Taylor Laura L, Peña Edsel A
Department of Mathematics and Statistics, Elon University, Elon.
Department of Statistics, University of South Carolina, Columbia, NC, SC.
JIRSS. 2013;12(1):153-181.
A resource-efficient approach to making inferences about the distributional properties of the failure times in a competing risks setting is presented. Efficiency is gained by observing recurrences of the competing risks over a random monitoring period. The resulting model is called the recurrent competing risks model (RCRM) and is coupled with two repair strategies whenever the system fails. Maximum likelihood estimators of the parameters of the marginal distribution functions associated with each of the competing risks and also of the system lifetime distribution function are presented. Estimators are derived under perfect and partial repair strategies. Consistency and asymptotic properties of the estimators are obtained. The estimation methods are applied to a data set of failures for cars under warranty. Simulation studies are used to ascertain the small sample properties and the efficiency gains of the resulting estimators.
提出了一种资源高效的方法，用于在竞争风险环境中对失效时间的分布特性进行推断。通过在随机监测期内观察竞争风险的复发来提高效率。由此产生的模型称为复发竞争风险模型（RCRM），并且每当系统发生故障时，该模型与两种修复策略相结合。给出了与每个竞争风险相关的边际分布函数以及系统寿命分布函数的参数的最大似然估计量。估计量是在完全修复和部分修复策略下推导出来的。获得了估计量的一致性和渐近性质。将估计方法应用于汽车保修期间的故障数据集。通过模拟研究来确定所得估计量的小样本性质和效率提升。
