Use of Phase Type Distributions in Reliability Modelling of Systems with a Small Number of Components

摘要

The utility of the probability distributions of phase type (PH-distributions) in the construction of algorithmic solutions to reliability models is considered. A specific model is used to illustrate the general procedure. It is assumed that the time-to-failure and repair time distributions are of phase type. Thus, a variety of reliability models with a small number of components may be studied in terms of finite-state Markov processes. Although the state spaces of these processes are typically large, their infinitesimal generators are highly structured. By using the formalism of PH-distributions, it is possible to construct efficient algorithms to evaluate a large number of quantities of interest. Some new properties of PH-distributions are also established.