Optimal reliability design of a system with k-out-of-n subsystems considering redundancy strategies

•Markov chains for describing the mechanisms of k-out-of-n systems are introduced.•The Markov chains provide the various characteristics for the system lifetime.•Approximation error of a previous reliability model is analyzed.•The error could have an effect on the decision making for the reliability design.•New versions of reliability optimization problems are proposed. This study presents new reliability models for k-out-of-n systems using a structured continuous-time Markov chain. The approach makes it comfortable to identify the characteristics of the lifetime of the system, such as reliability and expected lifetime. To demonstrate the advantage, the analysis results of them for the multi-spectral camera system, which is the only payload of Korea multi-purpose satellite-2 as an example of a real system. Furthermore, existing studies on a k-out-of-n system with standby redundancy has provided the approximated reliability for it. In this paper, it is confirmed that the approximation error could have an effect on the reliability design for a system. Moreover, new versions of reliability optimization problems, redundancy allocation problem (RAP) and reliability-redundancy allocation problem(RRAP), are proposed. In order to maximize system reliability, they further determine the redundancy strategy, either active or standby redundancy for each k-out-of-n subsystem from the traditional problems. A parallel genetic algorithm is proposed for an RRAP modeled by nonlinear mixed integer programming.