Delayed Reporting of Faults in Warranty Claims

In this article, we present a model for delayed reporting of faults: multiple nonfatal faults are accumulated and then simultaneously reported and repaired. The reporting process is modeled as a stochastic process dependent on the underlying stochastic process generating the faults. We derive the joint distribution of the reporting times and numbers of reported faults, giving general results and results specific to faults generated by a Poisson process. We investigate a number of extensions to the basic model, including multiple fault types (including invisible and fatal faults), preventative maintenance, and customer rush. We show how to simulate from the model and implement maximum likelihood parameter estimation in a simulated dataset and a real dataset of warranty claims from a car manufacturer.