existing data range for scaling.

FIG. 11 is a diagram showing the number of operation factor space divisions and model errors when the above data is analyzed by the operation and quality relation analysis apparatus of the present invention. The horizontal axis indicates the number of divisions, and the vertical axis indicates the error obtained by squaring the difference between the actual quality value and the model prediction value and normalizing the number of data points. In the figure, for comparison, an example in which the region with the largest error is simply divided into two equal parts without considering the data distribution when subdividing the region is also indicated by a broken line. In the case of analysis according to the present invention, even when the number of divisions was increased from 4 to 5, the amount of decrease in the error was slight, and it was considered that the convergence was achieved with the number of region divisions of 4. On the other hand, when the region is divided into two equal parts, it is necessary to divide into 15 regions before reaching the same convergence situation, and detailed analysis of the local quality model in each region is difficult. there were. Therefore, the area division pattern of the mathematical model shown in the analysis result display unit 115 and the local quality model in each local area were analyzed to analyze the cause of surface flaws. Specifically, the line format of the local quality model in each of the four local regions was as follows.
Local area 1 centroid: (u1, u2, u3) = (0.5, 0.12, 0.18, 0.5)
y = 13.7079 + 2.7834u1-1.0689u2 + 4.8713u3-0.2589u4
Local area 2 center of gravity: (u1, u2, u3) = (0.5, 0.12, 0.65, 0.5)
y = -0.1959 + 2.7234u1-0.2624u2 + 2.4480u3-0.2712u4
Local area 3 center of gravity: (u1, u2, u3) = (0.5, 0.61, 0.53, 0.5)
y = -1.4710 + 2.4671u1 + 6.5374u2-0.4656u3-0.1833u4
Local area 4 center of gravity: (u1, u2, u3) = (0.5, 0.61, 0.89, 0.5)
y = 5.5674 + 3.4088u1 + 7.9233u2 + 0.3592u3-0.2276u4

  As a result of analyzing the constant term of the quality model as a result of the above results, it was found that the occurrence of wrinkles was particularly large in the local regions 1 and 4. Further, as a result of analyzing the coefficients of the local quality model, in the local region 1, the influence of the operation factor u3 is the largest, and operating u3 on the low frequency side is the direction of reducing wrinkles, and for the local region 4, It was shown as an analysis result that it is effective to set the operation factor u2 having a high influence level to the low frequency side.

  Based on the above results, we changed the operation standard when producing plated steel sheets for automobiles, and changed the operating conditions. As a result, the occurrence rate of surface flaws decreased, yield improved, labor saving in product maintenance, and delay in delivery time Effects such as avoidance could be obtained.

  In the present embodiment, the related analysis device is realized as a program on a computer, but it may be configured by hardware combining an arithmetic device, a memory, and the like.

  Further, the operation / quality relation analysis apparatus of the present invention may be composed of a plurality of devices or a single device. Further, the above-described embodiment is configured by a CPU or MPU of a computer, a RAM, a ROM, etc., and is implemented by operating a program recorded in the RAM or ROM. Therefore, means for supplying the computer with program code of software for realizing the functions of the above-described embodiments, for example, a storage medium storing such program code is included in the scope of the present invention.

It is a figure which shows the structure of the relationship analysis apparatus of the operation and quality in the manufacturing process of this Embodiment. It is a figure explaining the case where it divides | segments with the line parallel to u2 axis | shaft taking the two-dimensional operation factor space as an example. It is a figure explaining the process of selecting a division | segmentation object area | region and subdividing an area | region. It is a figure explaining a "data grouping area division" process. It is a figure explaining the example which divided | segmented the area | region hard so that two data points which exist on a one-dimensional space might be isolate | separated. It is a figure explaining the concept of area division by a membership function taking two data points on a one-dimensional space as an example. It is a figure explaining the example of the membership function which carries out the soft division | segmentation of the two-dimensional operation factor space into three area | regions. It is a figure explaining the membership function derived | led-out based on four normal distribution functions on a one-dimensional space. It is a figure explaining calculation of parameter (sigma) of a normal distribution function by EM algorithm. It is a figure explaining the example of a whole quality model at the time of carrying out the soft division | segmentation of the two-dimensional operation factor space into 3 area | regions. It is a figure explaining the area division | segmentation number and model error of the example which analyzed the relationship between the manufacturing data of the manufacturing process of the plated steel plate for motor vehicles which is a steel product, and surface defect number data by this invention. It is a figure which shows the structure of the related analysis apparatus of the operation in a manufacturing process including the process which determines an appropriate division | segmentation means. It is a figure which shows the histogram of the operation data with the appropriate division | segmentation by data grouping. It is a figure which shows the histogram of the operation data in which equal data number division | segmentation is appropriate.

