JP2009282740A - Product quality prediction and control method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a control product quality method for controlling the quality of a product on the basis of a highly precise prediction result, and to provide a product quality control device for implementing the control method. <P>SOLUTION: This method for controlling the quality of a product includes: a first step for defining the quality of a product corresponding to manufacturing conditions by a linear regression formula; a second step for digitizing the quality of a product to be controlled by using a probability model based on discrete probability distribution; a third step for digitizing the actual variation of manufacturing conditions in the product manufacturing step by using an arbitrary probability model; and a fourth step for predicting the quality of the product at an arbitrary point of time during the product manufacturing step by using the linear regression formula defined by the first step, a formula specified by the second step and the probability model formula of the variation of the manufacturing conditions specified by the third step. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a method for controlling the quality of products represented by steel products and the like, and a product quality control device used for controlling the product quality.

  The number of defects on the surface defects and internal defects of the product, and the number of defective products are count values represented by discrete random variables. The number of defects can be modeled as following a Poisson distribution and the number of defective products according to a binomial distribution. Conventionally, the c control chart and u control chart are used to manage the number of defects according to the Poisson distribution, and the np control chart and p control chart are used to manage the number of defective products according to the binomial distribution. When the line is exceeded, or when the control limit line is likely to be exceeded due to the temporal trend of the graph, a method of investigating abnormal manufacturing conditions has been taken (JIS Z 9020: 1999).

  According to the product quality control based on these control charts, it can be detected that the quality tends to be deteriorated, but it is unclear which manufacturing condition is bad and in which direction the improvement is made. For this reason, methods for predicting product quality indicators from manufacturing condition data and methods for controlling manufacturing conditions based on the prediction results have been proposed so far in order to identify manufacturing conditions that cause quality deterioration and improve quality. ing.

For example, Patent Document 1 discloses a product quality control device that outputs a lower process operation condition instruction value capable of manufacturing a product that satisfies a required specification from an upper process manufacturing result, a material estimated value, and an estimated error thereof. Has been. Further, Non-Patent Document 1 discloses a method called a generalized linear model that can be applied to quality prediction.
JP 2003-268428 A P.McCullagh, by JANelder, “Generalized Linear Models”, 2nd edition, Chapman & Hall, August 1, 1989

  In the technique disclosed in Patent Document 1, it is assumed that the product material to be controlled is a physical continuous value such as a mechanical test characteristic value. Therefore, the material under the operation condition of the estimation target can be estimated by using the average of the material actual value corresponding to the past operation condition actual value similar to the operation condition of the estimation target. However, quality indicators such as the number of product defects and the defective product rate are based on discretely distributed counts, and the probability distribution is approximated by discrete probability distributions typified by Poisson distribution and binomial distribution. It is different from normal distribution which is probability distribution. That is, as in the technique disclosed in Patent Document 1, even if the standard deviation of the actual value is calculated for calculating the estimated variation, the variation under the estimation target operation condition cannot be estimated correctly. For this reason, when product quality is controlled using the technique disclosed in Patent Document 1, there is a problem that the quality estimation accuracy is low, and there is a risk of deviating from the quality range required particularly in the downstream process.

  Further, in the technique disclosed in Patent Document 1, it is necessary to accumulate past operation conditions and material performance values and search for operation conditions similar to the prediction target operation conditions. Therefore, in order to realize the technique disclosed in Patent Document 1, not only a computer device but also a large-scale and high-performance online database search system is required, and there is a problem that enormous costs are required. .

  Non-Patent Document 1 does not disclose a method applied to product quality control. In order to apply the method disclosed in Non-Patent Document 1 to control of product quality, the explanatory variable for one item of product quality of the objective variable usually has several times to several tens of times the number of items. Because of this, there was a technical impediment that it was difficult to determine the optimal value of the explanatory variables.

  Therefore, the present invention provides a product quality control method capable of controlling product quality based on a highly accurate prediction result, and a product quality control apparatus capable of executing the control method. This is the issue.

  The present invention will be described below. In order to facilitate understanding of the present invention, reference numerals in the accompanying drawings may be added in parentheses, but the present invention is not limited to the illustrated form.

  A first aspect of the present invention is a method for controlling the quality of a product, wherein the quality of the product according to manufacturing conditions is defined by a linear regression equation, and the quality of the controlled product is determined by a discrete probability. Defined using a probability model based on the distribution, defined in the second step, the third step, and the first step, formulating the actual manufacturing condition variation in the product manufacturing process using an arbitrary probability model The product quality is predicted at an arbitrary point in the product manufacturing process using the linear regression formula, the formula specified in the second process, and the probability model formula of the variation in manufacturing conditions specified in the third process. The above-mentioned problem is solved by a product quality control method comprising: a fourth step.

