Phase type stress–strength models with reliability applications

Abstract

The stress–strength model has attracted a great deal of attention in reliability analysis, and it has been studied under various modeling assumptions. In this article, the stress–strength reliability is studied for both single unit and multicomponent systems when stress and strength distributions are of phase type. Phase-type distributions, besides their analytical tractability, are a versatile tool for modeling a wide range of real life systems/processes. In particular, matrix-based expressions are obtained for the stress–strength reliability, and mean residual strength for an operating system. The results are illustrated for Erlang-type stress–strength distributions for a single unit system and a system having a general coherent structure. An example on the comparison of two multi-state units in stress–strength ordering is also presented.

KEYWORDS:

• Coherent system
• Phase-type distributions
• Residual life
• Stress–strength reliability

MATHEMATICAL SUBJECT CLASSIFICATION:

• Primary 90B25
• Secondary 62N05

Acknowledgments

The author thanks the referees for their helpful comments and suggestions that were very useful in improving this article.