Warranty return data from repairable systems, such as home appliances, lawn mowers, computers and automobiles, result in recurrent event data. The nonhomogeneous Poisson process (NHPP) model is used widely to describe such data. Seasonality in the repair frequencies and other variabilities, however, complicate the modeling of recurrent event data. Not much work has been done to address the seasonality, and this paper provides a general approach for the application of NHPP models with dynamic covariates to predict seasonal warranty returns. The methods presented here, however, can be applied to other applications that result in seasonal recurrent event data. A hierarchical clustering method is used to stratify the population into groups that are more homogeneous than the overall population. The stratification facilitates modeling the recurrent event data with both time-varying and time-constant covariates. We demonstrate and validate the models using warranty claims data for two different types of products. The results show that our approach provides important improvements in the predictive power of monthly events compared with models that do not take the seasonality and covariates into account.

中文翻译：

---

基于定期事件数据的季节性保修预测

来自可修复系统（例如家用电器，割草机，计算机和汽车）的保修返回数据会导致重复事件数据。非均匀泊松过程（NHPP）模型被广泛用于描述此类数据。然而，维修频率的季节性和其他可变性使重复事件数据的建模变得复杂。解决季节性问题并没有做很多工作，本文为使用带有动态协变量的NHPP模型预测季节性保修回报提供了一种通用方法。但是，此处介绍的方法可以应用于导致季节性重复事件数据的其他应用程序。使用层次聚类方法将总体分层为比总体总体更均匀的组。分层有助于使用时变和时间常数协变量对重复事件数据进行建模。我们使用两种不同类型产品的保修索赔数据来演示和验证模型。结果表明，与不考虑季节性和协变量的模型相比，我们的方法在每月事件的预测能力方面提供了重要的改进。