Reliability analysis of a redundant series system with common cause failures and delayed vacation

• Published in: Reliability engineering & system safety Vol. 239; p. 109467
• Main Authors: Gao, Shan, Wang, Jinting, Zhang, Jie
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2023
• Subjects: Cost–benefit analysis; Delayed vacation; Markov renewal technique; Series system; Switching failure; secondary; Delayed vacation; Switching failure; Markov renewal technique; Series system; primary; Cost–benefit analysis
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2023.109467

We study a redundant series system with a single repairman in which each primary unit has a standby one. The system is subject to common cause failure (CCF), and it may also break down either when a failed primary unit is unsuccessfully switched to the standby, or when all units are down in a subsystem. If no failed units exist in the system, the repairman takes a delayed vacation. For such a system, by establishing the system’s balance equations and solving a second-order linear nonhomogeneous difference equation with variable coefficients, we first obtain the steady-state distribution of the system and derive some reliability and queueing measures. Moreover, by adopting Markov renewal technique, we carry out an extensive reliability analysis and obtain the Laplace-transform of the time to first failure starting from an arbitrary working state. Some numerical examples arising from a solar energy generating system are presented to illustrate the applicability and effectiveness of the proposed model and results. Finally, a cost-benefit discussion is presented from the perspective of economic profit analysis and some managerial insight. •Investigate a redundant series system subject to three types of failures with delayed server vacation.•Obtain the analytic expressions of various performance measures of the system.•Provide the cost benefit analysis (CBA) to get the maximum benefit with the minimum cost in decision-making.•Develop an SLSQP method for determining the optimal repair rate to minimize the expected cost function per unit time.