  In the first invention and the invention shown below (hereinafter simply referred to as “the present invention”), “product quality” is not particularly limited as long as the probability of occurrence of quality defects is small. Specific examples thereof include the number of defects represented by surface flaws and internal defects of steel materials, the number of defective products, and the like. Specific examples of “manufacturing conditions” include the set values of the manufacturing equipment, the physical quantities (temperature, shape, composition, etc.) of products or intermediate products represented by steel materials, and the time of each process for manufacturing the products. Can be mentioned. Furthermore, “formation of actual manufacturing condition variations in the product manufacturing process with an arbitrary probability model” means that manufacturing condition variations that do not necessarily become target values (set values) during product manufacturing By formulating with a probability model, this means specifying a probability model formula for variations in manufacturing conditions.

  In the first aspect of the present invention, the quality is predicted by the fourth step before the production of all the products is completed, and when the quality predicted in the fourth step does not belong to the predetermined target range, It is preferable that a fifth process for changing the manufacturing conditions of the subsequent manufacturing process is provided so that the quality belongs to the target range.

  In the first aspect of the present invention provided with the fifth step, the manufacturing condition changed in the fifth step is a linear expression using a coefficient for the manufacturing condition in the linear regression equation defined in the first step. It is preferable that the objective function is specified by solving an optimization problem using a mathematical expression relating to the manufacturing condition changed in the fifth step as a constraint.

  In the present invention, the method used when solving the optimization problem is not particularly limited. Specific examples of the method include linear programming.

  In the first aspect of the present invention (including modifications, the same shall apply hereinafter), the coefficient of the linear regression equation defined in the first step is based on the quality measurement result and / or the production condition actual data. It is preferable that the calculation process calculated in this step is provided as a previous process of the first process.

  In the first aspect of the present invention, when the quality of the controlled product is the number of defects, the Poisson distribution is preferably used as the probability model used in the second step.

  In the first aspect of the present invention, when the quality of the controlled product is the number of defective products or the defective product rate, it is preferable to use a binomial distribution as a probability model used in the second step.

  In the first aspect of the present invention, the product is preferably a steel material.

  In the present invention, specific examples of steel products include steel products.

  The second aspect of the present invention is a control device used for controlling the quality of a product, and is controlled by a regression equation defining unit (1) that defines the quality of a product according to manufacturing conditions by a linear regression equation. Formulating the quality of the product using a probability model based on a discrete probability distribution, and formulating a variation in actual manufacturing conditions during the product manufacturing process using an arbitrary probability model, The variation formulation unit (3), the linear regression formula defined by the regression formula definition unit, the formula specified by the formula formulation unit, and the probability model formula of the variation of the manufacturing conditions specified by the variation formulation unit And a quality prediction unit (4) for predicting the quality of the product at an arbitrary point in time during the product manufacturing process.

  In the second aspect of the present invention, the quality is predicted by the quality prediction unit (4) before the production of all the products is finished, and the quality predicted by the quality prediction unit does not belong to a predetermined target range. Is preferably further provided with a manufacturing condition changing unit (7) for changing the manufacturing conditions of the subsequent manufacturing process so that the quality belongs to the target range.

  Here, the “subsequent manufacturing process” refers to a manufacturing condition of the second manufacturing process based on a result predicted after the first manufacturing process when the product manufacturing line includes the first manufacturing process and the second manufacturing process. When is changed, it means the second manufacturing process.

  In the second aspect of the present invention provided with the manufacturing condition changing unit, the manufacturing condition specified by the manufacturing condition changing unit is 1 using a coefficient for the manufacturing condition in the linear regression equation defined by the regression equation defining unit. It is preferable that the following equation is used as an objective function, and is specified by solving an optimization problem using a mathematical expression relating to the manufacturing condition changed by the manufacturing condition changing unit as a constraint.

  In the second aspect of the present invention (including modifications, the same shall apply hereinafter), the coefficient of the linear regression equation defined by the regression equation definition unit (1) is further used as the quality measurement result and / or manufacturing. It is preferable that a calculation unit (5) for calculating based on the condition result data is provided.

  In the second aspect of the present invention, when the quality of the controlled product is the number of defects, the Poisson distribution is preferably used as the probability model used in the formulating unit.

  In the second aspect of the present invention, when the quality of the controlled product is the number of defective products or the defective product rate, a binomial distribution is preferably used as a probability model used in the formulating unit.

  In the second aspect of the present invention, the product is preferably a steel material.

  According to the first aspect of the present invention, the quality of a product is predicted using a mathematical expression specified by a probability model based on a discrete probability distribution and a probability model expression of variation in actual manufacturing conditions in a subsequent manufacturing process. Therefore, the product quality represented by the number of defects of the product, the number of defective products, etc. can be predicted with high accuracy in consideration of the manufacturing condition control accuracy in the subsequent manufacturing process. Therefore, according to the first aspect of the present invention, it is possible to provide a product quality control method capable of controlling the quality of a product based on a highly accurate prediction result. Furthermore, in the first aspect of the present invention, since the fifth process for changing the manufacturing conditions of the subsequent manufacturing process based on the predicted product quality is provided, there is a problem that the quality of the product deteriorates in the upstream process. In addition, it is possible to provide a product quality control method capable of preventing the deterioration of the final product quality by changing the manufacturing conditions in the subsequent manufacturing process.

