A non-homogeneous Poisson process predictive model for automobile warranty claims

Automobile warranties and thus lifetimes are characterized in the two-dimensional space of time and mileage. This paper presents a non-homogenous Poisson process (NHPP) predictive model for automobile warranty claims consisting of two components: a population size function and a failure or warranty claim rate. The population size function tracks the population in the time domain and accounts for mileage by removing vehicles from the population when they exceed the warranty mileage limitation. The model uses the intensity function of a NHPP—the instantaneous probability of failure—to model the occurrence of warranty claims. The approach was developed to support automobile manufacturers’ process of using claims observed during the early portion (first 7 months) of vehicle life to predict claims for the remainder of coverage, typically between 3 and 5 years. This paper uses manufacturer provided warranty data from a luxury car to demonstrate the NHPP model by predicting claims for three vehicle subsystems. Warranty predictions are then compared with the actual observed values and predictions made with a standard forecasting technique.