Bayesian Reliability—Growth Analysis for Statistical of Diverse Population Based on Non-homogeneous Poisson Process

Abstract

New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aiming at the test process which is high expense and small sample-size in the development of complex system,the specific methods are studied on how to process the statistical information of Bayesian reliability growth regarding diverse populations. Firstly,according to the characteristics of reliability growth during product development,the Bayesian method is used to integrate the testing information of multi-stage and the order relations of distribution parameters. And then a Gamma-Beta prior distribution is proposed based on non-homogeneous Poisson process(NHPP) corresponding to the reliability growth process. The posterior distribution of reliability parameters is obtained regarding different stages of product,and the reliability parameters are evaluated based on the posterior distribution. Finally,Bayesian approach proposed in this paper for multi-stage reliability growth test is applied to the test process which is small sample-size in the astronautics filed. The results of a numerical example show that the presented model can make use of the diverse information synthetically,and pave the way for the application of the Bayesian model for multi-stage reliability growth test evaluation with small sample-size. The method is useful for evaluating multi-stage system reliability and making reliability growth plan rationally.