Explanation of symbols

DESCRIPTION OF SYMBOLS 101: Data input part 102: Initial division | segmentation preparation part 103: Division object area | region selection part 104: Local data selection part 105: Initial centroid point preparation part 106: Centroid point-operation data distance evaluation part 107: Operation data group preparation part 108 : Centroid update unit 109: grouping result determination unit 110: area subdivision unit 111: local quality model creation unit 112: overall quality model creation unit 113: minimum error model selection unit 114: convergence determination unit 115: analysis result display unit 116 : Proper division method determination unit 117: equal data number division position calculation unit 118: equal data number division group creation unit 119: equal data number division centroid calculation unit

Claims (10)

In analyzing the relationship between each operation factor and quality based on the quality data corresponding to the data ( hereinafter referred to as “ operation data ” ) of multiple operation items ( hereinafter referred to as “ operation factors ” ) in the manufacturing process,
A data input means for inputting quality data corresponding to operation data of the manufacturing process;
An operation space dividing means for dividing an operation factor space having an operation factor as a base vector based on a plurality of operation data of the manufacturing process input by the data input means into a plurality of local regions;
Determining a local quality model based on a linear polynomial representing a relation between an operation factor and quality based on a plurality of operation data and quality data in each local region, and determining an undetermined coefficient so that a prediction error due to the local quality model is minimized. and local quality model creation means be constructed by,
A global quality model creating means for creating a global quality model that represents the quality characteristics of the entire operating range by adding the local quality model of each local region multiplied by a weighting function for all local regions ,
When the overall quality model created by the overall quality model creating means satisfies a predetermined condition, an operation and quality related analysis device in an operation process presenting at least a local quality model for creating the overall quality model ,
The operating space dividing means is
A division target area selecting means for selecting a local area to be divided;
Local data selection means for selecting and extracting operation data distributed within the range of each local area selected by the division target area selection means;
Based on the distribution information obtained by projecting the operation data extracted by the local data selection unit onto the axis of each operation, an appropriate division that selects any one of the data grouping area division unit and the equal data number division group unit as the division unit Legal decision means;
Area subdivision means for performing subdivision of a local area based on information obtained by the data grouping area division means or the equal data number division group means,
The data grouping area dividing means includes
An initial barycentric point creating means for creating an initial barycentric point of operation data extracted by the local data selecting unit;
Center-of-gravity point-operation data distance evaluation means for calculating the distance between the operation data extracted by the local data selection means and the center of gravity point;
Based on the distance calculated by the center-of-gravity point-operation data distance evaluation means, operation data group creation means for grouping operation data that can be regarded as being close to each other;
For the group created by the operation data group creating means, the center-of-gravity point updating means for updating the center-of-gravity point using the operation data coordinates belonging to the group;
Based on the center of gravity point before and after the update and the information on the group creation result created by the operation data group creation means, it is determined whether it has converged to an appropriate grouping result, and if it has converged, the center of gravity point and the operation data group A grouping result determination unit that delivers information to the region subdivision unit;
The equal data number division group means includes:
An equal data number division position calculating means for calculating an equal data number division position for each operation axis in which the number of operation data extracted by the local data selection means is equal in each area after subdivision;
An equal data number division group creating means for calculating and grouping which region the operation data extracted by the local data selection means belongs to which region after the subdivision by the equal data number division position calculating means,
An equal data number division position obtained by the equal data number division position calculating means and the equal data number division group creating means by calculating a barycentric point of the area after subdivision by the equal data number division position calculating means, and an operation An apparatus for analyzing the relation between operation and quality in a manufacturing process , comprising: a data grouping result and an equal data number dividing barycentric point calculating means delivered to the area subdivision means . The region subdivision means comprises:
A normal distribution function that approximates the data distribution of each group with a normal distribution function centered on the barycentric point using the information of each group created by the data grouping area dividing unit or the equal data number dividing unit. has a distribution function number creating means,
