Imperfect rail-track inspection scheduling with zero-inflated miss rates

Despite the technological advances in track monitoring, track quality control systems are not always reliable. Inspections may miss defects; all defects may not be registered or recorded due to human or mechanical errors. In this study, first, we develop a zero-inflated Bayesian approach to model the rate of missed defects during imperfect inspections where defect arrivals follow a Poisson process. The proposed model reveals information on two parameters: the actual defect arrival rate and the probability of not finding any defects, namely, the zero-inflation rate. Then, we study optimizing the track maintenance based on this model. We demonstrate that a temporal threshold-type inspection policy is optimal, and we derive this threshold under imperfect inspections. Furthermore, we implement a Gibbs sampler for drawing inferences on the posterior distribution of the aforementioned Poisson process parameters from data. Application results provide a realistic perspective on imperfect inspections and offer risk and cost savings in railway systems and, by and large, in other imperfect maintenance systems.