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A new δ-shock model for systems subject to multiple failure types and its optimal order-replacement policy

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  • Yi Jiang

Abstract

In this article, a generalized δ -shock model with multi-failure thresholds is studied. For the new model, the system fails depending on the interval times between two consecutive shocks which arrive according to a Poisson process. The shorter interval times may cause more serious failures and thus result in longer down times and more costs for repair. Assuming that the repair is imperfect, an order-replacement policy N is adopted. Explicitly, the spare system for replacement is ordered at the end of ( N  – 1)th repair and the aging system is replaced at the N th failure or at an unrepairable failure, whichever occurs first. In addition, the system must meet the requirement of availability, that is, the long-run average operating time per unit time should not be lower than a certain level. The average cost rate C ( N ) and the stationary availability A ( N ) are derived analytically. Some convergence properties of A ( N ) and C ( N ) are also investigated. The optimal order-replacement policy N * can be obtained numerically with the constraint of availability. Finally, an illustrative example is given and some sensitivity analyses are conducted to demonstrate the proposed shock model.

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  • Yi Jiang, 2020. "A new δ-shock model for systems subject to multiple failure types and its optimal order-replacement policy," Journal of Risk and Reliability, , vol. 234(1), pages 138-150, February.
    • Handle: RePEc:sae:risrel:v:234:y:2020:i:1:p:138-150
    DOI: 10.1177/1748006X19865801
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    References listed on IDEAS

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    5. Zhao, Xian & Wang, Siqi & Wang, Xiaoyue & Cai, Kui, 2018. "A multi-state shock model with mutative failure patterns," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 1-11.
    6. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
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    Cited by:

    1. Coskun Kus & Altan Tuncel & Serkan Eryilmaz, 2022. "Assessment of Shock Models for a Particular Class of Intershock Time Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 213-231, March.
    2. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2022. "On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1627-1650, September.
    3. Stathis Chadjiconstantinidis & Altan Tuncel & Serkan Eryilmaz, 2023. "Α new mixed δ-shock model with a change in shock distribution," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 491-509, October.
    4. Mohsen Bohlooli-Zefreh & Majid Asadi & Afshin Parvardeh, 2021. "On the reliability and optimal maintenance of systems under a generalized mixed δ -shock model," Journal of Risk and Reliability, , vol. 235(5), pages 909-922, October.
    5. Yu, Xiaoyun & Hu, Linmin & Ma, Mengrao, 2023. "Reliability measures of discrete time k-out-of-n: G retrial systems based on Bernoulli shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).

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