Modeling of dependent competing risks by first passage times of Wiener processes

Abstract

Consider the competing risks situation for a component which may be subject to either a failure or a preventive maintenance action, where the latter will prevent the failure. It is then reasonable to expect a dependence between the time to failure and the time to preventive maintenance. This paper briefly reviews some modeling approaches and introduces a new approach based on modeling of the degradation of a component by means of Wiener processes, with failure corresponding to the first crossing of a certain level, and potential time for maintenance corresponding to the crossing of a certain lower degradation level.

Keywords:

• Competing risks
• first passage time
• random signs censoring

Acknowledgements

The authors would like to thank two referees for their instructive comments and suggestions which helped to improve the paper. The first author thanks Roger Cooke for stimulating discussions on competing risks and random signs censoring. It is worth mentioning that Roger Cooke did his initial work on random signs while on sabbatical at University of California, Berkeley, working with Richard Barlow.