Reliability evaluation of a system with active redundancy strategy and load-sharing time-dependent failure rate components using Markov process

• Published in: Communications in statistics. Theory and methods 2023-07, Vol.52 (13), p.4514-4533
• Main Authors: Sharifi, Mani, Pourkarim Guilani, Pedram, Zaretalab, Arash, Abhari, Abdolreza
• Format: Article
• Language: English
• Subjects: Computational efficiency; Computing time; Failure rates; Load sharing; Markov analysis; Markov process; Markov processes; Redundancy; Reliability; Reliability analysis; simulation; System reliability; Time dependence; time-dependent failure rates; Weibull distribution
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2021.1995433

Due to the high sensitivity in applying electronic and mechanical equipment in functional systems, creating conditions to increase a system's reliability is always critical for system designers. In most of the studies in the reliability area, it is assumed that the failure rates of the system's components are constant but considering time-dependent failure rates for the components is more realistic and draws the models near to real conditions. This paper presents a framework to use Markov process to obtain the system's reliability under some assumptions. In this regard, we worked on a load-sharing system with identical time-dependent failure rate components and used Markov process to calculate the system reliability. First, we define the requirements for using Markov process, and it is shown that it is possible to use it to calculate the considered system's reliability. Then, a formula is presented to calculate the reliability of the considered system using the Markov process through solving the Chapman Kolmogorov equation, when the components' life has Weibull Distribution. Next, we validate the results of the presented formula using the simulation technique. Finally, we compare the computational time of the proposed model for solving large-size problems with the simulation technique. The results show the superiority of the proposed model in terms of computational time.