A bi-objective model to optimize reliability and cost of k-out-of-n series-parallel systems with tri-state components

Redundancy allocation problem (RAP) is one way to increase system reliability. In most of the models developed so far for the RAP, system components are considered to have a binary state consisting of «working perfect» or «completely failed.» However, to suit real-world applications, this assumption has been relaxed in this paper such that components can have three states. Moreover, a bi-objective RAP (BORAP) is modeled for a system with serial subsystems, in which non-repairable tri-state components of each subsystem are configured in parallel and the subsystem works under the k-out-of-n policy. Furthermore, to enhance system reliability, technical and organizational activities that can affect failure rates of the components and hence can improve the system performance are also taken into account. The aim is to find the optimum number of redundant components in each subsystem such that the system reliability is maximized while the cost is minimized within some real-world constraints. In order to solve the complicated NP-hard problem at hand, the multi-objective strength Pareto evolutionary algorithm (SPEA-II) is employed. As there is no benchmark available, the non-dominated sorting genetic algorithm (NSGA-II) is used to validate the results obtained. Finally, the performances of the algorithms are analyzed using 20 test problems.