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A Random Shock Model with Mixed Effect, Including Competing Soft and Sudden Failures, and Dependence

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  • Sophie Mercier

    (Université de Pau et des Pays de l’Adour)

  • Hai Ha Pham

    (Duytan University)

Abstract

A system is considered, which is subject to external and possibly fatal shocks, with dependence between the fatality of a shock and the system age. Apart from these shocks, the system suffers from competing soft and sudden failures, where soft failures refer to the reaching of a given threshold for the degradation level, and sudden failures to accidental failures, characterized by a failure rate. A non-fatal shock increases both degradation level and failure rate of a random amount, with possible dependence between the two increments. The system reliability is calculated by four different methods. Conditions under which the system lifetime is New Better than Used are proposed. The influence of various parameters of the shocks environment on the system lifetime is studied.

Suggested Citation

  • Sophie Mercier & Hai Ha Pham, 2016. "A Random Shock Model with Mixed Effect, Including Competing Soft and Sudden Failures, and Dependence," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 377-400, June.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:2:d:10.1007_s11009-014-9423-6
    DOI: 10.1007/s11009-014-9423-6
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    References listed on IDEAS

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    6. Fermín Mallor & Javier Santos, 2003. "Reliability of systems subject to shocks with a stochastic dependence for the damages," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 427-444, December.
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    Cited by:

    1. Liu, Yao & Wang, Yashun & Fan, Zhengwei & Bai, Guanghan & Chen, Xun, 2021. "Reliability modeling and a statistical inference method of accelerated degradation testing with multiple stresses and dependent competing failure processes," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    2. Sophie Mercier & Carmen Sangüesa, 2023. "A general multivariate lifetime model with a multivariate additive process as conditional hazard rate increment process," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 91-129, January.

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