Probabilistic optimization of preventive maintenance inspection rates by considering correlations among maintenance costs, duration, and states transition probabilities

Abstract

Power system degradation has highly motivated utilities to perform preventive maintenance. Inadequate inspection and maintenance could lead to early failures. However, too much of them could be very costly; thus, many studies have been conducted to achieve the optimal inspection and maintenance rates. Previous studies have only considered the transition from a deterioration, repair, or inspection state to another one probabilistically. However, in practice, repair and maintenance costs and duration also vary randomly and are correlated with each other. This study proposes a probabilistic approach by considering all the aforementioned correlations and uncertainties to find the optimal inspection rates. The approach can incorporate the dependent deterioration phenomenon among different system/equipment components in the maintenance process. Additionally, a simple judgment matrix is assumed to estimate the present deterioration state before performing inspections or maintenance activities. The matrix makes classical approaches more usable from a practical point of view. A semi-Markov chain based on Monte Carlo simulations employing 95 percentiles of the total cost is utilized to determine the optimal inspection rates. Finally, the proposed method is applied to the distribution circuit breakers (CBs) of the Roy Billinton test system (RBTS) for illustration. The numerical results show that considering the correlations and uncertainties can change the optimal inspection rates and reduce the calculated costs and/or unavailability in comparison to the conventional approaches. Furthermore, the results indicate that the method is simple and accurate and can be integrated into asset management tools for the maintenance decision-making process.