Fleet Service Reliability Analysis of Self-Service Systems Subject to Failure-Induced Demand Switching and a Two-Dimensional Inspection and Maintenance Policy

A fleet of self-service systems, such as electric vehicle charging piles (EVCPs), is usually installed in a specific location. During operation, these systems are subject to random failures. However, they are usually operated without on-site staff. It is quite common that a customer may switch to other unoccupied systems for service when the initially selected system is found to have failed or fails during service. This is called failure-induced demand switching (FDS). With continuous customer arrivals and system failures, such FDS events occur repeatedly and interact dynamically, making modeling and enhancing service levels quite difficult. The challenge becomes even greater when a unique two-dimensional inspection and maintenance (IM) policy is adopted to handle the maintenance needs of self-service systems in hopes of retaining their service level with respect to long-run demand satisfaction. In this paper, we investigate the long-term service reliability of a fleet of self-service systems subject to FDS and a two-dimensional IM policy. First, we model the fleet state transition process and characterize its analytical properties. Next, we measure the fleet’s long-term service reliability and obtain the analytical expressions for crucial service level metrics, such as the expected number of failed systems, the expected length of an operation cycle, and service reliability loss due to imperfect monitoring. The managerial implications regarding the selections of EVCPs and IM policy are proposed based on a numerical study of two fleets of EVCPs in Hong Kong. These implications are expected to assist the operators in ensuring fleet service levels in the long run at a minimal operation and maintenance cost. Note to Practitioners—This paper models the service reliability of a fleet of self-service systems (e.g., EVCPs) over time. Service reliability, reflecting the fleet’s service level, is defined as the proportion of demands being fulfilled and is of the utmost concern of system operators. However, under repeated FDS due to continuous customer arrivals and system failures, it is difficult to assess the fleet’s service reliability using existing methodologies. The task becomes more challenging when failures of such systems are not perfectly detected in practice. This paper develops mathematical models and a novel two-dimensional inspection and maintenance policy to overcome the technical barriers. The models enable assessing the service reliability of various self-service systems experiencing non-constant service rates. Two case studies of fleets of AC and DC EVCPs in Hong Kong are provided to demonstrate the practical applicability of the proposed models. Indeed, the core findings of this work assist practitioners in: (i) finding the optimal maintenance policy that maximizes the fleet’s service reliability, (ii) assessing the service reliability loss due to imperfect failure detection, and (iii) evaluating the sensitivity of the optimal service reliability with respect to the customer arrival rate, system failure rate, and customer behavior in reporting system failures. We also show that the proposed models provide the exact solutions to the above-mentioned metrics when the maintenance duration is longer than the service duration.