Reliability analysis of Markov history-dependent repairable systems with neglected failures

Abstract : Markov history-dependent repairable systems refer to the Markov repairable systems in which some states are changeable and dependent on recent evolutional history of the system. In practice, many Markov history-dependent repairable systems are subjected to neglected failures, i.e., some failures do not affect system performances if they can be repaired promptly. In this paper, we develop a model based on the theory of aggregated stochastic processes to describe the history-dependent behavior and the effect of neglected failures on the Markov history-dependent repairable systems. Based on the developed model, instantaneous and steady-state availabilities are derived to characterize the reliability of the system. Four reliability-related time distributions, i.e., distribution for the k th working period, distribution for the k th failure period, distribution for the real working time in an effective working period, distribution for the neglected failure time in an effective working period, are also derived to provide a more comprehensive description of the system's reliability. Thanks to the power of the theory of aggregated stochastic processes, closed-form expressions are obtained for all the reliability indexes and time distributions. Finally, the developed indexes and analysis methods are demonstrated by a numerical example.
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Submitted on : Tuesday, January 21, 2020 - 5:40:22 PM
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Shijia Du, Zhiguo Zeng, Lirong Cui, Rui Kang. Reliability analysis of Markov history-dependent repairable systems with neglected failures. Reliability Engineering and System Safety, 2017, 159, pp.134-142. ⟨10.1016/j.ress.2016.10.030⟩. ⟨hal-02447684⟩

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