Reliability of load-sharing systems subject to proportional hazards model

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This paper presents a new model for load-sharing systems using k-out-of-n structure. It is assumed that the failure distribution of each component at a baseline load follows a general failure time distribution. Hence, the model can be used for analyzing the systems where components' failure times follow Weibull, Gamma, Extreeme Value, and Lognormal distributions. In a load-sharing system, the system components experience different loads at different time intervals due to the load-sharing policy. Therefore, to analyze the reliability of load-sharing systems, the failure rate of each component must be expressed in terms of the current load and the current age of the component. In this paper, the load-dependent time-varying failure rate of a component is expressed using Cox's proportional hazards model (PHM). According to the PHM the effects of the load is mulitplicative in nature. In other words, the hazard (failure) rate of a component is the product of both a baseline hazard rate, which can be a function of time t, and a multiplicative factor which is function of the current load on the component. The load-sharing model also considers the switchover failures at the time of load redistribution. We first show that the model can be described using a non-homogeneous Markov chain. Therefore, for the non-identical component case, the system reliability can be evaluated using well established methods for non-homogenerous Markov chains. In addition, when all components are identical, the paper provides a closed-form expression for the system reliability even when the underlying baseline failure time distribution is non-exponential. The method is demonstrated using a numerical example with components following Weibull baseline failure time distribution. The numerical results from non-homogeneous Markov chains, closed-form expressions, and Monte Carlo simulation are compared.