Reliability models of a series-parallel system with replacement at failure
by Nura Khalil; Ibrahim Yusuf
International Journal of Operational Research (IJOR), Vol. 40, No. 4, 2021

Abstract: The paper deals with the availability analysis of a series-parallel system consisting of four subsystems: A₁₁, B, C and A₁₂. Subsystem B contains units' b₁₁ and b₁₂ arranged in active parallel, subsystem C contains units' c₁₁ and g₁₂ arranged in active parallel. The system is exposed to two types of failure. Type I failure is a unit failure called partial failure where the failed unit is replaced with new and identical one while type II is a common cause failure to either subsystem B or C in which the failed subsystem is replaced with new one. Two probabilistic models are discussed. In model I (system without common cause failure), the system has type I failure while in model II (system with common cause failure) the system has both type I and II failure. In both models, the system has three modes: full capacity, reduced capacity and failure mode. Failure and replacement rate were assumed to be exponentially distributed. Through the transition diagram, system of first order linear differential equations were developed and solved to obtain the explicit expressions for steady-state availability. At last, some numerical examples have been taken to clarify the results.

Online publication date: Mon, 10-May-2021

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