Redundancy allocation problem in repairable k-out-of-n systems with cold, warm, and hot standby: A genetic algorithm for availability optimization

In this paper, a single-objective redundancy allocation problem (RAP) is considered for a series system with k-out-of-n subsystems. In each subsystem, the components are binary, homogeneous, and repairable. Component failure and repair processes are independent and exponentially distributed. Three standby modes of systems are considered: cold, warm, and hot. Assuming a constant number of components in the entire system, component allocation aims to maximize system availability. A continuous-time Markov chain (CTMC) model is developed to calculate system availability. A genetic algorithm (GA) is developed to optimize the system configuration. A new way of encoding chromosomes as a sequence of binary numbers that represents the priority of the subsystem in component allocation is proposed. This method achieves feasible solutions through crossover and mutation for the entire population in each generation. First, using a hybrid of GA and CTMC, research is conducted on the solution of RAP in a series system with 10 k-out-of-n subsystems. Optimal system configurations are determined for a total number of components equal to 80, 90, 100, 110, 120, and 130. Then, a sensitivity analysis is performed to determine the impact of the model parameters and the standby mode on system availability. Finally, an analysis of performance and computation time is performed depending on the parameters of the genetic algorithm. The results demonstrate the high efficiency of the GA-CTMC algorithm in solving RAP in complex technical systems. Less than 0.01 % of feasible solutions are estimated to find an optimal solution. Furthermore, GA-CTMC is distinguished by a short computation time compared to other algorithms in the literature. •The Redundancy Allocation Problem (RAP) in a series system was investigated.•Binary, homogeneous, and repairable components were considered.•An analysis of the impact of cold, warm, and hot standby on system availability was performed.•A hybrid genetic algorithm and Markov chains were developed to solve the RAP.