Redundancy strategies assessment and optimization of k-out-of-n systems based on Markov chains and genetic algorithms

Abstract

The existing reliability formulation regarding mixed and K-mixed strategies considers only one component as the minimum number of required components for each subsystem. In this paper, we develop a Continuous-Time Markov Chain model for both mixed and K-mixed strategies while the minimum number of required components can be more than one and take any values. In addition, the drawbacks of the classical model, which are complicated formulation, approximate solution and time-consuming problem-solving process, have been addressed. The proposed model estimates the reliability under different redundancy strategies more efficiently and in a straightforward way. To validate the proposed approach, a sequential Monte Carlo model is also developed for the reliability analysis. Besides, the existing strategies are applied to a series-parallel system and an efficient genetic algorithm is developed to solve the resulting optimization problem. The numerical results confirm the accuracy of the Continuous-Time Markov Chain model in estimating k-out-of-n system reliability under standby, mixed and K-mixed strategies with a major reduction in the computation time.