CN113705112B - Identification method of important factors of life DOE of thermostat - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 22
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- 238000012417 linear regression Methods 0.000 claims abstract description 37
- 238000012360 testing method Methods 0.000 claims abstract description 35
- 238000009792 diffusion process Methods 0.000 claims abstract description 6
- 230000007797 corrosion Effects 0.000 claims description 3
- 238000005260 corrosion Methods 0.000 claims description 3
- 230000001186 cumulative effect Effects 0.000 claims description 3
- 238000005315 distribution function Methods 0.000 claims description 3
- 238000009827 uniform distribution Methods 0.000 claims description 3
- 108010014173 Factor X Proteins 0.000 claims description 2
- 238000004140 cleaning Methods 0.000 claims 4
- QAOWNCQODCNURD-UHFFFAOYSA-N Sulfuric acid Chemical compound OS(O)(=O)=O QAOWNCQODCNURD-UHFFFAOYSA-N 0.000 claims 2
- 239000011248 coating agent Substances 0.000 claims 2
- 238000000576 coating method Methods 0.000 claims 2
- 229910000881 Cu alloy Inorganic materials 0.000 claims 1
- DMFGNRRURHSENX-UHFFFAOYSA-N beryllium copper Chemical compound [Be].[Cu] DMFGNRRURHSENX-UHFFFAOYSA-N 0.000 claims 1
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- 230000032683 aging Effects 0.000 description 1
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- G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
Abstract
The invention discloses a method for identifying DOE important factors of product life data, which effectively solves the problems that the prior art cannot solve the problems of smaller test sample size and incapability of applying priori distribution information when identifying important factors, firstly establishes a linear regression model according to the product life data obeying Weibull distribution, and determines parameters to be estimated by using diffusion priori distributionβAnd parameters to be estimatedθThe prior distribution in the linear regression model is used for obtaining parameters to be estimated in the linear regression model according to the Bayes theoremβAnd parameters to be estimatedθPosterior distribution estimation of (a) and parameters to be estimatedβAnd parameters to be estimatedθThe important factors are identified in posterior distribution of parameters to be estimated, and the accuracy of identifying the important factors is improved.
Description
Technical Field
The invention relates to the DOE field, in particular to a method for identifying important factors of a life DOE of a thermostat.
Background
The ever-evolving technology and the ever-increasing market competition place a growing reliability demand on thermostats. Classical reliability theory has evolved well, but most deal with the large sample problem, i.e. the problem of a large number of thermostats. In practical engineering, the number of samples is always very limited, and classical reliability theory cannot be systematically adopted to solve the problem. The design of test DOE is an important branch of statistics, and is mainly used for researching the theory and method how to formulate a proper test scheme and how to perform effective statistical analysis on test data. In life management activities of thermostats, DOE is widely used, and the life of the thermostat is mainly performed through quantitative analysis of parameters such as quality and process of the thermostat, so that important factors are searched, and factors related to the important factors are controlled to accurately obtain the life of the thermostat.
In the prior art, two methods, namely a Bootstrap-based important factor identification method and a double-response curved surface modeling and optimization under the condition of timing deletion data, are provided, and the two methods can identify the important factors, but cannot solve the problems that the test sample size in the field of reliability engineering is smaller and prior distribution information cannot be applied.
The present invention thus provides a new solution to this problem.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a method for identifying important factors of a life DOE of a thermostat, which effectively solves the problems that the prior art cannot solve the problems that the test sample size is smaller and the prior distribution information cannot be applied when the important factors are identified.
