Degradation Data Analysis And Experimental Design Based On Stochastic Processes

Reliability modeling methods based on degradation data can assess life characteristics of highly reliable products effectively.The degradation data of the product's quality charac-teristic(QC)can be obtained from rated stress degradation test,constant stress accelerated degradation test(CSADT)and step stress accelerated degradation test(SSADT).Under var-ious test methods,the degradation process of product's QC exhibits randomness,thus it can be described by a stochastic process model such as Wiener process,gamma process,inverse Gaussian(IG)process,exponential dispersion(ED)process,etc.This dissertation aims to solve two main issues include the problems of reliability assessment and experimental design for the degradation data based on stochastic process models.Reliability assessment issues include the assessment of reliability metrics such as reliability,mean lifetime,remaining useful life(RUL),and so on.Specifically,firstly,some parameter estimation methods are used to gain the estimators of unknown parameters of the stochastic process model.Secondly,these parameter estimators are substituted into the mathematical expression of the reliability metric to obtain the corresponding estimation result.Design issues of degradation test include rated stress degradation test design,CSADT design and SSADT design,etc.Experimental design is essentially an optimization problem,whose aim is to improve the estimation accuracy of reliability metrics by arranging sample size,measurement frequency,number of measurements,stress level,etc.The specific research contents of this paper include the following aspects:(1)The method for evaluating product's reliability and mean lifetime based on IG process is proposed from the perspective of Bayesian Statistics.Assume that a product has two QCs and each of the QCs is governed by an IG process.The dependence of the QCs is described by a copula function.A bivariate simple IG process model and three bivariate IG process models with random effects(random drift model,random volatility model,random drift volatility model)are investigated by applying Bayesian method.The unknown model parameters of each model are estimated by using the Bayesian Markov Chain Monte Carlo(MCMC)algorithm.The mathematical expressions of the product's reliability and mean lifetime are given by the concept of first hitting time(FHT).Finally,a set of simulation data and instance data are used to illustrate the effectiveness of the proposed models and methods.(2)The evaluation of product's lifetime and RUL based on the ED process is discussed.The ED process is a generalized stochastic process,which includes the Wiener,gamma and IG processes as its special cases.The independent increment of the ED process follows ED distribution.The probability density function(PDF)of the ED distribution is approximated by the saddlepoint approximation approach.Random effects are incorporated into the ED process to reflect the unit-to-unit variability,and covariates are introduced to describe the effect of environment factors on the degradation process.For the ED model with random effects and covariates,the expectation maximization(EM)algorithm is applied to estimate the model parameters.The cumulative distribution functions(CDFs)of the lifetime and RUL of products are approached by the Birnbaum-Saunders(BS)distribution.Finally,the developed models are applied to two illustrative examples,and the analysis result of ED process is compared with that of Wiener process,gamma process and IG process.The comparison results show that the ED process performances better than the other three commonly used processes for the two sets of instance data.(3)The theoretical plan of the CSADT design problem based on gamma process is given.Three optimization problems(D-optimization,V-optimization and A-optimization)are con-sidered for the fixed-effect and random-effect gamma process models.Under a certain of model assumptions,for the three optimization problems,we prove that the optimal CSADT plans with multiple stress levels degenerate to two-stress-level test plans only using the minimum and maximum stress levels.The optimal sample size allocation proportions for the minimum and maximum stress levels are determined theoretically.The influence of stress level selection on the objective functions is also discussed.We find that the lower stress level should be arranged as low as possible,and the higher stress level should be arranged as high as possible.Finally,a set of instance data and simulation data are used to validate the theoretical results.(4)The SSADT plan based on non-stationary gamma process model is proposed.The ran-dom effect is included into the non-stationary gamma process.The cumulative exposure(CE)model is used to link the degradation paths of the SSADT under different stress levels.The CE model assumes that the degradation path depends only on the degradation magnitude already accumulated and the current stress level,and has nothing to do with the way of accumulation.For the SSADT model based on non-stationary gamma process with random effects,the EM algorithm is used to estimate the unknown parameters.The design variables such as sample size,the measurement frequency at each stress level,and the number of measurements at each stress level are obtained by minimizing the asymptotic variance of the estimated reliability of the product at a predesigned mission time,under the budget and boundary constraints.In the end,an illustrative example is used to describe the proposed model and method.(5)The SSADT design problem based on IG process is solved.The IG process is used to describe the degradation of product's QC.A proportional degradation rate(PDR)model is proposed to link the degradation paths of the SSADT with stress levels.The PDR model assumes that the ratio of the average degradation rates under two constant stress levels is an exponential function of the difference of the two stress levels.For the SSADT model based on the IG process,two optimization problems are investigated,including minimizing the asymptotic variance of the product's estimated mean lifetime under usage conditions and minimizing the asymptotic variance of the estimated reliability of the product at a predesigned mission time.The optimal settings such as sample size,measurement frequency and the number of measurements for each stress level are determined within a given budget constraint for the two optimization problems.Finally,a set of instance data is used to illustrate the proposed model and method.