Multi-objective redundancy allocation problem considering instantaneous availability, reparability, interference factor and load share

Redundancy Allocation Problem (RAP) is one of the most well-known and widely applicable optimization problems that has been considered by the researchers and designers over the recent decades. Several factors influence the redundancy allocation decisions in a system. Some of these factors are as follows: availability in repairable systems, redundant system configuration in parallel or standby systems, and time and dependent failures in case of common cause factors (CCF) and load share. These features should be incorporated into the RAP modeling to obtain logical/realistic solutions. In this paper, a RAP in a k-out-of-n system by considering several features of availability, reparability, interference factor, and load sharing is formulated. The Markov chain is used to formulate the RAP and the repair rate is assumed to be dependent on the number of repairmen. In other words, it is assumed that the higher the number of repairmen is, the higher the repair rate and as a result, the higher the availability of the system is; however, in real situations, it is possible that the excessive increase in the number of repairmen decreases the availability due to the repairmen work interference. To resolve this problem, a parameter called interference factor is defined and incorporated into the modeling and calculations for each subsystem. RAP is among the optimization problems that are categorized under NP-hard class of problems. Therefore, NSGA-II algorithm is utilized to solve the proposed model. Finally, a special problem is solved as a sample and the obtained results are discussed.