The technical scheme is that the identification method of the important factors of the DOE of the life data of the thermostat comprises the following steps:
s1, establishing a linear regression model according to life data of a thermostat obeying Weibull distribution, wherein the linear regression model comprises a scale parameter lambda, a shape parameter v, a parameter to be estimated beta and a parameter to be estimated theta;
s2, determining prior distribution of a parameter beta to be estimated and a parameter theta to be estimated in a linear regression model by using diffusion prior distribution:
β i ～dunif(a 1 ,b 1 )；θ i ～dunif(c 1 ,d 1 )
β i ～dnorm(a 2 ,b 2 )；θ i ～dnorm(c 2 ,d 2 )
wherein a is 1 ，b 1 ，c 1 ，d 1 ，a 2 ，b 2 ，c 2 ，d 2 Is a super 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 the 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 lifetime data of the thermostat in the step S1 are as follows:
x1, thermostat life data obeys the Weibull distribution, i.e. y dweibull (lambda, v)
Weibull distribution probability density function: f (y|λ, v) =λv (y) v-1 exp[-λ(y) v ] (1)
Weibull distribution cumulative distribution function: f (y|λ, v) =1-exp [ - λ (y) v ] (2)
The contribution of non-truncated data to the likelihood function is:
the contribution of the right truncated data to the likelihood function is:
wherein m is the number of combinations of the levels of the test factors, and n samples are taken, y ij Life data represented as the ith set of jth sample thermostats, and i=1, 2, m; j=1, 2,. -%, n;
and X2, analyzing the level combination of the test factors X in the i-th group, wherein the likelihood function of life data under the Weibull distribution is as follows:
x3, establishing a linear regression model between related scale parameters lambda and shape parameters v and test factors X under Weibull distribution, namely:
wherein k represents k test factors x, x in DOE ik Is a covariate.
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 a Bayes theorem:
the edge probability density function m (y) = ≡l (data|θ) f (θ) dθ 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 posterior distribution of the parameter to be estimated beta and the parameter to be estimated theta, and obtaining a linear regression concrete 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 important factors of the life DOE of the thermostat, the important factors are identified from the confidence interval of the parameter to be estimated by carrying out prior distribution and posterior distribution on the parameter to be estimated beta and the parameter to be estimated theta, so that the problem of inaccurate identification of the important factors caused by smaller test sample size in the field of reliability engineering is solved, a mechanism for containing prior information into a linear regression model is provided by using a Bayesian method, when the test sample size is smaller, the sample information size can be increased by using prior distribution information, posterior distribution of the parameter to be estimated beta and the parameter to be estimated theta is continuously corrected through actual measurement data, the important factors are identified according to the confidence interval of the parameter to be estimated, and the accuracy of identifying the important factors is improved.
Drawings
FIG. 1 is a diagram of the beta 0 An autocorrelation graph.
FIG. 2 is a diagram of the beta 11 An autocorrelation graph.
FIG. 3 is a view of the θ of the present invention 3 An autocorrelation graph.
FIG. 4 is a graph of θ of the present invention 9 An autocorrelation graph.
FIG. 5 is a diagram of the beta 0 Sample trace map.
FIG. 6 is a diagram of the beta 11 Sample trace map.
FIG. 7 is a view of the θ of the present invention 3 Sample trace map.
FIG. 8 is θ of the present invention 9 Sample trace map.
Detailed Description
The foregoing and other features, aspects and advantages of the present invention will become more apparent from the following detailed description of the embodiments, which proceeds with reference to the accompanying figures 1-8. The following embodiments are described in detail with reference to the drawings.
Exemplary embodiments of the present invention will be described below with reference to the accompanying drawings.
