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Article

Reliability Evaluation and Optimization of a System with Mixed Run Shock

by
Yanqing Wen
,
Baoliang Liu
*,
Haiyan Shi
,
Shugui Kang
and
Yuejiao Feng
School of Mathematics and Statistics, College of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China
*
Author to whom correspondence should be addressed.
Axioms 2022, 11(8), 366; https://doi.org/10.3390/axioms11080366
Submission received: 9 July 2022 / Revised: 24 July 2022 / Accepted: 25 July 2022 / Published: 27 July 2022
(This article belongs to the Special Issue Stochastic Processes: Theory and Application)
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Abstract

In this paper, we investigate a wear and mixed shock model in which the system can fail due to internal aging or external shocks. The lifetime of the system, due to internal wear, follows continuous phase-type (PH) distributions. The external random shocks arrive at the system according to a PH renewal process. The system will fail when the internal failure occurs or k1 consecutive external shocks, the size of at least d1 or k2 consecutive external shocks the size of at least d2 occur, where d1<d2, k1>k2. The failed system can be repaired immediately, and the repair times of the system are governed by continuous PH distributions. The system can be replaced by a new and identical one based on a bivariate replacement policy (L,N). The long-run average profit rate for the system is obtained by employing the closure property of the PH distribution. Finally, a numerical example is also given to determine the optimal replacement policy.
Keywords: competing failure processes; mixed shock model; phase-type distribution; geometric process; average profit rate competing failure processes; mixed shock model; phase-type distribution; geometric process; average profit rate

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MDPI and ACS Style

Wen, Y.; Liu, B.; Shi, H.; Kang, S.; Feng, Y. Reliability Evaluation and Optimization of a System with Mixed Run Shock. Axioms 2022, 11, 366. https://doi.org/10.3390/axioms11080366

AMA Style

Wen Y, Liu B, Shi H, Kang S, Feng Y. Reliability Evaluation and Optimization of a System with Mixed Run Shock. Axioms. 2022; 11(8):366. https://doi.org/10.3390/axioms11080366

Chicago/Turabian Style

Wen, Yanqing, Baoliang Liu, Haiyan Shi, Shugui Kang, and Yuejiao Feng. 2022. "Reliability Evaluation and Optimization of a System with Mixed Run Shock" Axioms 11, no. 8: 366. https://doi.org/10.3390/axioms11080366

APA Style

Wen, Y., Liu, B., Shi, H., Kang, S., & Feng, Y. (2022). Reliability Evaluation and Optimization of a System with Mixed Run Shock. Axioms, 11(8), 366. https://doi.org/10.3390/axioms11080366

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