  According to the second aspect of the present invention, a formulating unit that formulates product quality using a probability model based on a discrete probability distribution, and a variation in actual manufacturing conditions in a subsequent manufacturing process is expressed by an arbitrary probability model. Because it is equipped with a variation formulation unit, it is possible to predict the product quality represented by the number of product defects and the number of defective products with high accuracy in consideration of the manufacturing condition control accuracy in the subsequent manufacturing process. . Therefore, according to the second aspect of the present invention, a product quality control device capable of controlling the quality of a product based on a highly accurate prediction result can be provided. Further, in the second aspect of the present invention, a manufacturing condition changing unit that changes the manufacturing conditions of the subsequent manufacturing process based on the predicted product quality is provided, thereby causing a problem that the quality of the product deteriorates in the upstream process. However, it is possible to provide a product quality control device capable of preventing the deterioration of the final product quality by changing the manufacturing conditions of the subsequent manufacturing process.

  Hereinafter, embodiments of the present invention will be described.

1. Product Quality Control Method Product manufacturing conditions in the manufacturing process of industrial products are measured results of physical quantities (temperature, shape, composition, etc.) related to products or intermediate products in the manufacturing process, measured results of physical quantities (temperature, pressure, etc.) related to manufacturing equipment, These physical quantities are configured by one or a plurality of manufacturing conditions selected from a group consisting of control target values, operating condition setting values, values measured and set between manufacturing apparatuses, and the like. In the following description of the present invention, the production condition is represented by x, and x _n (where n is an integer of 1 or more) is used to indicate the production condition for a certain product n. Further, in case of manufacturing conditions x _n to the product n is more, if it is necessary to distinguish them, one of the production conditions x _{nk (Here,} k is an integer of 1 or more.) Represented by. Furthermore, when there are K manufacturing conditions x _n, a vector obtained by combining all of them is set to x _nv = [x _n1 x _n2 ... X _nK ] ^T.

  Moreover, the measurement data regarding quality represented by the number of defects, the number of defective products, etc. is represented by y. In the present invention, the quality model is constituted by a regression model having the measurement data y related to quality as an objective variable and the manufacturing condition x as an explanatory variable. In the present invention, in constructing the quality model, a discrete probability distribution such as a binomial distribution or a Poisson distribution is assumed as a probability model of the objective variable, the expected quality value for the manufacturing conditions is converted by a monotonically increasing function, and a linear regression equation A method called a generalized linear model is used. In the configuration of the quality model in the present invention, the coefficient of the linear regression equation is estimated by the maximum likelihood method.

1.1. First Embodiment FIG. 1 is a flowchart showing steps provided in a product quality control method of the present invention according to a first embodiment (hereinafter referred to as “control method according to the first embodiment”). As shown in FIG. 1, the control method according to the first embodiment includes a data aggregation step (step S11), a first step (step S12), a second step (step S13), and a third step (step S14). ) And a fourth step (step S15).

<Step S11>
In step S11, manufacturing condition data or quality data in which individual products are associated with manufacturing conditions and quality realization values are created, and a set of manufacturing condition data or quality data is created. The product condition data is represented as a vector x _nv where n = 1, 2,... The set of manufacturing condition data is a set having one or a plurality of manufacturing condition data x _nv as elements, and is a matrix X = [x _1v x _2v ... _{N N} ] ^T in which the vector x _nv is transposed and arranged in the row direction. To express. Furthermore, product quality is represented by the count value of interest is the y, represents the product quality data and y _n. The set of product quality data is a set having one or a plurality of product quality data y _n as elements, and is represented by a vector Y = [y ₁ y ₂ ... Y _N ] ^T obtained by transposing y _n and arranging them in the row direction. .

<Step S12>
Step S12 is a step of defining the quality of the product according to the manufacturing conditions by a linear regression equation. When a regression coefficient vector (hereinafter also referred to as “regression parameter”) is c = [c ₀ c ₁ ... C _K ] ^T , the linear regression equation can be expressed by the following equation 1.

<Step S13>
Step S13 is a step of formulating the quality of the controlled product using a probability model based on a discrete probability distribution. If the quality of the controlled product is a discrete value of zero or more and the upper limit is unknown, such as the number of surface defects and the number of internal defects per steel product, If the average of the number of defects is λ, the number of defects y in the target amount W (one lot consisting of W products) is a random variable according to the Poisson distribution of the average λW, and the probability can be expressed by the following equation 2. it can.

However, since the number of defects is compared by the number per product, the average λ of the number of defects per product is defined as in the following equation 3.
λ (x, c) = expS (x, c) (Formula 3)

  When the above formulas 2 and 3 are used, the probability distribution of the number of defects y in the target amount W with respect to the manufacturing condition x can be expressed by the following formula 4. Here, since the variable x (manufacturing condition) is a random variable that varies during the product manufacturing process, the probability distribution of the number of defects y is expressed as a conditional probability with x as a condition.

  Next, the regression parameter c is estimated. The estimation of the regression parameter c can be performed by the maximum likelihood method. Specifically, the log likelihood L is defined by the following equation 5 using the product quality data set Y and the manufacturing condition data set X, and a regression parameter c that maximizes this is obtained.