A method of identifying a thermostat life DOE importance factor, the method comprising the steps of:
s1, establishing a linear regression model according to life data of a thermostat obeying Weibull distribution, wherein the linear regression model comprises a scale parameter lambda and a shape parameter v, wherein the log (lambda) and the 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 a negative type and a positive type;
s2, determining prior distribution of the scale parameter lambda and the shape parameter v in a linear regression model by using diffusion prior distribution:
β i ～dunif(a 1 ,b 1 )；θ i ～dunif(c 1 ,d 1 )
β i ～dnorm(a 2 ,b 2 )；θ i ～dnorm(c 2 ,d 2 )
wherein a is 1 ，b 1 ，c 1 ，d 1 ，a 2 ，b 2 ，c 2 ，d 2 Is super-parameter, theta i ～dnorm(c 2 ,d 2 ) θ in (a) i Obeying the normal ethernet 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 the 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 life data of the thermostat in the step S1 are as follows:
x1, thermostat life data obeys the Weibull distribution, i.e. y dweibull (lambda, v)
Weibull distribution probability density function: f (y|λ, v) =λv (y) v-1 exp[-λ(y) v ] (1)
Weibull distribution cumulative distribution function: f (y|λ, v) =1-exp [ - λ (y) v ] (2)
The contribution of non-truncated data to the likelihood function is:
the contribution of the right truncated data to the likelihood function is:
wherein m is the number of combinations of the levels of the test factors, and n samples are taken, y ij Life data represented as the ith set of jth sample thermostats, and i=1, 2, m; j=1, 2,. -%, n;
and X2, analyzing the level combination of the test factors X in the i-th group, wherein the likelihood function of life data under the Weibull distribution is as follows:
x3, establishing a linear regression model containing the scale parameter lambda, the shape parameter v and the test factor X under Weibull distribution, namely:
wherein k represents k test factors x, x in DOE ik As covariates, equation (6) and equation (7) are linear regression models.
The diffuse prior distribution in step S2 comprises a uniform distribution and a normal distribution, and if there is sufficient prior information about the parameters to be estimated, the prior distribution with information can be used, in which reliability problems the prior distribution about the parameters to be estimated can be determined in combination with some general reliability data, information about similar thermostats and experience with the engineers in the field of work with respect to the test and the operating environment of the thermostat.
The step S3 specifically includes the following steps:
y1, obtaining linear regression model parameters by using a Bayes theorem:
the edge probability density function m (y) = ≡l (data|θ) f (θ) dθ 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, after aging, randomly fluctuating the data in the stable period up and down on the mean value, reaching the 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 the stable state and 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 the 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 a confidence interval of 95% of the parameter to be estimated: if the confidence interval of the 95% 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 specifically used, firstly, a linear regression model is established according to the life data of the thermostat obeying the Weibull distribution, the prior distribution of the parameter beta to be estimated and the parameter theta to be estimated in the linear regression model is determined by using the 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 the Bayesian theorem, and important factors are identified in the posterior distribution of the parameter beta to be estimated and the parameter theta to be estimated;
examples of the invention in a thermostat product are: a key problem affecting the reliability of the thermostat product is the perforation of the diaphragm due to corrosion, and therefore the aim of this test is to find out the key factors affecting corrosion. In this test, 11 factors, i.e., test factors, were considered in total, as shown in table 1 below; the problem adopts an orthogonal test design method to obtain an optimal test scheme under different level combinations, wherein the covariates x i k is selected according to table 2; for each set of experiments, 10 samples were input for a time of 7342 (×1000) cycles, and samples that remained undisturbed after 7342 (×1000) cycles were treated as timed right truncations as shown in table 3 below, wherein the values carried in table 3 are right truncations; the importance factors are selected from table 4:
table 1 test factors:
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 thermostat life data:
table 4 summary of posterior distribution estimates of parameters to be estimated:
establishing a linear regression model according to the step S1, and determining prior distribution of a parameter to be estimated beta and a parameter to be estimated theta in the linear regression model of the related scale parameter lambda and the shape parameter v:
in analyzing lifetime data, if there is no limitation on the parameters and the prior distribution information about their distribution is good, one method of selecting the prior distribution information of the parameters is to assume that each of its components is independent of each other and is distributed in Normal (0, 10 t Wherein t is a sufficiently large integer; different non-information priors have little influence on Bayesian inference and have little influence on results. If a priori information is present, the mean of the normal distribution may be shifted from the origin in accordance with the a priori information while properly narrowing the variance of the normal distribution.
