Bayesian Inference for the Piecewise Exponential Model for the Reliability of Multiple Repairable Systems

Abstract

The piecewise exponential (PEXP) model for the reliability of multiple repairable systems is considered, and classic (maximum likelihood) and Bayesian inference are discussed under different model assumptions. In particular, inference using empirical and hierarchical Bayesian approaches are discussed. The PEXP model assumes that the times between failure are independent and exponentially distributed, but the mean is allowed to either increase or decrease with each failure. It can be an appropriate model for repairable systems in the context of reliability growth, specifically, test, analyze, and fix (TAAF), where the failure intensity remains constant as long as the system is working and can take discrete jumps at the time of a failure. It can also be applied when failures cause damage to the system, while system reliability remains constant during operation. By contrast, the nonhomogeneous Poisson process assumes that the reliability changes continuously and is unaffected by a failure. The application of this model to a real data set is presented under the hierarchical Bayesian approach and the classic and parametric empirical Bayes approach.

• Hierarchical Bayes
• Markov Chain Monte Carlo
• Maximum Likelihood
• Parametric Empirical Bayes
• Reliability Growth
• Test
• Analyze and Fix

Additional information

Notes on contributors

Ali Arab

Dr. Arab is Assistant Professor in the Department of Mathematics and Statistics. His email address is [email protected].

Steven E. Rigdon

Dr. Rigdon is Distinguished Research Professor in the Department of Mathematics and Statistics. He is a Senior Member of ASQ. His email address is [email protected].

Asit P. Basu

Dr. Basu is Professor Emeritus in the Department of Statistics. His email address is [email protected].