Bayesian Inference of the Phase-Type Stress-Strength Reliability Models

Abstract

Stress-strength modeling has achieved considerable attention in recent years due to its applicability in various areas like engineering, quality control, psychology, biology, genetics, medicine etc. Phase-type distribution is a generalized class of distributions that is closed under several mathematical operations like maxima, minima, convolution, finite mixture etc and any discrete or continuous probability distributions on the positive real line can be represented as phase-type. Hence stress-strength reliability models based on phase-type distributions give a generalized structure for the stress-strength models. Moreover, matrix representation of the parameters helps in their flexible evaluation and easy manipulation. In Bayesian inference, we combine the prior knowledge with the information provided by the set of current observations to make more reliable inferences. Bayesian approach has the advantage of providing more meaningful inferences by making use of all available information. In this paper, we assume that the strength of the system and the stress imposed on the system are phase-type random variables, and the Bayesian inference of stress-strength reliability is discussed for the single-component systems and multi-component systems. The computation of the Bayes estimate of stress-strength reliability using the Markov Chain Monte Carlo method, based on continuous and discrete phase-type distributions are explained.

KEYWORDS AND PHRASES:

• Stress-strength reliability
• phase-type distribution
• Markov Chain Monte Carlo method
• Gibbs sampling method