Seasonal warranty prediction based on recurrent event data

Abstract

Warranty return data from repairable systems, such as vehicles, usually 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. A hierarchical clustering method is used to stratify the population into groups that are more homogeneous than the 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 vehicles. The results show that our approach provides important improvements in the predictive power of monthly events compared with models that do not take the season-ality into account.

Predicting the Number of Future Events

“…Despite the complicated nature of their data (random right censoring and truncation and combinations of categorical covariates with small counts in some cells), Hong et al (2009) were able to use the fractional random-weight method (e.g., Xu et al, 2020) to generate bootstrap estimates. Shan et al (2020) used time-varying covariates to account for seasonality in two different warranty prediction applications. As mentioned by one of the referees, if there is seasonality and data from only part of one year is available, there is a difficulty.…”

Rejoinder to “Specifying Prior Distribution in Reliability Applications”

“…14 Because of large amount of unit-to-unit variability in product-use environments, we have found it necessary to use unit-level random effects in our models so that the NHPP assumption of independent increments can be relaxed. See, for example, Shan et al 15 and Min et al 16 In these two applications, there was no need for Bayesian methods because there was much information in the available field data. Nevertheless, we agree with Professor Suárez-Llorensis that it would be useful to investigate appropriate prior distributions for the NHPP model.…”

Prediction intervals for Poisson‐based regression models

“…We also briefly mention a sequence of studies that investigated the methods for recurrent events modeled by the NHPP, initiated by Lawless (1987b). Given the NHPP setting, Fredette and Lawless (2007) involved random effects to handle possible heterogeneity among individuals and Shan et al (2020) further incorporated seasonal effects into the model to deal with seasonality. For the PI constructions, those studies commonly utilized the calibration approach as in Lawless and Fredette (2005).…”