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Parametric Estimation for Window Censored Recurrence Data

Summary: [This abstract is based on the authors' 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, this article derives 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. The authors assume independence among different sample paths. They 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.

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  • Topics: Data Quality
  • Keywords: Recurrence data, Censored data, Parametric models, Failure rate, Lognormal distribution, Maintenance, Maximum likelihood estimate (MLE), Weibull distribution, Inference procedures
  • Author: Zhu, Yada; Yashchin, Emmanuel; Hosking, J.R.M.;
  • Journal: Technometrics