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

Shijia Du, Zhiguo Zeng, Lirong Cui and Rui Kang

Reliability Engineering and System Safety, 2017, vol. 159, issue C, 134-142

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.

Keywords: Markov repairable system; Markov history-dependent repairable systems; Neglected failure; Availability; Aggregated stochastic process (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:159:y:2017:i:c:p:134-142

DOI: 10.1016/j.ress.2016.10.030

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