Automotive warranty data: stratification approach for estimating the mean cumulative function

This study extends previous work that accounts for mileage accumulation in automotive warranty data analysis. Warranty coverage is typically limited by age as well as mileage. Age is known for all sold vehicles all the time, but mileage is only observed for a vehicle with a claim and only at the time of the claim. Here we consider either age or mileage as the usage measure. We evaluate the mean cumulative number of claims or cost of claims and its standard error as functions of the usage measure. Within a nonparametric framework, we account the rate of mileage accumulation and allow for variation in the rate of mileage accumulation over a vehicle's lifetime. We illustrate the ideas with real data on four cases based on whether the usage measure is age or miles and whether the results are adjusted for withdrawals from the warranty coverage.