Reliability Statistical Inferences And Application Studies Based On Lifetime Data And Degradation Data

Reliability data of products or systems are the important resources of information to measure reliability indexes in reliability engineering.However,the data are commonly incomplete no matter in what forms,such as lifetime data and degradation data.The incomplete data are obtained mainly due to the various limitations,such as operating environments,detection methods,and costs of inspections.Different types of censored lifetime data and multi-stage degradation performance data are the studies of interest in this dissertation,for instance,alternative interval-censored lifetime data,embedded complete data,and multi-stage degradation data with change points.And so,both proper reliability models and the parameter estimates should be given based on the kinds of reliability data.Firstly,continuous inspections of lifetime could not be executed on products in some special applications,wherein both the continuous detection and the censored detection could be carried out alternatively.Then the alternative interval-censored and some complete lifetime data will be obtained under the reliability test design.For this incomplete data,an imputation algorithm of single-point quantile for general distributions is proposed under moment estimation criterion.By the algorithm,virtual complete data are obtained.Therefore,it is a generalized imputation method to the censored data.For Exponential and Weibull distributions,the algorithm convergence are also demonstrated,respectively.The numerical results show that the algorithm performs well in estimation.Secondly,as the limited detection equipment or the varied operating fields for units,their lifetime can not be recorded by a continuous inspection manner.In this case,some of the units will be detected continuously in a certain interval;and the others are not.Then some complete lifetimes of the units could be embedded in the censoring intervals.A single-point imputation algorithm under stochastic quantile probabilities is proposed,called stochastic quantile-filling augmentation to the mixed observations.The algorithm has iterative thoughts of stochastic multiple imputation to obtain the virtual data.Its convergence is verified under both the criterion of moment estimation and maximum likelihood estimation.The complete procedures are given detailed for the Weibull distribution and the Gamma distribution with closed-form estimates.Furthermore,numerical examples and simulations illustrate that the proposed augmentation performs better on estimating parameters than the conventional iterative algorithm under equipartition quantile probabilities.Thirdly,some degradation systems like guide system operate under periodical or deterministic calibrations which can rejuvenate the system’s performance.A problem of assessing the reliability of a degradation system wherein calibration of a development program is carried out,within multiple phases,by Bayesian inference,is proposed in the thesis.The posterior distributions are obtained in each testing stage by an assumption that degradation performance follows Normal distributions.Then two Bayesian models are presented to evaluate the system reliability by inspecting the performance degradation indicators based on two cases,whose mean or variance can be accurately measured during a certain calibration period.Meanwhile,an important conclusion is derived as well,which the variance of a random variable of a coefficient will decrease as the number of testing stage grows.In addition,numerical examples are given to demonstrate the Bayesian results of the reliability models’ parameters and indexes.Fourthly,from a two-phase degradation path of the bearing performance observations,there exists an abrupt increase in degradation measurement at a change point.Then by the degradation data,here,some stochastic process-based degradation models are constructed to interpret the jump at the change point in the degradation process which is governed by the Wiener process.Then,the distribution of the first passage time over a pre-specified threshold for the process is discussed.Meanwhile,for the estimations of the parameters in the models,the expectation-maximization algorithm is utilized since the change points are unobservable.Furthermore,to demonstrate the model’s advantages over estimates,a comparison is made between the proposed and the existing known models from the literature.The results reveal that considering the jump in degradation process can significantly improve the accuracy of estimations in real applications.Finally,when both degradation data and lifetime data could be obtained for the products,this thesis reports how to address the estimations by using the mixed data under the Wiener and Gamma processes in real applications.Although the estimations could be given in this study under the two scenarios,much more complicated problems will arise under other kinds of data and stochastic processes.Besides,some conclusions on these studies are summarized in addition to some discussions on the further works.In summary,the related studies of the thesis verify that the proposed reliability models and estimates are available in reality.These statistical inferences and conclusion could be devoted to reliability engineering which prompt the decision makers execute the related strategies well.