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.

本文聚焦于可修复系统的失效历程，其关联数据集包含某重复发生现象的连续事件时刻序列与事件计数指示变量。本文针对存在多种失效模式的可修复系统的失效数据分析展开研究。基于幂律过程（power-law process）的参数化框架，本文对单系统下成簇重复事件的失效数据开展研究——该模型在工业应用中已获得广泛关注。在此研究背景下可得到若干颇具价值的非标准渐近结果，本文将对其展开详细探讨。本文开展了大量仿真实验以佐证理论研究结论。此外，本文还详细研究了失效具体原因缺失场景下的方法拓展问题。本研究方法已在某汽车车队保修索赔数据库中的重复失效数据上完成应用落地。本文配套补充材料可在线获取。