Bayesian Computations for a Class of Reliability Growth Models

Abstract

In this article, we consider the development and analysis of both attribute- and variable-data reliability growth models from a Bayesian perspective. We begin with an overview of a Bayesian attribute-data reliability growth model and illustrate how this model can be extended to cover the variable-data growth models as well. Bayesian analysis of these models requires inference over ordered regions, and even though closed-form results for posterior quantities can be obtained in the attribute-data case, variable-data models prove difficult. In general, when the number of test stages gets large, computations become burdensome and, more importantly, the results may become inaccurate due to computational difficulties. We illustrate how the difficulties in the posterior and predictive analyses can be overcome using Markov-chain Monte Carlo methods. We illustrate the implementation of the proposed models by using examples from both attribute and variable reliability growth data.

KEY WORDS:

• Bayesian inference
• Gibbs sampling
• Markov-chain Monte Carlo methods
• Ordered Dirichlet distribution