CN113705112A - Identification method of DOE (design of analysis) important factors of product life - Google Patents

Identification method of DOE (design of analysis) important factors of product life Download PDF

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CN113705112A
CN113705112A CN202111111679.8A CN202111111679A CN113705112A CN 113705112 A CN113705112 A CN 113705112A CN 202111111679 A CN202111111679 A CN 202111111679A CN 113705112 A CN113705112 A CN 113705112A
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王国东
邵梦颖
孔美迪
薛丽
陈洪根
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Zhengzhou University of Aeronautics
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Abstract

The invention discloses a method for identifying DOE (data of origin) important factors of product life data, which effectively solves the problems that the prior art cannot solve the problems that the test sample size is small and prior distribution information cannot be applied when identifying the important factorsβAnd the parameter to be estimatedθObtaining the parameters to be estimated in the linear regression model according to Bayesian theorem by prior distribution in the linear regression modelβAnd the parameter to be estimatedθAnd estimating the parameters to be estimatedβAnd the parameter to be estimatedθIdentifying important factors in the posterior distribution, and estimating confidence interval of the parameter to be estimatedAnd the important factors are identified, so that the accuracy of identifying the important factors is improved.

Description

Identification method of DOE (design of analysis) important factors of product life
Technical Field
The invention relates to the field of DOE (design of article of manufacture), in particular to a method for identifying DOE (design of article of manufacture) important factors of product life.
Background
The constantly developed science and technology and the increasingly intense market competition put forward increasingly strong reliability requirements on products. The classical reliability theory is well developed, but most of the problems are large samples, namely the problem of large product quantity. In practical engineering, the number of samples is always very limited, and classical reliability theory cannot be systematically adopted to solve the problem. Design of experiments DOE is an important branch of statistics, and is mainly used for researching theories and methods for establishing proper experimental schemes and carrying out effective statistical analysis on experimental data. In the life management activity of products, DOE is widely used, and the DOE is mainly used for carrying out quantitative analysis on parameters such as product quality, process and the like, so that important factors are searched, factors related to the factors are controlled, and the product life is accurately obtained.
For example, two methods are proposed in the prior art, namely a method for identifying important factors based on Bootstrap and modeling and optimization of a double-response curved surface under the condition of deleting data regularly, the two methods can identify the important factors, but the problems that the test sample size in the field of reliability engineering is small and prior distribution information cannot be applied cannot be solved.
The present invention therefore provides a new solution to this problem.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method for identifying DOE (DOE-identity) important factors in the service life of a product, and effectively solves the problems that the prior art cannot solve the problems that the test sample size is small and the prior distribution information cannot be applied when identifying the important factors.
The technical scheme for solving the problem is that the identification method of the DOE (product object) important factor of the product life data comprises the following steps:
s1, establishing a linear regression model according to the product life data subjected to Weibull distribution, wherein the linear regression model comprises a scale parameter lambda, a shape parameter v, a parameter beta to be estimated and a parameter theta to be estimated;
s2, determining the prior distribution of the parameter beta to be estimated and the parameter theta to be estimated in the linear regression model by using the diffusion prior distribution:
βi～dunif(a1，b1)；θi～dunif(c1，d1)
βi～dnorm(a2，b2)；θi～dunif(c2，c2)
wherein, a1，b1，c1，d1，a2，b2，c2，c2Is a hyper-parameter;
s3, obtaining posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated in the linear regression model according to Bayesian theorem, and identifying important factors from the posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated.
Further, the specific steps of establishing the linear regression model by using the product life data in the step S1 are as follows: x1, the product life data obey Weibull distribution, namely y-dweibull (lambda, v)
Weibull distribution probability density function: f (y | λ, v) ═ λ v (y)v-1exp[-λ(y)v] (1)
Weibull cumulative distribution function: f (y | λ, v) ═ 1-exp [ - λ (y)v] (2)
The contribution of the non-truncated data to the likelihood function is:
Figure BDA0003274168820000021
the contribution of the right truncated data to the likelihood function is:
Figure BDA0003274168820000022
where m is the number of combinations of test factor levels, and n samples are total, then yijIs expressed as the life data of the ith group of jth sample products, and i is 1, 2.m；j＝1，2，...，n；
And X2, analyzing the horizontal combination of the ith test factor X, wherein the likelihood function of the life data under the Weibull distribution is as follows:
Figure BDA0003274168820000023
x3, establishing a linear regression model between the relevant scale parameter lambda and the shape parameter v under Weibull distribution and the test factor X, namely:
Figure BDA0003274168820000024