In the above formula 5, W _n = [W ₁ W ₂ ... W _N ] ^T.

  From Equation 3 to Equation 5, the log likelihood L can be expressed by Equation 6 below.

  The regression parameter c for maximizing the log likelihood L expressed by Equation 6 is obtained by finding a solution satisfying the requirements expressed by the following Equation 7 by the Newton method or the like, and the log likelihood L is maximized from the solution. This can be obtained by a method of selecting a target to be selected or by a nonlinear optimization method such as successive quadratic programming.

  On the other hand, if the quality of the controlled product is a discrete value of zero or more, such as the number of defective products in one lot, and the upper limit is finite, the number of defective products with respect to the target product number M y (in this case, 0 ≦ y ≦ M) is a random variable that follows a binomial distribution with respect to the number of occurrences when an event with a probability of ρ occurring once is tried M times, and the probability distribution is The probability that one product will be defective can be expressed by the following equation (8).

上記式８において、

In Equation 8 above,

は、相異なるＭ個の中からｙ個を抽出する組合せの数である。

Is the number of combinations that extract y out of the different M.

  Here, the occurrence probability ρ of a defective product can be expressed by the following formula 9.

  Further, the probability distribution of the number of defective products y in the target number M with respect to the manufacturing condition x can be expressed by the following formula 10 using the above formula 8 and formula 9.

  When the quality of the controlled product is the number of defective products, the regression parameter c is estimated by the maximum likelihood method. The log likelihood L is defined by the following equation 11 using the product quality data set and the manufacturing condition data set, This is done by determining the regression parameter c to be maximized.

上記式１１において、Ｍ＝[Ｍ_１ Ｍ_２ … Ｍ_Ｎ]^Ｔである。

In the above formula 11, M = [M ₁ M ₂ ... M _N ] ^T.

  From the above formulas 9 to 11, the log likelihood L can be expressed by the following formula 12.

  The regression parameter c that maximizes the log likelihood L expressed by the above equation 12 can be obtained by the same method as in the case where the quality of the controlled product is the number of defects.

<Step S14>
Step S14 is a step of specifying the probability density distribution of actual values during the product manufacturing process of the manufacturing conditions represented by the variable x in the linear regression equation defined in step S12. If there manufacturing conditions x _c is controlled to match the target value t _c, x _c is not necessarily coincident with t _c, variations occur depending on the situation of the unknown disturbance or control device. In this case, the probability distribution of the variation is represented by p (x _c , t _c ). This probability distribution can be approximated by a probability density function such as a normal distribution from, for example, a histogram of actual control deviation values.

<Step S15>
Step S15 is a step of predicting product quality using the linear regression equation defined in step S12, the equation specified in step S13, and the probability model equation specified in step S14. When predicting the quality of a product at a specific time determined in the middle of a manufacturing process, a vector in which planned values in a prediction stage of a changeable manufacturing condition in a subsequent manufacturing process (downstream process) are arranged is set to x _e. In addition, let x _p be a vector in which scheduled production values that cannot be changed out of the actual manufacturing condition values in the upstream process or the manufacturing conditions in the downstream process are arranged. In particular, the linear regression equation expresses x _p and x _e as S (x _p , x _e , c).

In the course of manufacturing process, the probability distribution of the product number of defects or defectives is, (y, x _c), the peripheral distribution about x _c of the joint probability distribution of using the probability distribution of the values and x _c of x _p,

と表される。さらに、条件付確率の公式から確率分布ｐ（ｘ_ｃ）を用いて、

It is expressed. Furthermore, using the probability distribution p (x _c ) from the conditional probability formula,

に基づき、製造工程上の品質予測時点における製品品質を予測することができる。ただし、式４および式１０に共通に現れる変数ｘに関係するｘ_ｐ、ｘ_ｃおよび定数ベクトルｃだけを用いて表現している。

Based on the above, the product quality at the time of quality prediction in the manufacturing process can be predicted. However, it is expressed using only x _p , x _c and a constant vector c related to the variable x appearing in common in Expression 4 and Expression 10.

For integration of the equation 14 x _c is to be multi-dimensional in the case of vector, it is difficult to determine analytically. In such a case, by the Monte Carlo method using a sufficiently large number of N samples x _c1 ,..., X _cN generated from the probability distribution p (x _c , t _c ),

として近似する。

Approximate as

  As described above, in the control method according to the first embodiment, the number of defects and defects are determined by using the mathematical expression specified by the probability model based on the discrete probability distribution and the probability model expression of the variation in the manufacturing condition in the subsequent manufacturing process. Product quality such as the number of products is predicted in consideration of manufacturing condition control accuracy in the subsequent manufacturing process. The probability distribution of objects with low probability of occurrence, represented by the number of defects and the number of defective products, is significantly different from the normal distribution and can be approximated with high accuracy by discrete probability distributions such as Poisson distribution and binomial distribution. According to the control method according to the embodiment, the quality of the product can be predicted with high accuracy, and the quality of the product can be controlled based on the prediction result.

