Practical Applications of Bayesian Reliability

8Bayesian Hierarchical Model

This chapter introduces the basics of Bayesian hierarchical models. For a family of products whose designs are similar in nature, under the assumption of exchangeability, Bayesian hierarchical models can be applied to allow partial information to be leveraged among different products. The potential benefits of applying Bayesian hierarchical models include reducing sample size and/or reducing the uncertainty of predicted reliability for a new product when there is no other prior information of its reliability performance. Specifically, in this chapter a Bayesian hierarchical binomial model and a Bayesian hierarchical Weibull model are discussed with examples.

8.1 Introduction

In Chapter 2 we demonstrated that if an informative prior distribution is available and if it indicates high reliability, to demonstrate the same level of confidence/reliability sample size could be reduced by using an informative prior distribution, compared to using a vague/noninformative prior. This is one benefit of Bayesian analysis. Let us briefly refresh here.

There are a few methods to convert this reliability prior information into a distribution. For example, the reliability of a product is believed to have a mean of 0.95 and a standard deviation of 0.01 based on other sources of information. Let us convert this information to a distribution. A standard beta distribution can be a good choice to model probability, since it is a continuous distribution defined on the ...