Figure BDA0003274168820000025
wherein k represents k experimental factors x, x in DOEikAre covariates.
Further, the diffusion prior distribution in the step S2 includes a uniform distribution and a normal distribution.
Further, the step S3 specifically includes the following steps:
y1, obtaining linear regression model parameters by using Bayesian theorem:
Figure BDA0003274168820000031
the edge probability density function m (y) ═ L (data | θ) f (θ) d θ is constant;
y2, carrying out convergence judgment on the parameter beta to be estimated and the parameter theta to be estimated;
and Y3, identifying important factors from the posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated, and obtaining a linear regression specific model containing the scale parameter lambda and the shape parameter v.
Due to the adoption of the technical scheme, compared with the prior art, the invention has the following advantages:
according to the identification method of the DOE important factors of the product life, the problem of inaccurate identification of the important factors caused by small test sample amount in the reliability engineering field is solved by carrying out prior distribution and posterior distribution on the beta parameter to be estimated and the theta parameter to be estimated and identifying the important factors from the confidence interval of the beta parameter to be estimated.
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FIG. 1 shows beta in the present invention0And (4) carrying out an autocorrelation graph.
FIG. 2 shows beta in the present invention11And (4) carrying out an autocorrelation graph.
FIG. 3 is a view showing the angle theta of the present invention3And (4) carrying out an autocorrelation graph.
FIG. 4 shows the invention9And (4) carrying out an autocorrelation graph.
FIG. 5 shows beta in the present invention0A sample trace plot.
FIG. 6 shows beta in the present invention11A sample trace plot.
FIG. 7 shows the invention3A sample trace plot.
FIG. 8 shows the invention9A sample trace plot.
Detailed Description
The foregoing and other technical and functional aspects of the present invention will be apparent from the following detailed description of the embodiments, which proceeds with reference to the accompanying figures 1-8. The structural contents mentioned in the following embodiments are all referred to the attached drawings of the specification.
Exemplary embodiments of the present invention will be described below with reference to the accompanying drawings.
A method of identifying a product lifetime DOE significance factor, the method comprising the steps of:
s1, establishing a linear regression model according to the product life data subject to Weibull distribution, wherein the linear regression model comprises a scale parameter lambda and a shape parameter v, wherein log (lambda) and log (v) of the Weibull distribution under each horizontal combination of test factors x have a linear relation with the test factors x, and the horizontal combination of the test factors x comprises negative and positive;
s2, determining prior distribution of the scale parameter lambda and the shape parameter v in the linear regression model by using diffusion prior distribution:
βi～dunif(a1，b1)；θi～dunif(c1，d1)
βi～dnorm(a2，b2)；θi～dunif(c2，c2)
wherein, a1，b1，c1，d1，a2，b2，c2，c2To be hyperparametric, θi～dnorm(c2，c2) Theta in (1)iObeying a positive solar distribution;
s3, obtaining posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated in the linear regression model according to Bayesian theorem, and identifying important factors from the posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated.
The specific steps of establishing the linear regression model by using the product life data in the step S1 are as follows:
x1, the product life data obey Weibull distribution, namely y-dweibull (lambda, v)
Weibull distribution probability density function: f (y | λ, v) ═ λ v (y)v-1exp[-λ(y)v] (1)
Weibull cumulative distribution function: f (y | λ, v) ═ 1-exp [ - λ (y)v] (2)
The contribution of the non-truncated data to the likelihood function is:
Figure BDA0003274168820000041
the contribution of the right truncated data to the likelihood function is:
Figure BDA0003274168820000042
where m is the number of combinations of test factor levels, and n samples are total, then yijIs expressed as the lifetime data for the ith group of jth sample products, and i ═ 1, 2.. multidata, m; j is 1, 2,. n;
and X2, analyzing the horizontal combination of the ith test factor X, wherein the likelihood function of the life data under the Weibull distribution is as follows:
Figure BDA0003274168820000051
and X3, establishing a linear regression model under Weibull distribution and including a scale parameter lambda and a shape parameter v and a test factor X, namely:
Figure BDA0003274168820000052
Figure BDA0003274168820000053
wherein k represents k experimental factors x, x in DOEikFor covariates, equations (6) and (7) are linear regression models.
The diffusion prior distribution in step S2 includes a uniform distribution and a normal distribution, if there is enough prior information about the parameter to be estimated, the prior distribution with information can be used, and in the reliability problem, the prior distribution about the parameter to be estimated can be determined by combining some general reliability data, information about similar products, and experience that engineers in the work field have about tests and operating environments of the products.
The step S3 specifically includes the following steps:
y1, obtaining linear regression model parameters by using Bayesian theorem:
Figure BDA0003274168820000054
the edge probability density function m (y) ═ L (data | θ) f (θ) d θ is constant;
