An Accelerated Model for Recurrence Data

Abstract

Recurrence data usually come from sampling a system in different ages. It is common in areas of manufacturing, reliability, medicine, and risk analysis. In this article, an accelerated model for recurrence data is proposed. The model is based on the time between failures (TBFs) for an accelerated time regression method using the number of failures as a dummy covariate. Using this model, the repair (or cure) effect can also be studied. A graphical display of recurrence data created by plotting the log-TBFs versus the number of failures is proposed to detect any linear or nonlinear trend for log-TBFs. The model is then extended to incorporate covariates and/or time factors. Two data sets are used to demonstrate the usefulness of the proposed model.

Keywords:

• Age-dependent repair
• Age-free repair
• First failure time
• Recurrent events
• Renewal processes
• Time between failures

Mathematics Subject Classification:

• Primary 62N05
• Secondary 90B25

Acknowledgments

The author is grateful to the editor-in-chief and a referee for their constructive suggestions and comments that substantially improved this article.