Phase type stress-strength models with reliability applications

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.