Reliability analysis and optimization for a redundant system with dependent failures and variable repair rates

This paper considers the reliability analysis and the bi-objective optimal problem for a redundant system with two dependent failures: common cause failure (CCF) and load-sharing failure, where the system contains N active components, W warm standbys and C cold standbys, a K-mixed redundancy strategy is considered. In the system, there is a repair team providing variable repair rates according to differential situations: when there are standby components available in the system, the repair team assigns a regular repairman to repair the failed components, with the known fact that regular repairman is not as skilled as an expert repairman in doing some complex repair; when all the spares are exhausted, the repair team assigns an expert repairman to attend failed components; when the system breaks down due to a CCF's occurrence, the repair team provides a very special repair service to restore the system to normal working state. The steady-state distribution of the system is obtained by matrix-analytic method. The sets of equations satisfied by the reliability functions and transient availabilities from arbitrary initial state are respectively presented and solved by Markov renewal theory, Laplace-Stieltjes transform (LST) and Laplace transform (LT) technique. Based on the obtained results, sensitivity analysis is performed by some numerical experiments. From economic view point, the bi-objective optimization problem is constructed and solved by NSGA-II algorithm for the minimal expected total cost and maximal availability.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.