y2, carrying out convergence judgment on the parameter beta to be estimated and the parameter theta to be estimated, extracting a certain number of simulation samples from the samples, aging, judging whether the data in a stable period fluctuate randomly around the mean value and reach a stable state, and judging whether the autocorrelation of the simulation samples tends to 0 in a short period, thereby judging whether the posterior sampling value of the parameter to be estimated reaches a stable state and whether the posterior sampling value converges to a certain stable distribution;
y3, obtaining posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated in the linear regression model according to Bayesian theorem, identifying important factors from the posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated, and judging the important factors according to 95% confidence intervals of the parameter beta to be estimated: if the 95% confidence interval of the parameter to be estimated does not contain 0, the parameter is an important factor, otherwise, the parameter is an unimportant factor.
When the method is used specifically, firstly, a linear regression model is established according to product service life data obeying Weibull distribution, prior distribution of a parameter beta to be estimated and a parameter theta to be estimated in the linear regression model is determined by diffusion prior distribution, posterior distribution estimation of the parameter beta to be estimated and the parameter theta to be estimated in the linear regression model is obtained according to Bayesian theorem, and important factors are identified from the posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated;
the embodiments of the invention in the thermostat product are: a key issue affecting the reliability of thermostat products is membrane perforation due to corrosion, and therefore the purpose of this test was to find out the key factors affecting corrosion. In this test, a total of 11 factors, test factors, were considered, as shown in table 1 below; the problem is solved by adopting an orthogonal test design method to obtain optimal test schemes under different horizontal combinations, wherein a covariate xikSelecting according to the table 2; for each set of tests, 10 samples were dosed, with test times of 7342 (1000) cycles, which remained after 7342 (1000) cyclesSamples without failures were treated as timed right-tailed as shown in table 3 below, where the values with x in table 3 are right-tailed data; the important factors were selected from table 4:
table 1 test factors:
Figure BDA0003274168820000061
Figure BDA0003274168820000071
table 2 covariates:
experiment number A B C D E F G H I J K
1 - - - - - - - - - - -
2 - - - - - + + + + + +
3 - - + + + - - - + + +
4 - + - + + - + + - - +
5 - + + - + + - + - + -
6 - + + + - + + - + - -
7 + - + + - - + + - + -
8 + - + - + + + - - - +
9 + - - + + + - + + - -
10 + + + - - - - + + - +
11 + + - + - + - - - + +
12 + + - - + - + - + + -
Table 3 product life data:
Figure BDA0003274168820000072
table 4 posterior distribution estimation summary table of parameters to be estimated:
Figure BDA0003274168820000081
establishing a linear regression model according to the step S1, and determining prior distribution of the parameter beta to be estimated and the parameter theta to be estimated in the linear regression model related to the scale parameter lambda and the shape parameter v:
in analyzing lifetime data, if there is no restriction on the parameter and the a priori distribution information about its distribution is good, then one way to select a priori distribution information for the parameter is to assume that each of its components is independent of each other and is identically distributed to Normal (0, 10)tWhere t is a sufficiently large integer; different no-information priors have little influence on Bayesian inference, and rarely have great influence on results. If a priori information is present, then the mean of the normal distribution can be shifted from the origin according to the a priori information, while the variance of the normal distribution is appropriately reduced.
When the service life data are analyzed, probability density functions of Weibull distribution corresponding to each test data form likelihood functions together. Suppose that the prior distributions of the parameter β to be estimated and the parameter θ to be estimated are independent of each other and are both Normal (0, 10000), i.e., βk～dnorm(0，10000)，θk～dnorm(0，10000)，k＝0，1，2，...，11；
The simulation results are as follows:
1. and (3) convergence judgment:
as can be seen from fig. 1 to 4, the autocorrelation of the simulation sample under each parameter gradually goes to 0 in a short period, and the simulation sample under each parameter randomly fluctuates around the mean value from fig. 5 to fig. 8. Therefore, the posterior sampling value of the parameter to be estimated can be judged to reach a stable state and be converged to certain stable distribution.
2. Judging the important factors:
the method is obtained by analyzing a posterior distribution estimation summary table of a simulation sample, and important factors in a model of the scale parameter lambda are E, F, H, I and K; the important factor in the model of the shape parameter v is B, F, G, H, I, K;
3. linear regression model:
the linear regression model established by the scale parameter lambda and the shape parameter v with the test factor x is as follows:
log(λ)＝-12.58+4.045E+2.356F-4.185H-2.988I-2.428K (9)
log(v)＝0.3562-0.3243B-0.319F+0.1907G+0.3443H+0.3644I+0.2701K (10)。
according to the identification method of the DOE important factors of the product life, the problem of inaccurate identification of the important factors caused by small test sample amount in the reliability engineering field is solved by carrying out prior distribution and posterior distribution on the beta parameter to be estimated and the theta parameter to be estimated and identifying the important factors from the confidence interval of the beta parameter to be estimated.

