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System availability in a shock model under preventive repair and phase‐type distributions

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  • Delia Montoro‐Cazorla
  • Rafael Pérez‐Ocón

Abstract

A device that can fail by shocks or ageing under policy N of maintenance is presented. The interarrival times between shocks follow phase‐type distributions depending on the number of cumulated shocks. The successive shocks deteriorate the system, and some of them can be fatal. After a prefixed number k of nonfatal shocks, the device is preventively repaired. After a fatal shock the device is correctively repaired. Repairs are as good as new, and follow phase‐type distributions. The system is governed by a Markov process whose infinitesimal generator, stationary probability vector, and availability are calculated, obtaining well‐structured expressions due to the use of phase‐type distributions. The availability is optimized in terms of the number k of preventive repairs. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • Delia Montoro‐Cazorla & Rafael Pérez‐Ocón, 2010. "System availability in a shock model under preventive repair and phase‐type distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(6), pages 689-704, November.
    • Handle: RePEc:wly:apsmbi:v:26:y:2010:i:6:p:689-704
    DOI: 10.1002/asmb.811
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    Cited by:

    1. Dembińska, Anna & Eryilmaz, Serkan, 2021. "Discrete time series–parallel system and its optimal configuration," Reliability Engineering and System Safety, Elsevier, vol. 215(C).

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