Optimal selective maintenance for multi-state systems under imperfect maintenance

Many systems are required to perform a series of missions with finite breaks or limited maintenance resources between successive missions. In such cases, one of the most widely used maintenance policies is a selective maintenance in which a subset of feasible maintenance actions is chosen to satisfy the subsequent mission requirements. Traditional selective maintenance optimization problems reported in the literature focus on simple binary state systems. Most of systems in industries have more than two states in the process of deterioration, however. In this paper, we consider a selective maintenance problem of multi-state systems (MSS). In order to develop a selective maintenance model, we review Kijima´s imperfect maintenance model and suggest age reduction factor as a function of cost. The extended universal generation function (UGF) is used to evaluate the probability of completing a single mission successfully. The non-linear 0-1 programming in binary selective maintenance optimization is extended to non-linear continuous programming which is difficult to solve through previously reported enumeration methods. We adapt the genetic algorithm (GA) method to solve the problem. A case study of a power station coal transportation system is presented to illustrate the proposed methodology. Finally, comparisons between the strategies with imperfect and without imperfect maintenance are given, and it is shown that incorporating imperfect maintenance quality into selective maintenance provides better solutions.