Statistical Inferences Of Performance Index Of Burr Distribution Family Based On The Various Progressively Censored Schemes

The Burr families of distributions contain 12 types continuous life distributions,which gain plenty of attentions on various fields.The Burr ? and Burr ? distributions are two popular ones to be used on statistical research.In the industrial field,the reliability index and the lifetime performance index are two popular statistical indexes,which are able to assess and analyze the quality of target products efficiently.Besides,due to the constraints of time and cost of lifetime experiences,the progressively censoring schemes have a good performance on generating the incomplete lifetime data.Therefore,based on the pro-gressively censored schemes,it has significance and practical value to research statistical inferences of industrial indexes on Burr ? and Burr ? distributions.Burr ? distribution is an important continuous life distribution in reliability engineer-ing research.This paper focuses on studying the statistical inference of reliability of Burr ? distribution,under the progressively type-II censored data.First we obtain the estimates through maximum likelihood estimation.With Bootstrap-p and Bootstrap-t methods,we estimate the confidence intervals of target indexes.In addition,the Bayes estimation of the reliability function is carried out by adopting importance sampling and the Gibbs sampling methods.Under the Bayesian methods,the point estimation and HPD confidence inter-val estimation are carried out respectively.The Monte Carlo numerical simulation and a real data example are used to illustrate the performance of proposed inference methods.Finally,the approximate estimation of stress-strength reliability is further discussed.Burr ? distribution is of real significance to evaluate performance of products qual-ity on the industrial fields.Assessing the lifetime performance of the products is an effec-tive and important topic in the manufacturing fields.In this paper,based on the progres-sive first failure censored scheme,we evaluate the lifetime performance index of products with the lower required limit,and the lifetime of products follows the Burr ? distribu-tion.The relationship between lifetime performance index and products conforming rate is discussed to illustrate the significance of this statistical research.Besides,The maximum likelihood estimator is derived and used as the basis for studying the confidence intervals of the index.We also establish statistical testing processes to evaluate whether the index fits the requirement.Finally,the Monte Carlo simulations and the real data example are illustrated to present the statistical performance of proposed inference methods.