A Joint Reliability and Imperfect Opportunistic Maintenance Optimization for a Multi‐State Weighted k‐out‐of‐n System Considering Economic Dependence and Periodic Inspection

This paper formulates a model to simultaneously optimize the redundancy and imperfect opportunistic maintenance of a multi‐state weighted k‐out‐of‐n system. Different from existing approaches that consider binary or multi‐state elements, our approach considers modular redundancy in which each module/subsystem is composed of several multi‐state components in series. The status of each component is considered to degrade with use. Therefore, a new condition‐based opportunistic maintenance approach using three different thresholds for a component health state is developed. The objective is to determine 1) the minimal‐cost of k‐out‐of‐n system structure, 2) optimal imperfect opportunistic maintenance strategy, 3) optimal maintenance capacity, and 4) optimal inspection interval subject to an availability constraint. System availability is defined as the ability to satisfy consumer demand. Based on the three‐phase approach, a simulation procedure is used to evaluate the expected multi‐state system availability and life cycle costs. Also, a multi‐seed Tabu search heuristic algorithm with a proper neighborhood generation mechanism is proposed to solve the formulated problem. An application to the optimal design of a wind farm is provided to illustrate the proposed approach. Sensitivity analysis is conducted to discuss the influence of the different parameters of the simulation model. Copyright © 2017 John Wiley & Sons, Ltd.