1.2. Second Embodiment FIG. 2 is a flowchart showing steps provided in a product quality control method of the present invention according to a second embodiment (hereinafter referred to as “control method according to the second embodiment”). As shown in FIG. 2, the control method according to the second embodiment includes a data aggregation step (step S21), a first step (step S22), a second step (step S23), and a third step (step S24). ) And a fourth step (step S25), and further includes a fifth step (step S26).

<Step S21>
In step S21, manufacturing condition data or quality data in which individual products are associated with manufacturing conditions and quality realization values are created, and a set of manufacturing condition data or quality data is created. Since step S21 is the same as step S11, description thereof is omitted.

<Step S22>
Step S22 is a step of defining the quality of the product according to the manufacturing conditions by a linear regression equation. Since step S22 is the same as step S12, description thereof is omitted.

<Step S23>
Step S23 is a step of formulating the quality of the controlled product using a probability model based on a discrete probability distribution. Since step S23 is the same as step S13, description thereof is omitted.

<Step S24>
Step S24 is a step of specifying the probability density distribution of actual values during the product manufacturing process of the manufacturing conditions represented by the variables in the linear regression equation defined in step S22. Since step S24 is the same as step S14, description thereof is omitted.

<Step S25>
Step S25 is a step of predicting product quality using the linear regression equation defined in step S22, the equation specified in step S23, and the probability model equation specified in step S24. Since step S25 is the same as step S15, description thereof is omitted.

<Step S26>
Step S26 is a step of calculating a probability that the quality predicted in step S25 belongs to a predetermined range. The probability that the product quality exceeds the predetermined upper limit value can be calculated from the probability distribution regarding the number of defects and the number of defective products. For example, if the quality is controlled is the number of drawbacks, probability estimate _{y e} number shortcomings in the target amount W exceeds the upper limit value ^{_{y * p (y e> y}} *) of the formula 3, formula 4, formula 14 And can be represented by Equation 16 below.

ただし、

However,

Also, if the quality is controlled is defectives, probability estimate y _e of defectives in a subject production number M exceeds the defectives upper limit _{^{y * p (y e> y}} *) of the formula 8, formula 9 and Equation 14 and Equation 17 below.

ただし、

However,

Further, determine the distribution of p ^(y> y ^*) with respect to the target value _{t c} of _{x c} at step S26, the probability p ^(y> y ^*) is a target value _{t c} quality control standards ^{p *} from the small _{x c} An inequality 18 using the regression parameter c that represents the range is obtained.

F (t _c ) = f ₀ + c _c ^T · t _c > 0 (Equation 18)
Here, f ₀ is an intercept, and vector c _c is a regression parameter c for subsequent manufacturing conditions.

Calculated in step S25, the probability p ^(y> y ^*), if you are determined numerically by the Monte Carlo method using Equation 15, while changing repeatedly the target value _{t c} p a ^(y> y ^*) Then, Equation 18 is obtained as an inequality that satisfies the target value t _c when the probability p (y> y ^* ) <p ^* . At this time, f ₀ is obtained as a numerical solution of the simultaneous equations of the following equations 19 and 20.

F (t _c ) = f ₀ + c _c ^T · t _c = 0 (Equation 19)
p (y> y ^* ) = p ^* (Formula 20)

The manufacturing conditions of the subsequent manufacturing process (downstream process) are such that the probability that the number of defects and the number of defective products are larger than the standard is smaller than the standard probability, and operational constraints (temperature upper and lower limits, physical upper and lower limits of transport time), etc. Choose from those that meet When the operational constraints in the subsequent manufacturing process are expressed by a linear expression or a linear inequality regarding t _c , one of the feasible solutions of the following linear programming problem, t _c = t _ca is obtained. I can return.

`` Problems for determining manufacturing conditions for subsequent manufacturing processes ''
・ Variable: t _c
Objective function: F (t _c ) → maximization −F (t _c ) → minimization / constraint condition t _c ≦ x _{c, max} (Equation 21)
x _{c, min} ≦ t _c (Formula 22)
dt _c ^T + d ₀ ≧ 0 (Equation 23)
F (t _c ) = f ₀ + c _c ^T · t _c > 0 (Equation 24)

However, x _{c, max} in the above formula 21 is a vector in which the upper limit values of the manufacturing conditions in the subsequent manufacturing process are arranged, and x _{c, min} in the above formula 22 shows the lower limit values of the manufacturing conditions in the subsequent manufacturing process. Is a vector. Moreover, the said Formula 23 is a type | formula showing the relationship between a manufacturing schedule and manufacturing conditions. Further, the above equation 24 is an equation representing a condition in which the probability that the number of defects or the number of defective products exceeds a predetermined number is below a predetermined quality standard.

If there is no feasible solution in this linear programming problem, there is no manufacturing condition for the subsequent manufacturing process with probability p (y _e > y ^* ) <p ^* . In this case, the subsequent manufacturing process On the other hand, it is possible to attach attribute information or the like to call attention to the possibility that the quality is likely to deteriorate (attach a caution code or the like to the product quality).

