# Parametric estimation for window censored recurrence data

## Abstract

Many applications, in particular the failure, repair, and replacement of industrial components or physical infrastructure, involve recurrent events. Frequently, the available data are window-censored: only events that occurred during a particular interval are recorded. Window censoring presents a challenge for recurrence data analysis. For statistical inference from window censored recurrence data, we derive the likelihood function for a model in which the distributions of inter-recurrence intervals in a single path need not be identical and may be associated with covariate information. We assume independence among different sample paths. We propose a distribution to model the effect of external interventions on recurrence processes. This distribution can represent a phenomenon, frequently observed in practice, that the probability of process regeneration increases with the number of historical interventions; for example, an item that had a given number of repairs is generally more likely to be replaced in the wake of a failure than a similar item with a smaller number of repairs. The proposed model and estimation procedure are evaluated via simulation studies and applied to a set of data related to failure and maintenance of water mains. This article has online supplementary material. © 2014 American Statistical Association and the American Society for Quality TECHNOMETRICS.