Joint optimization of redundancy level and spare parts for redundant system based on Markov process

To reasonably and efficiently decrease the life cycle cost of a redundant system, this paper proposes an availability model of a k/n based on the Markov process and mixed criterion to perform joint optimization of spare parts inventory allocation and the redundancy level, by considering the failure process, maintenance turnover and the ordering and replenishment process of spare parts. The availability model is firstly established through the formula of system failure rate and maintenance rate in hot standby and cold standby modes. Then the life cycle cost is calculated based on the steady-state probability, and the joint optimization algorithm of spare parts inventory allocation and the redundancy level is used to solve the model. Finally, the correctness of the availability model is validated and the validity of the joint optimization is verified by numerical calculation. Through the numerical calculation results, it is shown that the proposed availability model is an improvement of the traditional model and processes the universality. The joint optimization results show that the redundancy system availability increases with the increase of the redundancy level and the spare parts inventory. However, further improvement of availability will lead to a sharp increase in cost when it is close to 1. The proportion of spare parts inventory cost is the highest in the life cycle cost, while the spare parts ordering cost is the lowest. Compared with the method that only considers spare parts inventory optimization, the life cycle cost of the joint optimization method is reduced by 8.01%. © 2019, Editorial Office of Systems Engineering and Electronics. All right reserved.