2. Product quality control device 2.1. First Embodiment FIG. 3 is a conceptual diagram showing a configuration example of a product quality control apparatus (hereinafter referred to as “control apparatus according to a first embodiment”) according to the first embodiment of the present invention. As shown in FIG. 3, the control device 10 according to the first embodiment includes a regression equation defining unit 1, a formulating unit 2, a variation formulating unit 3, a quality predicting unit 4, a calculating unit 5, and a result. And a display unit 6.

  Information relating to the manufacturing condition data and quality data input by the operator is sent to the calculation unit 5, and the operations of the above-described steps S11 and S21 are performed based on the information. Further, the calculation unit 5 calculates a coefficient of a linear regression equation. Information relating to the numerical values calculated by the calculation unit 5 is sent to the regression equation definition unit 1, and the regression equation definition unit 1 defines the operations of the above-described steps S 12 and S 22, that is, a linear regression equation.

  On the other hand, the variation formulation unit 3 formulates a probability model of the variation based on the data related to the manufacturing conditions of the subsequent manufacturing process calculated by the calculation unit 5. That is, in the variation formulation unit 3, the operations of the above-described step S14 and step S24 are performed.

  The formulating unit 2 includes a quality model calculated by the calculation unit 5, a probability model regarding realization variation of subsequent manufacturing conditions calculated by the variation formulating unit 3, and a probability model based on a discrete probability distribution. Use to formulate the controlled product quality. That is, in the formulating unit 2, the operations of the above step S13 and step S23 are performed.

  In this way, when the linear regression equation is defined by the regression equation defining unit 1, the mathematical formula is specified by the formulating unit 2, and the probability distribution representing the variation of the manufacturing conditions is further specified by the variation formulating unit 3, Information is sent to the quality prediction unit 4, and the quality prediction unit 4 predicts the quality of the product. That is, in the quality prediction unit 4, the operations of the above step S15 and the above step S25 are performed.

  The result display unit 6 is a part that displays the quality prediction value calculated by the quality prediction unit 4.

  Thus, according to the control apparatus 10, since the control method concerning the said 1st Embodiment can be implemented, according to this invention, quality of a product can be controlled based on a highly accurate prediction result. A possible product quality control device 10 can be provided. Note that the regression equation defining unit 1, the formulating unit 2, the variation formulating unit 3, the quality predicting unit 4, and the calculating unit 6 in the control device 10 are actually a central processing unit (CPU) of a personal computer or a process computer. ) Etc. can be assigned the function.

2.2. Second Embodiment FIG. 4 is a conceptual diagram showing an example of a product quality control apparatus (hereinafter referred to as “control apparatus according to a second embodiment”) of the present invention according to a second embodiment. 4, components having the same configuration as in FIG. 3 are denoted by the same reference numerals as those used in FIG. 3, and description thereof is omitted as appropriate. Hereinafter, the control apparatus according to the second embodiment will be described with reference to FIGS. 3 and 4.

  As shown in FIG. 4, the control device 20 according to the second embodiment includes a regression equation defining unit 1, a formulating unit 2, a variation formulating unit 3, a quality predicting unit 4, and a manufacturing condition changing unit 7. , A calculation unit 5 and a result display unit 6.

  The manufacturing condition changing unit 7 is a part that performs the operation of the above-described step S26, and should change the manufacturing conditions of the subsequent manufacturing process so that the quality predicted by the quality prediction unit 4 falls within a predetermined target range. For example, the changed manufacturing conditions are specified by solving the linear programming problem. In addition, the result display unit 6 in the control device 20 indicates the result regarding the predicted quality, the probability that the number of defects and the number of defective products exceed the standard, and the instruction value regarding the manufacturing conditions of the subsequent manufacturing process obtained by the linear programming problem. In addition, information on the need for attention code assignment when there is no executable solution is displayed.

  Thus, according to the control apparatus 20, since the control method concerning the said 2nd Embodiment can be implemented, even if the malfunction which the quality of a product deteriorates in an upstream process arises according to this invention. By changing the manufacturing conditions of the subsequent manufacturing process, it is possible to provide the product quality control device 20 that can prevent the deterioration of the final product quality. Note that the regression equation defining unit 1, the formulating unit 2, the variation formulating unit 3, the quality predicting unit 4, the manufacturing condition changing unit 7, and the calculating unit 5 in the control device 20 are actually a personal computer or a process computer. The central processing unit (CPU) or the like can be assigned the function.

  The present invention will be further described with reference to the results of the examples.

  FIG. 5 shows an example of the manufacturing process of the steel product taken up in this embodiment. Bloom slabs cast by a continuous casting machine after secondary refining are heated and slabbed in a heating furnace, and then steel strip products such as bar and wire rods are manufactured through the slabbing and strip rolling processes. . In this example, after the end of casting in the continuous casting machine, after performing the block rolling and the steel bar rolling, the defect rate due to the product surface defects generated due to the production conditions upstream of the steel bar rolling was predicted. In this example, it was assumed that the production conditions that could be changed were the transportation time to the block heating furnace and the in-furnace time in the heating furnace. In the sum of these two variables, there is an upper limit value and a lower limit value in order to keep the split rolling schedule.