A normal membership function is constructed by combining the normal distribution functions of each group created by the normal distribution function creating means, and the ratio of the operation data belonging to the divided region is determined based on the value of the normal membership function. it is, operations in the manufacturing process according to claim 1, characterized in that to perform region segmentation and quality-related analysis apparatus. The quality data is applied to a steel process, and the quality data is a shape index such as the number of product surface and internal defects, a steepness ratio of a steel plate, or a material index such as a tensile strength or elongation rate of a steel material. An operation and quality related analysis device in the manufacturing process according to 1 or 2 . The appropriate division method determining means selects the equal data number dividing means if the distribution information is operation data of a single peak histogram, and selects the data grouping area dividing means if operation data is a multimodal histogram. The operation and quality related analysis apparatus in the manufacturing process according to any one of claims 1 to 3. In analyzing the relationship between each operation factor and quality based on the quality data corresponding to the data ( hereinafter referred to as “ operation data ” ) of multiple operation items ( hereinafter referred to as “ operation factors ” ) in the manufacturing process,
A data input step in which the data input means inputs quality data corresponding to operation data of the manufacturing process;
An operation space dividing step of dividing the operation factor space into a plurality of local regions, the operation factor space having the operation factor as a basis vector based on the plurality of operation data of the manufacturing process input by the data input step ,
The local quality model creating means is adapted to minimize a prediction error caused by the local quality model by using a linear polynomial representing a relation between the operation factor and the quality based on the plurality of operation data and the quality data in each local region. A local quality model creation process constructed by determining undetermined coefficients in
The overall quality model creation means creates the overall quality model that represents the quality characteristics of the entire operating range by adding the local quality model of each local area multiplied by the weight function for all the local areas. A process,
When the overall quality model created by the overall quality model creating means satisfies a predetermined condition, an operation and quality related analysis method in an operation process presenting at least a local quality model for creating the overall quality model ,
The operation space dividing step is
A division target region selection step in which the division target region selection means selects a local region to be divided;
A local data selection step for selecting and extracting operation data distributed within the range of each local region selected by the division target region selection step; and
Based on the distribution information obtained by projecting the operation data extracted in the local data selection step onto the axis of each operation, the appropriate division method determination means performs either one of the data grouping region division step and the equal data number division group step. An appropriate division method determination step to be selected as a division step; and
An area subdivision means has an area subdivision process for performing subdivision of a local area based on information obtained by the data grouping area division process or the equal data number division group process,
The data grouping area dividing step includes:
An initial barycentric point creation means for creating an initial barycentric point of operation data extracted by the local data selection step,
Center-of-gravity point-operation data distance evaluation means calculates a distance between the operation data extracted by the local data selection step and the center-of-gravity point;
The operation data group creation means groups operation data that can be regarded as being close to each other based on the distance calculated by the center of gravity point-operation data distance evaluation step,
Center of gravity point update means, for the group created by the operation data group creation step, the center of gravity point update step of updating the center of gravity point using the operation data coordinates belonging to the group,
The grouping result determination means determines whether or not the grouping result has converged to an appropriate grouping result based on the center of gravity points before and after the update and the group creation result information created by the operation data group creation step. A grouping result determination step of transferring information on points and operation data groups to the region subdivision step,
The equal data number division group process includes:
Equal data number division position calculating means calculates the equal data number division position for each operation axis, where the number of operation data extracted by the local data selection step is equal in each area after subdivision A division position calculating step;
The equal data number division group creation means calculates and groups which operation data extracted by the local data selection step belongs to which region after subdivision by the equal data number division position calculation step belongs Split group creation process,
The equal data number division centroid calculation means calculates the centroid of the area after the subdivision by the equal data number division position calculation step, and is obtained by the equal data number division position calculation step and the equal data number division group creation step. A method for analyzing the relation between operation and quality in a manufacturing process , comprising: an equal data number division position, and a grouping result of operation data, and an equal data number division centroid calculation step delivered to the region subdivision step . The region subdivision step includes
The normal distribution function creating means approximates the data distribution of each group with a normal distribution function centered on the barycentric point using the information of each group created in the data grouping region dividing step or the equal data number dividing step . has a normal distribution function number generation step of generating a normal distribution function,
