Stochastic modeling and cost-benefit evaluation of consecutive k/n: F repairable retrial systems with two-phase repair and vacation. (January 2023) - Wang, Yan; Hu, Linmin; Zhao, Bing; Tian, Ruiling
Abstract: In this paper, a reliability model of consecutive k / n : F linear retrial system with two-phase repair and Bernoulli vacation is investigated, where failure may occur to all non-failed components even though the system has failed. The failed component joins retrial space and attempts repeatedly for repair if the repairman is not idle. The repairman provides two-phase repair for each component that has failed, namely the first essential repair and the second optional repair. After completing the repair of a failed component, the repairman may leave for a vacation at a probability p . The developed system model is investigated as a Markov process. Various reliability indexes are derived by means of matrix analysis, state set analysis method and the technique of solving differential equations. Numerical experiments are executed to discuss how performance indexes vary as system parameters. Moreover, the system models with and without retrial or vacation in terms of cost-benefit ratio are compared numerically. A relevant potential application is provided to illustrate the proposed model as well. Highlights: Two-phase repair and vacation are considered in consecutive k / n : F retrial system. Phase-type distribution governs the repair time of failed components in both phases. The state set analysis method is used to analyze the state probability of the system. Reliability indexes and cost-benefit ratio of the system are evaluated. System models with and without retrial or vacation are compared numerically.