Statistical Inference for Power-Law Process With Competing Risks

The focus of this article is on failure history of a repairable system for which the relevant data comprise successive event times for a recurrent phenomenon along with an event-count indicator. We undertake an investigation for analyzing failures from repairable systems that are subject to multiple failure modes. Failure data representing a cluster of recurrent events from a single system are studied under the parametric framework of a <i>power-law process</i>, a model that has found considerable attention in industrial applications. Some interesting and nonstandard asymptotic results ensue in this context that are discussed in detail. Extensive simulation has been carried out that supplements the theoretical findings. An extension to the case where the specific cause of failure may be missing is investigated in detail. The methodology has been implemented on recurrent failure data obtained from a warranty claim database for a fleet of automobiles. Supplementary material for this article is available online.