Selecting and implementing phase approximations for semi-Markov models

Abstract

Markov chains are commonly used for reliability, availability, and performability modeling. A central assumption in Markov reliability analysis is that failure and repair-time distributions are exponential. Unfortunately, in many real-life applications, assuming exponential distributions can be a significant oversimplification. Semi-Markov chains provide a simple mathematical structure for including general distributions in the Markov model framework. Three methods for analyzing semi-Markov chains are numerical solution, discrete-event simulation, and phase approximation. In this paper, we discuss a complete approach to phase approximation, including choice of phase approximation class, numerical fitting of appropriate parameters, and implementation of the approximation approach in a modeling toolkit. We describe a new hybrid approach for parameter fitting that combines moment-matching with least-squares fitting