Optimization of selective maintenance problem with stochastic durations in mission-oriented system subjecting to [formula omitted]-dependent competing risks

Abstract

The mission-oriented systems (MOS) are often required to operate a consecutive of missions interspersed with finite breaks. For MOS, an appropriate maintenance strategy is the selective maintenance (SM). The SM problem (SMP) aims then to identify an optimal set of components to be maintained under maintenance resource constraints such as limited break durations. However, most existing SM models merely deals with either stochastic independent (s-independent) components in MOS or deterministic mission and break durations. To overcome this unrealistic restriction, this paper develops a novel SM model for optimizing the SMP in MOS operating under stochastic mission and break durations and s-dependent competing risks (CRs). Durations of missions and breaks are respectively governed by normal and uniform distributions, while the s-dependent CRs are captured by the copula function of which the unknown parameters are estimated relying on the two-stage MLE method. Furthermore, due to the stochastic break durations, an integrated importance measure (IIM) is introduced to measure the maintenance priority on selected components. The resulting SM optimization model is therefore formulated as a mixed-integer nonlinear program (MINLP) whose objective is to minimize the total cost while ensuring the required minimum mission reliability. A differential evolution (DE) algorithm is designed to solve the MINLP. Two numerical experiments are conducted on a ball screw system. Results obtained demonstrate the validity of our proposed model, in addition to the robustness of the solution algorithm designed.