Monte Carlo method for reliability of parallel system with dependent failures of component

A problem of parallel system reliability with dependent failures of components is presented in the paper. It is assumed that lifetimes of components are independent random variable having Weibull distribution. We take under consideration a parallel (in reliability meaning) system consisting of n independent at the beginning of work and identical components. We assume that a load of the working system affects on the reliability of its components and the load of the system is distributed on all working components. Therefore, a failure rate of each component is changeable during run of the system and depends on a number of working elements at this point in time. As a model of the system failures we construct a stochastic process which value at the moment t denotes the number of working components. Generally it is neither Markov nor semi-Markov process. To assess the reliability characteristics of the system we simulate this stochastic process using the Monte-Carlo method and we calculate values of nonparametric kernel density and reliability functions estimators.

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Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).