  In the control apparatus in the present embodiment, the product surface defect rate was selected as the quality index, and a total of 14 items were selected as the production conditions, such as the molten steel component, the production conditions in continuous casting, and the production conditions in block rolling. . Further, the calculation unit normalized each manufacturing condition so that the average was 0 and the variance 1 for each item, and the regression parameter c was calculated using past manufacturing performance data. Table 1 shows the calculated regression parameter c. FIG. 6 shows the relationship between the value of the linear regression equation and the estimated value of the defective product rate in the calculation of the coefficient of the linear regression equation using past manufacturing performance data.

In Table 1, x _p1 , x _p2 ,..., X _p12 mean manufacturing conditions for the upstream process.

  In addition, the standard of the defect rate in this embodiment is “the defect rate is 5% or less”, and “the probability that the defect rate is 5% or less is the reference value p * = 0.999 or more” at the time of quality prediction. is there. The planned production number of production lots used in this example is 1700.

  The linear regression equation S (x, c) is defined by applying the coefficients shown in Table 1 and the selected 14 manufacturing conditions to Equation 1 above. Here, since 1700 production lots provided for this example were scheduled to be produced, the probability that the number of defective products due to defects is 85 or less must be 0.999 or more. Table 2 shows the standardized values of the manufacturing conditions for each upstream process at the end of continuous casting of this production lot.

In Table 2, x _p1 , x _p2 ,..., X _p12 are manufacturing conditions in the upstream process.

  As a result of investigating the control variation of the transportation time and the in-furnace time, it was found that the transportation time can be approximated to follow the normal distribution with a standard deviation of 5 minutes and the in-furnace time with a standard deviation of 8 minutes. . The standard deviation of the control variation of the standardized transportation time is 0.253, and the standard deviation of the control variation of the standardized in-furnace time is 0.347. Using these normalized standard deviations and a normal distribution determined by an average of 0, for each value of transport time and in-furnace time, in Equation 17, M = 1700 and 85 defective products are obtained by the Monte Carlo method. Calculate the probability of exceeding. Fig. 7 shows the feasible solution on the contour map in the plane that can be defined by the transportation time and the in-furnace time. It is the figure which showed the presence area.

When the transport time is t _c1 , the in-furnace time is t _c2, and the manufacturing condition determination problem in the subsequent manufacturing process is expressed by a normalized value, it is as follows.
Variable: t _c = [t _c1 t _c2 ]
Objective function: f ₁ t _c1 + f ₂ t _c2 → minimization / constraint conditions:
-3.98 ≦ t _c1 ≦ 3.25 (Formula 25)
-4.26 ≦ t _c2 ≦ 3.39 (Formula 26)
-7.7839 ≦ 19.7405t _c1 + 23.0149t _c2 ≦ 92.2161 (Formula 27)
c _c1 t _c1 + c _c2 t _c2 <−3.3333256 (Formula 28)

  Expression 25 is an expression representing the constraint condition of the transportation time. The lower limit value −3.98 is a value specified from physical constraints such as the speed of the transporting equipment, and is 47 minutes when converted into actual time. On the other hand, the upper limit value 3.25 is a value set based on past operational experience, and is 190 minutes when converted into actual time.

  Moreover, Formula 26 is a formula showing the constraint condition of in-furnace time. The lower limit value -4.26 is a value specified from the conveying speed of the heating furnace and past operational experience, and is 34 minutes when converted into actual time. On the other hand, the upper limit value 3.39 is a value set based on past operational experience, and is 210 minutes when converted into actual time.

Moreover, Formula 27 is a formula showing the constraint conditions regarding the total time of the conveyance time and in-furnace time for matching with a rolling schedule. The lower limit constraint in the actual time is 250 minutes and the upper limit constraint is 350 minutes. However, the lower limit value −7.77839 in the above equation 23 is the lower limit value 250 minutes in the actual time, and each of the transport time and the in-furnace time. The upper limit value 92.2161 is the difference between the upper limit value 350 minutes in the actual time and the total value of the average values of the transportation time and the in-furnace time. On the other hand, the coefficient 19.7405 of t _c1 is a conversion scale to the normalization variable of the transportation time, and the coefficient 23.0149 of t _c2 is the conversion scale of the in-furnace time to the normalization variable.

  Moreover, the said Formula 28 is a type | formula showing the conditions from which the probability that the number of inferior goods will be 85 or more becomes 0.001 or less.

When the linear programming problem was solved, the minimum value of the objective function was −0.5247, and the optimal solutions were t _c1 = 0.7183 and t _c2 = 3.390. Therefore, the probability that the number of defective products <85 at this time is 0.000357 when the value of Expression 15 is calculated by the Monte Carlo method, which is below the standard. Further, when the optimal solutions of the above t _c1 and t _c2 are converted into actual values, the transportation time = 140 minutes and the in-furnace time = 210 minutes.

  In the production lot according to the present example, this production condition was targeted, but 1683 products were produced under conditions of a transportation time of 147 minutes and a furnace time of 153 minutes. As a result, the number of defective products was 45, and the effects of the present invention could be confirmed.