Claims (4)

1. A method for identifying DOE (product object) important factors of product life data is characterized by comprising the following steps:
s1, establishing a linear regression model according to the product life data obeying Weibull distribution, wherein the linear regression model comprises a scale parameter lambda, a shape parameter v, a parameter beta to be estimated and a parameter theta to be estimated;
s2, determining the prior distribution of the parameter beta to be estimated and the parameter theta to be estimated in the linear regression model by using the diffusion prior distribution:
βi～dunif(a1，b1)；θi～dunif(c1，d1)
βi～dnorm(a2，b2)；θi～dunif(c2，c2)
wherein, a1，b1，c1，d1，a2，b2，c2，c2Is a hyper-parameter;
s3, obtaining posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated in the linear regression model according to Bayesian theorem, and identifying important factors from the posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated.
2. The method for identifying the DOE (product lifetime) importance factor of the product lifetime as claimed in claim 1, wherein the specific steps of establishing the linear regression model by using the product lifetime data in the step S1 are as follows:
x1, the product life data obey Weibull distribution, namely y-dweibull (lambda, v)
Weibull distribution probability density function: f (y | λ, v) ═ λ v (y)v-1exp[-λ(y)v] (1)
Weibull cumulative distribution function: f (y | λ, v) ═ 1-exp [ - λ (y)v] (2)
The contribution of the non-truncated data to the likelihood function is:
Figure FDA0003274168810000011
the contribution of the right truncated data to the likelihood function is:
Figure FDA0003274168810000012
wherein m is the number of combinations of test factor levels,a total of n samples, then yijLife data for the ith set of jth samples, and i ═ 1, 2...., m; j is 1, 2,. n;
and X2, analyzing the horizontal combination of the ith test factor X, wherein the likelihood function of the life data under the Weibull distribution is as follows:
Figure FDA0003274168810000013
x3, establishing a linear regression model between relevant scale parameters lambda and shape parameters v under Weibull distribution and test factors X, namely:
Figure FDA0003274168810000021
Figure FDA0003274168810000022
wherein k represents k experimental factors x, x in DOEikAre covariates.
3. The method for identifying the DOE (product lifetime) significant factor of the product life as claimed in claim 1, wherein the prior distribution of diffusion in the step S2 includes a uniform distribution and a normal distribution.
4. The method for identifying the DOE (DOE) importance factor) of the product life as claimed in claim 1, wherein the step S3 specifically comprises the following steps:
y1, obtaining linear regression model parameters by using Bayesian theorem:
Figure FDA0003274168810000023
the edge probability density function m (y) ═ L (data | θ) f (θ) d θ is constant;
y2, carrying out convergence judgment on the parameter beta to be estimated and the parameter theta to be estimated;
and Y3, identifying important factors from the posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated, and obtaining a linear regression specific model containing the scale parameter lambda and the shape parameter v.
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