In today’s competitive markets, quality is a fundamental pillar for organizational survival. One important dimension of quality is reliability; therefore, improving reliability is considered essential. To enhance system reliability, approaches such as adding redundant and standby components can be employed, and an optimal design can be developed using available system data. In some cases, system data lack sufficient accuracy, and fuzzy logic is used to enable more precise analysis. In many practical applications, in addition to improving system reliability, other objectives such as minimizing system weight, volume, or cost are also considered in optimal design. Since these objectives are conflicting, the system design problem becomes a multi-objective optimization problem.
In this paper, a mathematical model is proposed with the objectives of maximizing reliability and minimizing cost for multi-stage series–parallel, standby, and k-out-of-n systems, subject to system volume and weight constraints. The decision variables in this problem are the optimal number of redundant components allocated to each stage. Finally, a numerical example is presented in which system component reliability over the life cycle is considered, and the cost, volume, weight, and failure rate parameters of components are modeled as triangular and trapezoidal fuzzy numbers. The resulting model is solved using the metaheuristic simulated annealing algorithm, and a set of Pareto-efficient solutions is obtained. The results indicate that standby systems achieve higher reliability compared to the other system configurations.