  Although the present invention has been described with reference to the most practical and preferred embodiments at the present time, the present invention is not limited to the embodiments disclosed herein. However, the present invention can be changed as appropriate without departing from the spirit or concept of the invention that can be read from the claims and the entire specification, and the product quality control method and control device accompanying such changes are also within the technical scope of the present invention. It must be understood as included.

It is a flowchart which shows the process with which the control method concerning 1st Embodiment is equipped. It is a flowchart which shows the process with which the control method concerning 2nd Embodiment is equipped. It is a conceptual diagram which shows the form example of the control apparatus concerning 1st Embodiment. It is a conceptual diagram which shows the form example of the control apparatus concerning 2nd Embodiment. It is a figure which shows the example of a manufacturing process of steel products. It is the figure which plotted the relationship between the linear regression value S of manufacturing conditions, and the defect-product incidence ρ as a result of determining the coefficient of the regression equation of Table 1 by the maximum likelihood method. The probability of Equation 15 is determined by the Monte Carlo method, and the probability that the number of defectives is 85 or less is 0.001 or less on the contour map formed by the transportation time and the in-furnace time. It is the figure which showed the existence area | region of the executable solution which satisfy | fills constraint conditions.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Regression formula definition part 2 ... Formulation part 3 ... Variation formulation part 4 ... Quality prediction part 5 ... Calculation part 6 ... Result display part 7 ... Manufacturing condition change part 10, 20 ... Control apparatus of product quality

Claims (14)

A method for controlling the quality of a product,
A first step of defining a quality of the product according to manufacturing conditions by a linear regression equation;
A second step of formulating the quality of the product to be controlled using a probability model based on a discrete probability distribution;
A third step of formulating the actual variation of the manufacturing conditions in the product manufacturing process with an arbitrary probability model;
During the product manufacturing process, using the linear regression equation defined in the first step, the mathematical formula specified in the second step, and the probability model formula of variation in the manufacturing conditions specified in the third step. A fourth step of predicting the quality of the product at any point in time;
A method for controlling product quality, comprising: Before the production of all the products is completed, the quality is predicted by the fourth step,
A fifth step of changing the manufacturing conditions of the subsequent manufacturing step so that the quality belongs to the target range when the quality predicted in the fourth step does not belong to the predetermined target range. The method for controlling product quality according to claim 1, wherein: The manufacturing condition changed in the fifth step is a linear function using a coefficient for the manufacturing condition in the linear regression equation defined in the first step as an objective function, and changed in the fifth step. The product quality control method according to claim 2, wherein the product quality control method is specified by solving an optimization problem using a mathematical expression related to the manufacturing condition as a constraint. The calculation step of calculating the coefficient of the linear regression equation defined in the first step based on the measurement result of the quality and / or the actual data of the manufacturing condition is a pre-step of the first step. The product quality control method according to claim 1, wherein the product quality control method is provided. The Poisson distribution is used as the probability model used in the second step when the quality of the product to be controlled is a number of defects, according to any one of claims 1 to 4. Product quality control method. The binomial distribution is used as the probability model used in the second step when the quality of the product to be controlled is the number of defective products or the defective product rate. 2. A method for controlling product quality according to item 1. The product quality control method according to claim 1, wherein the product is a steel material. A control device used to control the quality of the product,
A regression equation defining unit that defines the quality of the product according to manufacturing conditions by a linear regression equation;
A formulating unit for formulating the quality of the controlled product using a probability model based on a discrete probability distribution;
A variation formulation unit that formulates the actual variation of the manufacturing conditions during the product manufacturing process with an arbitrary probability model;
Using the linear regression formula defined by the regression formula definition unit, the formula specified by the formula formulation unit, and the probability model formula of the variation of the manufacturing conditions specified by the variation formulation unit, A quality prediction unit for predicting the quality of the product at an arbitrary point in the process;
A product quality control device comprising: Before the production of all the products is completed, the quality is predicted by the quality prediction unit,
When the quality predicted by the quality prediction unit does not belong to a predetermined target range, the manufacturing condition is changed to change the manufacturing condition in the subsequent manufacturing process so that the quality belongs to the target range. 9. The product quality control apparatus according to claim 8, further comprising a unit. The manufacturing condition specified by the manufacturing condition changing unit is a linear function using a coefficient for the manufacturing condition in the linear regression equation defined by the regression equation defining unit as an objective function, and the manufacturing condition changing The product quality control device according to claim 9, wherein the product quality control device is specified by solving an optimization problem using a mathematical expression relating to a manufacturing condition changed in a section as a constraint condition. The linear regression equation coefficient defined by the regression equation definition unit is further provided with a calculation unit that calculates the quality measurement result and / or the production condition actual data. The product quality control device according to any one of claims 8 to 10. The Poisson distribution is used as the probability model used in the formulating unit when the quality of the product to be controlled is the number of defects, according to any one of claims 8 to 11. Product quality control device. 12. The binomial distribution is used as the probability model used in the formulating unit when the quality of the product to be controlled is the number of defective products or the defective product rate. 2. The product quality control apparatus according to item 1. The product quality control device according to any one of claims 8 to 13, wherein the product is a steel material.

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