Bayesian Analysis of Stochastic Process Models

8

Reliability

8.1 Introduction

Reliability is a growing concern in a society in the quest for services and machines that operate correctly and on time. For example, we all would like to cross bridges that are not very likely to collapse, buy cars that last a long time, ride trains or buses that get us to our destination on time, or use a washing machine that does not spoil our clothes. Mathematically, reliability is the probability that a system operates correctly, under specified conditions, over a given time period. The failures of many systems can be modeled using stochastic processes such as the continuous time Markov chains presented in Chapter 4, the Poisson processes described in Chapter 5 and the stochastic differential equations introduced in Chapter 6. In the reliability context, Bayesian techniques are particularly important, as many systems such as nuclear plants, are designed to be highly reliable, and therefore, failure data are scarce. On the other hand, expert information is often available and this can be easily incorporated in Bayesian analyses as pointed out in Hamada et al. (2008). This chapter not only presents Bayesian inference and prediction based on widely used reliability models but also points out the importance of searching for optimal maintenance policies that strongly depend on the use of decision analysis. Other key aspects in reliability are also briefly discussed.

After the introduction of the basic concepts and definitions in Section 8.2, the ...