Optimal selective maintenance decisions for large serial k-out-of-n: G systems under imperfect maintenance

Highlights: • The selective maintenance problem for large serial k-out-of-n:G systems is studied. • Imperfect maintenance levels are considered for both PM and CM actions. • Two nonlinear and two BIP formulations are proposed. • Experiments show the efficiency of the new 2-phase approach for complex structures. The selective maintenance problem (SMP) arises in many large multicomponent systems which are operated for consecutive missions interspersed with finite breaks during which only a selected set of component repairs or replacements can be carried out due to limited time, budget, or resources. The problem is to decide which components and degree of repairs should be performed in order to guarantee a pre-specified performance level during the subsequent mission. Current SMP formulations in the literature are nonlinear, deal mainly with basic or series-parallel systems and mostly use heuristic methods to obtain solutions. This paper introduces the first SMP model for serial k-out-of-n systems. Two nonlinear formulations are developed, which can be used to solve the problem for small to moderate size k-out-of-n systems. For large k-out-of-n systems or complex reliability structures, we develop a new two-phase approach which transforms the problem into a multidimensional multiple-choice knapsack problem (MMKP). The new approach is shown to be efficient through multiple sets of numerical experiments.