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A stochastic alternating renewal process model for unavailability analysis of standby safety equipment

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  • van der Weide, J.A.M.
  • Pandey, Mahesh D.

Abstract

The paper presents a stochastic approach to analyze instantaneous unavailability of standby safety equipment caused by latent failures. The problem of unavailability analysis is formulated as a stochastic alternating renewal process without any restrictions on the form of the probability distribution assigned to time to failure and repair duration. An integral equation for point unavailability is derived and numerically solved for a given maintenance policy. The paper also incorporates an age-based preventive maintenance policy with random repair time. In case of aging equipment, the asymptotic limit or average unavailability should be used with a caution, because it cannot model an increasing trend in unavailability as a result of increasing hazard rate (i.e. aging) of the time to failure distribution.

Suggested Citation

  • van der Weide, J.A.M. & Pandey, Mahesh D., 2015. "A stochastic alternating renewal process model for unavailability analysis of standby safety equipment," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 97-104.
    • Handle: RePEc:eee:reensy:v:139:y:2015:i:c:p:97-104
    DOI: 10.1016/j.ress.2015.03.005
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    References listed on IDEAS

    as
    1. Li, Xiaohu & Zuo, Ming J. & Yam, Richard C.M., 2006. "Reliability analysis of a repairable k-out-of-n system with some components being suspended when the system is down," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 305-310.
    2. John J. Coleman & I. Jack Abrams, 1962. "Mathematical Model for Operational Readiness," Operations Research, INFORMS, vol. 10(1), pages 126-138, February.
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    Citations

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    Cited by:

    1. Shen, Lijuan & Cassottana, Beatrice & Tang, Loon Ching, 2018. "Statistical trend tests for resilience of power systems," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 138-147.
    2. Alberti, Alexandre R. & Cavalcante, Cristiano A.V., 2020. "A two-scale maintenance policy for protection systems subject to shocks when meeting demands," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    3. Chun Su & Longfei Cheng, 2018. "An availability-based warranty policy considering preventive maintenance and learning effects," Journal of Risk and Reliability, , vol. 232(6), pages 576-586, December.
    4. Radim Briš & Pavel Jahoda, 2022. "Really Ageing Systems Undergoing a Discrete Maintenance Optimization," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    5. Zhao, Qian Qian & Yun, Won Young, 2018. "Determining the inspection intervals for one-shot systems with support equipment," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 63-75.
    6. Chen, Ying & Wang, Ze & Li, YingYi & Kang, Rui & Mosleh, Ali, 2018. "Reliability analysis of a cold-standby system considering the development stages and accumulations of failure mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 1-12.
    7. Briš, Radim & Byczanski, Petr & Goňo, Radomír & Rusek, Stanislav, 2017. "Discrete maintenance optimization of complex multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 80-89.
    8. Radim Briš & Petr Byczanski, 2017. "On innovative stochastic renewal process models for exact unavailability quantification of highly reliable systems," Journal of Risk and Reliability, , vol. 231(6), pages 617-627, December.

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