Statistical Analysis Of Exponential Distribution Reliability In The Case Of Zero-Failure Data

With the rapid development of science and technology in the world and the great improvement of human living standards,the performance requirements of products are becoming more and more strict,not only requiring good performance,but also requiring the improvement of quality.Reliability is one of the important indexes of product quality,and researchers evaluate product quality by studying product reliability.In the process of testing and reliability statistical analysis of products,researchers usually adopt regular censored tests.However,based on the level of scientific nowadays,a large number of high reliability products and high life products are born,which makes it possible that zero-failure products often appear in the experiment and zero-failure data is generated.In order to solve this problem,more and more experts Scholars and researchers began to study the problem of zero-failure data.In this research background,under the situation of zero-failure data,this paper uses Bayesian method to analyze the reliability of exponential distribution.The specific research contents are as follows:In the case of zero-failure data,the failure probability,reliability and average life of products are studied and analyzed.In this paper,on the basis of the research about Han Ming used decrese function,determining the kernel of prior distributionon for failure probability,doing Bayes estimation for reliability based on the convexity of distribution function,it made a bayes estimation about the failure probability,reliability and average life of exponential distribution by using the unique memoryless of exponential distribution and making full use of prior information in the case of zero-failure data.Firstly,the kernel of prior distribution ln?dp_i?^-1 of the failure probability p_i is given.The prior distribution of R₂ is obtained by the convexity and memoryless of the exponential distribution,and the prior distribution of R_i is obtained by the prior distribution of R₂.Finally,the Bayes estimation of failure probability and reliability,as well as the estimation of product average life are obtained.Based on the statistical analysis of zero-failure data of Liu Yongfeng in exponential distribution,E-Bayes estimation and hierarchical Bayesian estimation are further made for reliability and failure probability,and the feasibility of the method is illustrated through the analysis of specific examples.