Statistical Inference And Application Of Several Stochastic Process Degradation Models With Small Samples

With the continuous advancement of science and technology and the con-tinuous improvement of the manufacturing level,more and more long-life and high-reliability products have emerged in the fields of engineering,machinery and electronics.These long-life,high-reliability products are almost impossible to fail in a relatively short period of time.There are many challenges to analyzing the life and reliability of these products with traditional time-of-failure accelerated life testing methods.Many studies have shown that when analyzing and eval-uating product reliability,degradation data usually provides more information about products than failure time data,and the results of the analysis are more accurate and reliable.The evaluation and inference of product life and reliability through the analysis of degraded path has become a hot and difficult problem in the field of reliability statistics,and there are many related research results.However,most of the current researches are based on the maximum likelihood method and the Bayesian method for statistical analysis of different degradation models.Obviously,when the degradation data is relatively small,the error of the maximum likelihood method will be larger.When the Bayesian method is used,since the prior selection is uncertain,different priors often lead to different inference results.For different degradation models,the generalized method is used to construct the generalized pivot quantity to solve the reliability modeling and statistical inference problems in the current small sample degradation test analysis.The optimization design problem of the test is also studied.The main contents are as follows:(1)Study the reliability analysis and statistical inference of gamma constant-stress accelerated degradation testing model.Based on the principle of invari-ance of degradation mechanism,a gamma constant-stress accelerated degradation testing model is proposed,and the maximum likelihood estimations of model pa-rameters are derived.Based on the Cornish-Fisher expansion,the approximate confidence interval of the shape parameter of the gamma degradation process is obtained.By constructing the generalized pivot quantities,the generalized con-fidence intervals for the other model parameters,the mean degradation in unit time,the quantile and the reliability function of the lifetime are studied.Through numerical simulation,the proposed generalized confidence intervals are compared with the traditional Wald and bootstrap-p confidence intervals.(2)The statistical inference and optimal design problem of the Wiener constant-stress accelerated degradation testing model are studied.The exact confidence intervals of the model parameters are derived.By constructing the generalized pivot quantity and using the alternative method,the generalized confidence inter-vals of the reliability function and the pth quantile of lifetime are studied.The prediction intervals for product performance degradation,lifetime and remain-ing useful life at design stress level are established.The proposed generalized confidence(or prediction)intervals are compared with the traditional bootstrap intervals.In addition,a new optimal criterion is proposed,which is to minimize the mean of the upper bound of the performance degradation under the design stress level.And the optimal plan of the model is given under the new optimal criterion.(3)The reliability analysis and statistical inference of the inverse Gaussian constant-stress accelerated degradation testing model are studied.Firstly,the maximum likelihood estimations of the model parameters are discussed,and the exact confidence intervals of the parameters ? and ?i are constructed.Second,based on the weighted least squares estimates of the parameters a,b,by con-structing the generalized pivot quantity,the generalized confidence intervals of the model parameters a,bare obtained.Using the alternative method,the gen-eralized confidence intervals of the reliability index such as the reliability func-tion R(t)and the p-quantile of lifetime are derived.In addition,the generalized prediction intervals of the mean lifetime and mean remaining useful life under the normal use stress level are established.In terms of the coverage percentage and the average interval length,the performances of the proposed generalized confidence intervals and generalized prediction intervals are simulated(4)The reliability analysis and statistical inference of competitive failure model with degradation failure and sudden failure are studied.Based on Wiener degradation failure and Weibull sudden failure,a competitive failure model is proposed.The maximum likelihood estimates of parameters ?,?2 and the inverse estimates of the parameters ?,? are derived.In addition,by constructing the generalized pivot quantity of parameter ?,the generalized confidence intervals of reliability function,the quantile of lifetime and the mean time to failure are obtained by using the alternative method.Based on the coverage percentage and the average interval length,the performances of the proposed generalized confidence intervals are simulatedAt the end of the paper,the last chapter summarizes and analyzes the pre-vious research contents,outlines the main research work of this thesis,and points out the deficiencies and and problems that need further research in the future.