Optimal maintenance strategy for multi-state systems with single maintenance capacity and arbitrarily distributed maintenance time

In engineering scenarios, failures of some components in a system may not always lead to the failure of an entire system. In such cases, the system can continuously operate while some components are being repaired. On the other hand, due to limited maintenance capacity, such as manpower and/or repair facility, maintenance actions can only be executed serially rather than in parallel. In this study, a new maintenance optimization problem for multi-state systems with single maintenance capacity is studied. The homogeneous continuous-time Markov process is used to characterize the deterioration of multi-state components in a system. In contrast to the exponential assumption for the distribution of maintenance time in most reported works, the time for each maintenance task can be arbitrarily distributed in our study. The embedded Markov chain is constructed to model the state transition process of a system by introducing decision epochs. Two optimization problems are formulated by treating either the stationary availability or the expected performance capacity of a system as an objective under the constraint of the average maintenance cost per unit time. The genetic algorithm is customized to resolve the resulting optimization problems. An illustrative example is given to demonstrate the effectiveness of the proposed method.