When life data are analyzed in the invention, probability density functions of Weibull distribution corresponding to each test data jointly form a likelihood function. Assuming that the a priori distributions of the parameter to be estimated beta and the parameter to be estimated theta are independent of each other and are both Normal (0, 10000), i.e. beta k ～dnorm(0，10000)，θ k ～dnorm(0，10000)，k＝0，1，2，...，11；
The simulation results are as follows:
1. and (3) convergence judgment:
from fig. 1 to fig. 4, it can be determined that the autocorrelation of the simulation sample for each parameter gradually goes toward 0 in a short period, and the simulation sample for each parameter fluctuates randomly up and down 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 a certain stable distribution.
2. Judging an important factor:
the analysis of a summary table is estimated by posterior distribution of simulation samples, and E, F, H, I, K is an important factor in a model of the scale parameter lambda; the important factors in the model of the shape parameter v are 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 and 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 important factors of the life DOE of the thermostat, the important factors are identified from the confidence interval of the parameter to be estimated by carrying out prior distribution and posterior distribution on the parameter to be estimated beta and the parameter to be estimated theta, so that the problem of inaccurate identification of the important factors caused by smaller test sample size in the field of reliability engineering is solved, a mechanism for containing prior information into a linear regression model is provided by using a Bayesian method, when the test sample size is smaller, the sample information size can be increased by using prior distribution information, posterior distribution of the parameter to be estimated beta and the parameter to be estimated theta is continuously corrected through actual measurement data, the important factors are identified according to the confidence interval of the parameter to be estimated, and the accuracy of identifying the important factors is improved.
Claims (3)
1. A method for identifying a thermostat life DOE importance factor, the method comprising the steps of:
s1, establishing a linear regression model according to life data of a thermostat obeying Weibull distribution, wherein the linear regression model comprises a scale parameter lambda, a shape parameter v, a parameter to be estimated beta and a parameter to be estimated theta;
s2, determining prior distribution of a parameter beta to be estimated and a parameter theta to be estimated in a linear regression model by using diffusion prior distribution:
β i ～dunif(a 1 ,b 1 )；θ i ～dunif(c 1 ,d 1 )
β i ～dnorm(a 2 ,b 2 )；θ i ～dnorm(c 2 ,d 2 )
wherein a is 1 ，b 1 ，c 1 ，d 1 ，a 2 ，b 2 ，c 2 ，d 2 Is super-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 the 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 life data of the thermostat in the step S1 are as follows:
x1, thermostat life data obeys the Weibull distribution, i.e. y dWeibull (lambda, v)
Weibull distribution probability density function: f (y|λ, v) =λv (y) v-1 exp[-λ(y) v ](1) Weibull distribution cumulative distribution function: f (y|λ, v) =1-exp [ - λ (y) v ](2)
The contribution of non-truncated data to the likelihood function is:
the contribution of the right truncated data to the likelihood function is:
wherein m is the number of combinations of the levels of the test factors, and n samples are taken, y ij Life data expressed as group i, j, samples, and i=1, 2,..m; j=1, 2,. -%, n; the impact on thermostat reliability is mainly due to diaphragm perforation caused by corrosion, and the test factors include: diaphragm coating rinsing, current density, sulfuric acid cleaning, diaphragm electrolytic cleaning, beryllium copper alloy grain size, stress direction, humidity, heat treatment, welding machine, power element electrolytic cleaning degree and power element coating cleaning;
and X2, analyzing the level combination of the test factors X in the i-th group, wherein the likelihood function of life data under the Weibull distribution is as follows:
x3, establishing a linear regression model between related scale parameters lambda and shape parameters v and a test factor X under Weibull distribution, namely:
wherein k represents k test factors x, x in DOE ik Is a covariate.
2. A method of identifying a thermostat life DOE importance factor according to claim 1, characterized in that said diffuse prior distribution in step S2 comprises a uniform distribution and a normal distribution.
3. A method for identifying a thermostat life DOE importance factor according to claim 1, characterized in that said step S3 comprises the steps of:
y1, obtaining linear regression model parameters by using a Bayes theorem:
the edge probability density function m (y) = ≡l (data|θ) f (θ) dθ 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 posterior distribution of the parameter to be estimated beta and the parameter to be estimated theta, and obtaining a linear regression concrete model containing the scale parameter lambda and the shape parameter v.
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