Reliability analysis and optimization design of a repairable k-out-of-n retrial system with two failure modes and preventive maintenance

This article deals with a repairable k-out-of-n: G system with retrial feature and two maintenance policies. All components in the system have two failure modes, mode a failure and mode b failure. When a component fails, the failed component will be repaired instantly if the repair equipment is idle. Otherwise, it enters into a retrial orbit and tries again after some time until it is repaired. The single repair equipment may be subject to breakdown in a busy period, and in order to improve system reliability, the idle repair equipment will be performed preventive maintenance. The Markov process theory and Laplace transform method are adopted to compute the reliability indexes of the system. Also, four optimization design models are constructed to determine the optimal repair rates of the components with two failure modes, and the minimization problems of the total expected cost function per unit time and the cost-effectiveness ratio are solved. To verify the correctness of the model, numerical analysis is executed to demonstrate the impact of each parameter on system reliability indexes, the optimal solutions of different optimization design models are obtained by using differential evolution algorithm and genetic algorithm.