A comparative study of numerical methods for reliability assessment based on semi-Markov processes

Bei Wu and Nikolaos Limnios

Reliability Engineering and System Safety, 2024, vol. 252, issue C

Abstract: The semi-Markov process, renowned for its versatile applications, has garnered significant attention in recent years. However, deriving closed-form expressions for computing reliability metrics proves challenging when sojourn times deviate from exponential distributions. This paper investigates three numerical techniques for computing the transition function matrix of the semi-Markov process, including the algebraic method, the truncated method, and the iterative method. It delves into their truncation and discretization errors, as well as their computational complexities. Additionally, the Laplace-based method and the semi-Markov-chain-based method are discussed to contrast their effectiveness with the three devised numerical approaches. Building on the linkage between the Markov renewal equation and system reliability metrics, five computational methods are applied to the evaluation of system reliability and availability. A case study on sequential cyber-attacks is presented to illustrate the applicability of these methods, considering sojourn times that follow exponential, gamma, lognormal, and Weibull distributions respectively. The results reveal that the three proposed numerical methods not only achieve high precision and rapid speed but also address scenarios beyond the capability of the Laplace-based method.

Keywords: Semi-Markov process; Numerical method; Markov renewal equation; Reliability; Availability (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:252:y:2024:i:c:s0951832024005039

DOI: 10.1016/j.ress.2024.110431

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