Redundancy optimization and reliability evaluation of (k1, k2)-out-of-n: G retrial system with redundant dependency and working vacation

Complex systems usually consist of multiple types of components. During system operation, the dependencies between components and the working mechanism of maintenance devices significantly impact system reliability. In this paper, we develop a reliability model of (k1,k2)-out-of-n: G mixed standby retrial system with redundant dependency and working vacation. Two different types of components are present in the system with redundant dependencies between them. The repairman do not cease repairing failed components entirely during their vacation but rather repair failed components at a lower rate. Using Markov process theory, the transition rate matrix and steady-state equations of the system state are given, and the steady-state availability of the system is obtained. The reliability function and mean time to first failure (MTTFF) of the system are derived, and the Runge-Kutta algorithm for calculating the reliability function of the system is given. A system cost optimization model under the availability constraint is constructed using the number of standby components as the decision variable. Based on the Particle Swarm Optimization (PSO) algorithm, an optimization algorithm is designed to solve the optimal standby scheme. Through numerical experiments, the influence of system parameters on the reliability indexes and the optimal standby scheme of the system is analyzed.