The Statistical Inference Of Reliability Based On Uncomplete Data

Since the 1960s,there have been much research on reliability of product by using probabilistic statistical theory,in which the incomplete data analyis contribute to guid-ing for analyzing the lifetime failure characteristics of products and providing correct scientific decision-making.Therefore,this paper aims to explore theoretical statistical mtehod on industrial reliability of incomplete data.The preface summarizes the origin and development of statistical analysis in re-liability among academic field.Then it introduces the knowledge of usual censored data type,lifetime distribution and realiability index.The second chapte discusses the parameter estimation of stress-strength reliability based on Weibull distribution.It derives the linear least square estimation and maximum likelihood esimation(mle)of R=P[Y<X],and Taylor expansion is considered to get the explicit approximate mle.What’s more,the Bayes estimation is obtained based on Metropolis sampling method.The simulation verifies effectiveness and accuracy of the above estimations.The third chapter studies the inference of generalized Pareto lifetime distribution base on progressively type Ⅱ censored data.The mle of S(t)is proposed based on EM algorithm,and the Bootstrap estimation and Bayes estimation are also considered in the next.The Markov Chain Monte Carlo sampling technique is proposed to solve the parameter estimation problem of complex density function.The simulation results proves the estimation based on EM algorithm and sampling method are better.The fourth chapter consider the goodness of fit based on progressively type I-I censored data.it presents the Kullback-Leibler test statistic and the approximated Kullback-Leibler by assuming the null hypothesis is generalized Pareto distribution.the paper explores and compares the test power of the two test statistics under different alternative hypothesis distributions through numerical simulation.