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

• Published in: Reliability engineering & system safety 2024-12, Vol.252, p.110431, Article 110431
• Main Authors: Wu, Bei, Limnios, Nikolaos
• Format: Article
• Language: English
• Subjects: Availability; Markov renewal equation; Numerical method; Reliability; Semi-Markov process
• ISSN: 0951-8320
• DOI: 10.1016/j.ress.2024.110431

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. •Develop numerical methods for transition probabilities of semi-Markov processes.•Analyze calculation errors and computation complexities of numerical methods.•Evaluate reliability and availability by numerical methods with traditional methods.•Propose a case study of sequential cyber-attacks to verify method effectiveness.