A Joint Redundancy and Imperfect Maintenance Strategy Optimization for Multi-State Systems

The redundancy allocation problem has been extensively studied with the aim of determining optimal redundancy levels of components at various stages to achieve the required system reliability or availability. In most existing studies, failed elements are assumed to be as good as new after repair, from a failure perspective. Due to deterioration, the repaired element cannot always be restored to a virtually new condition unless replaced with a new element. In this paper, we present an approach of joint redundancy and imperfect maintenance strategy optimization for multi-state systems. Along with determining the optimal redundancy levels, the element replacement strategy under imperfect repair is also optimized simultaneously, so as to reach the desired availability with minimal average expenditure. A generalized imperfect repair model is proposed to characterize the stochastic behavior of multi-state elements (MSEs) after repair, and a replacement policy under which a MSE is replaced once it reaches the pre-determined number of failures is introduced. The cost-repair efficiency relation, which regards the imperfect repair efficiency as a function of assigned repair cost, is put forth to provide a flexibility of assigning repair efforts strategically among MSEs. The benefits of the proposed method compared to the existing ones are demonstrated and verified via an illustrative case study of a three-stage coal transportation system.