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

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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.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et de leurs Applications – Pau (UMR CNRS 5142), Université de Pau et des Pays de l’Adour, Bâtiment IPRA, Avenue de l’Université, 64013, PAU Cedex, France

    Sophie Mercier

  2. Research and Development Institute, Duytan University, K7/25 Quang Trung, Da Nang, Vietnam

    Hai Ha Pham

Authors
  1. Sophie Mercier
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  2. Hai Ha Pham
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Correspondence to Sophie Mercier.

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Mercier, S., Pham, H.H. A Random Shock Model with Mixed Effect, Including Competing Soft and Sudden Failures, and Dependence. Methodol Comput Appl Probab 18, 377–400 (2016). https://doi.org/10.1007/s11009-014-9423-6

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  • DOI: https://doi.org/10.1007/s11009-014-9423-6

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