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Semi-Markov Reliability Model of the Cold Standby System
Keywords
: semi-Markov process, perturbed process, reliability model, renewal standby system
Abstract
The semi-Markov reliability model of the cold standby system with renewal is presented in the paper. The model is some modification of the model that was considered by Barlow & Proshan (1965), Brodi & Pogosian (1978). To describe the reliability evolution of the system, we construct a semi-Markov process by defining the states and the renewal kernel of that one. In our model the time to failure of the system is represented by a random variable that denotes the first passage time from the given state to the subset of states. Appropriate theorems from the semi-Markov processes theory allow us to calculate the reliability function and mean time to failure. As calculating an exact reliability function of the system by using Laplace transform is often complicated we apply a theorem which deals with perturbed semi-Markov processes to obtain an approximate reliability function of the system.