Sequence optimization in reliability problems with a mixed strategy and heterogeneous backup scheme

•This paper revisits the redundancy allocation problem with heterogeneous backup scheme (RAPMC).•The problem is investigated when mixed strategy is used for the redundant components.•For the first time, a Markov chain model is proposed for exact calculation of reliability in the RAPMC models.•Results demonstrate that the proposed Markov model leads to better results with higher reliability values. The redundancy allocation problem (RAP) is an interesting area of research in reliability optimization. A common constraint underlying most models developed for the RAP requires system designers to develop subsystems comprising homogeneous components. It is, however, impossible to achieve desirably high system reliability levels under this constraint. The present study is an effort to relax this constraint and to employ heterogeneous components in a subsystem; which will not only ensure higher system reliabilities but also offer more design options since the sequence of components is thus given in advance. For the purposes of this study, the mixed redundancy strategy with an imperfect switching mechanism is considered. A mathematical model based on the continuous-time Markov chain (CTMC) method is developed, which allows system reliability to be calculated exactly since it is sensitive to component sequencing. As RAP belongs to the NP-hard class of optimization problems, a modified genetic algorithm (GA) is implemented to solve the proposed model. The results obtained indicate the superior performance of the proposed CTMC model in improving system reliability.