The Bayes Reliability Analysis For Weibull Distribution Zero Failure Data

Weibull distribution is a mostly widely used model in applied probability and statistics and reliability analysis of product life. The Bayes reliability analysis for Weibull distribution Zero Failure Data is an issue of great theoretical significance and practical value. There have been numerous studies on analysis under zero failure data which are parameter estimation of shape parameter and scale parameters under zero failure data. Some studies are limited to exponential distribution. The paper gives the Bayes reliability analysis under Weibull distribution. Under zero failure data, the high failure probability is low while the low failure probability is high. In the paper, based on the characteristics of failure probability pi and a decreasing function on pi of Beta(a,b) as its prior distribution, reliability solution of the Bayes estimation was given and so was verification of Zero Failure Data issues. Based on the average rank Method, the estimation of product reliability was given. In addition, the average rank Method was used to give a reliability assessment of product life. Besides the simulation experiments of a set of specific failure data were carried out, which further illustrated the effectiveness of the method. Last, two different situations which present the reliability test plan of failure data were given. Not only were users’ interests considered, but also the producer’s interests by unconditional probability were ensured. The reliability test plan has certain reference value in evaluating product life.