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Article Citation - WoS: 22Citation - Scopus: 23On Residual Lifetime of Coherent Systems After the rth Failure(Springer, 2013) Eryilmaz, SerkanIn this article we study the residual lifetime of a coherent system after the rth failure, i.e. the time elapsed from the rth failure until the system failure given that the system operates at the time of the rth failure. We provide a mixture representation for the corresponding residual lifetime distribution in terms of signature. We also obtain some stochastic ordering results for the residual lifetimes.Article Citation - WoS: 12Citation - Scopus: 18Phase Type Stress-Strength Models With Reliability Applications(Taylor & Francis inc, 2018) Eryilmaz, SerkanThe 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.
