Markov-based reliability model for a mixed redundant system and parallel genetic algorithm with knowledge archives for a redundancy allocation problem

•The PHD applied as the components’ TTF is considered to be a general distribution.•System reliability model is established by structuring TTF distributions (PHDs).•Reliability model provides the accurate reliability of a mixed redundant system.•PGAKA dramatically reduced the computational cost of solving optimization problems. Some redundant design strategies of components are employed to enhance system reliability and are considered as a decision variable of design for reliability (DFR). The mixed redundancy is more recently suggested than other strategies; however, the reliability model for the strategy in existing studies either provides an approximated reliability or the components' time-to-failure (TTF) distributions are limited to the exponential and Erlang distributions. Thus, this study suggests a novel Markov-based reliability model that can consider various TTF distributions and an algorithm to solve the optimization problem for DFR efficiently. The model considers the TTF distribution as a generalized phase-type distribution (PHD). The PHD can describe the almost degradation patterns of components exposed to various operating environments. The model is implemented by structuring the PHDs for components considering the operating mechanism of the system, and it provides accurate system reliability. Furthermore, a parallel genetic algorithm with knowledge archives (PGAKA) with ‘parallelization’ and ‘knowledge archive’ strategies is proposed for a redundancy allocation problem (RAP). The parallelization prevents the PGAKA from prematurely converging to the local optimum and increases the chance of discovering the global optimum. The knowledge archive reduces computational costs by avoiding extra calculations by sharing search history.