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Reliability analysis of semi-Markov systems with restriction on transition times

Bei Wu, Lirong Cui and Chen Fang

Reliability Engineering and System Safety, 2019, vol. 190, issue C, -

Abstract: In this paper, a competing risk model with a restriction on transition times for semi-Markov multi-state repairable systems is proposed. The states of semi-Markov systems can be divided into three categories: a normal working subset, a defective working subset and a breakdown subset which contains an absorbing state where the system cannot escape once entering it. If the number of transitions between the normal and defective working subsets exceeds a given value, the system will be abandoned due to the high maintenance costs. The theory of aggregated stochastic process is employed to obtain the closed-form formulas of the probabilities of competing risks, distributions of survival times and point-wise availabilities. An integer nonlinear programming is presented which enables the system to satisfy the prescribed performance requirements and control its economic cost. A corresponding algorithm for solving the integer nonlinear programming is provided to find the optimal number of transition times. Two numerical examples including Markov process and semi-Markov process are conducted to illustrate the obtained results and proposed methods finally.

Keywords: Semi-Markov process; Point-wise availability; Competing risk; Integer nonlinear programming; Multi-state system (search for similar items in EconPapers)
Date: 2019
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