一个贝叶斯离散可靠性增长模型──多元Beta模型

本文提出了一个贝叶斯离散可靠性增长模型．本模型是Ｍａｚｚｕｃｈｉ—Ｓｏｙｅｒ模型［１］的一个推广．假设一个产品的开发过程由ｍ个阶段组成．在每一个阶段中，都进行一个成败型寿命试验．在试验结束后，再分析其结果，然后对产品进行修改或重新设计，以期提高产品的可靠性．产品的失效可分为不可修复的以及可修复的两种．假定产品的不可修复失效概率在各个阶段中保持相同，而可修复失效概率随着试验阶段的增加而减少．在此假定下，我们选用一个合理的分布作为产品失效概率的先验分布，它就是多元Ｂｅｔａ分布．然后，我们将先验信息与试验数据相结合进行贝叶斯分析．文中举了一个实例加以说明

A Bayesian discrete reliability growth model ──a multivariate Beta model

This paper presents a Bayesian discrete reliability growth model, which is a generalization of the Mazzuchi-Soyer model. We assume that a product development phase consists of m stages. At each stage, an attribute life test is conducted. Then test results are analyzed and modifications or redesign are taken in an attempt to improve the product reliability. Suppose that a failure can be categorized as either fi-cable or non-fix-cable. On the assumption that the non-fixable failure probability remains the same whereas the fi-cable failure probability decreases from stage to stage, a reasonable prior distribution, the multivariate beta distribution, is adopted for the failure probabilities. Then Bayesian analysis is conducted by incorporating prior information with test data. A numerical example is given for illustrative purpose.