A normal membership function is configured by combining the normal distribution functions of each group created in the normal distribution function creating step, and the ratio of the operation data belonging to the divided region is determined based on the value of the normal membership function. 6. The method for analyzing the relation between operation and quality in the manufacturing process according to claim 5 , wherein the region is divided. The quality data is applied to a steel process, and the quality data is a shape index such as the number of product surface and internal defects, a steepness ratio of a steel plate, or a material index such as a tensile strength or elongation rate of a steel material. A method for analyzing the relation between operation and quality in the manufacturing process according to 5 or 6. In the appropriate division method determining step, if the distribution information is operation data of a single peak histogram, the equal data number division step is selected, and if it is operation data of a multi-peak histogram, the data grouping region division step is selected. A method for analyzing the relation between operation and quality in the manufacturing process according to any one of claims 5 to 7. In analyzing the relationship between each operation factor and quality based on the quality data corresponding to the data ( hereinafter referred to as “ operation data ” ) of multiple operation items ( hereinafter referred to as “ operation factors ” ) in the manufacturing process,
A data input process for entering manufacturing process operation data and corresponding quality data;
An operation space dividing process for dividing an operation factor space having an operation factor as a base vector based on a plurality of operation data input by the data input process into a plurality of local regions;
Determining a local quality model based on a linear polynomial representing a relation between an operation factor and quality based on a plurality of operation data and quality data in each local region, and determining an undetermined coefficient so that a prediction error due to the local quality model is minimized. and local quality model creation process be constructed by,
The computer executes the overall quality model creation process for creating the overall quality model representing the quality characteristics of the entire operating range by adding the local quality model of each local area multiplied by the weight function for all the local areas. ,
When the overall quality model created by the overall quality model creation process satisfies a predetermined condition, a computer program that presents at least a local quality model for creating the overall quality model ,
The operation space dividing process is
A division target area selection process for selecting a local area to be divided;
Local data selection processing for selecting and extracting operation data distributed within the range of each local region selected by the division target region selection processing;
Proper division based on distribution information obtained by projecting the operation data extracted by the local data selection process onto the axis of each operation, and selecting either one of the data grouping area division process and the equal data number division group process as the division process Legal decision processing;
Causing the computer to execute an area subdivision process for performing subdivision of a local area based on information obtained by the data grouping area division process or the equal data number division group process,
The data grouping area dividing process includes:
An initial barycentric point creation process for creating an initial barycentric point of operation data extracted by the local data selection process;
Center-of-gravity point-operation data distance evaluation processing for calculating the distance between the operation data extracted by the local data selection processing and the center of gravity point;
Based on the distance calculated by the center-of-gravity point-operation data distance evaluation processing, operation data group creation processing for grouping operation data that can be regarded as close to each other,
For the group created by the operation data group creation process, the center of gravity point update process for updating the center of gravity point using the operation data coordinates belonging to the group, and
Based on the center of gravity point before and after the update and the information of the group creation result created by the operation data group creation process, it is determined whether or not it has converged to an appropriate grouping result. Causing the computer to execute a grouping result determination process for transferring information to the area subdivision process,
The equal data number division group processing is:
An equal data number division position calculation process for calculating an equal data number division position for each operation axis, in which the number of operation data extracted by the local data selection process is equal in each region after subdivision,
An equal data number division group creation process for calculating and grouping which region the operation data extracted by the local data selection process belongs to after subdivision by the equal data number division position calculation process;
Calculate the barycentric point of the area after the subdivision by the equal data number division position calculation process, the equal data number division position obtained by the equal data number division position calculation process and the equal data number division group creation process, and the operation A computer program for causing a computer to execute an equal data number division centroid calculation process handed over to the area subdivision process together with a data grouping result . A computer-readable recording medium having recorded thereon the computer program according to claim 9 .

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