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.