Optimal design of a multi-state system with uncertainty in supplier selection

•A stochastic model for redundancy and maintenance of a multi-state k-out-of-n system is developed.•The uncertain behavior of components suppliers is considered.•Three phase simulation method is developed to evaluate important performance measures of the system.•A multi-objective ant colony optimization algorithm is applied.•Numerical application to the optimal design of a 6 MW wind farm is provided.

This paper formulates a bi-objective two-stage stochastic programming model simultaneously for two conditions including a joint modular redundancy allocation, and an imperfect opportunistic maintenance optimization of a multi-state weighted k-out-of-n system. Although categorizing system elements based on cost and reliability characteristics is addressed by literature, this paper categorizes system elements considering the uncertain behavior of suppliers. Further more in this paper a condition based maintenance method is developed considering economic dependence and fixed inspection intervals. The objective is to determine jointly (1) an optimal system structure, (2) an imperfect opportunistic maintenance strategy, and (3) inspection intervals. This proposed approach not only is capable of minimizing the system life cycle cost, but also it addresses maximizing system availability. A three-phase simulation procedure is used to evaluate the performance terms of the studied system for several scenarios. To illustrate the proposed approach an optimal design of a wind farm is also provided. Sensitivity analysis is also investigated in this paper. To obtain Pareto optimal solutions, a multi-objective version of ant colony optimization is used.