Stefanka Chukova and Dimitar Christozov

Victoria University of Wellington & American University in Bulgaria

Analysing truncated warranty data: A stratification approach

Warranty data is of considerable interest to corporations for several reasons. Warranty claims are a liability incurred at the time of sale and represent a cost of doing business, so forecasting those costs is of interest. For engineers a secondary, but important, use of warranty data is to assess the reliability of products in the field. A third characteristic of warranty is that it is a product attribute valued by customers and affecting their buying decisions. For example increasing warranty coverage may attract more buyers but also increase servicing costs.

Vehicle age is known at all times because sales records are retained. It is also becoming technically feasible to track mileage accumulation on all vehicles in the field, but this is currently not a common practice for cost and privacy reasons. For vehicles that generate a warranty claim, the mileage at the time of a warranty repair are recorded at the dealership and included in the warranty database. Thus from a modeling standpoint we have two usage measures (age and mileage), but one of them (mileage) is incompletely observed. As is commonly done we model warranty claims as recurrent events from a repairable system. Also, we take a nonparametric approach because sample sizes are large. We note however that warranty forecasting, which requires extrapolation beyond the oldest age/mileage in the field, requires either a parametric model or the incorporation of past-model data on older vehicles. We deal explicitly with the problem of incomplete mileage information and also with the problem that repairs made beyond the age or mileage limits will not be part of the warranty database.

Usually a simple linear mileage accumulation model is adopted to estimate the number of units at risk at any given time from the incomplete mileage data. For mileage accumulation, we relax the linearity assumption, based on the information from the last warranty claim, by proposing a piece-wise linear model with nodes occurring at the observed mileages corresponding to the warranty repairs. For the piece-wise model, we use all claims in the database to characterise the mileage accumulation.

The main focus of this study is to provide an overview of different stratification approaches in analysing warranty data. These approaches are characterised by the choice of an appropriate integral measure, which depends on the usage measures (mileage and age) of the vehicles, and imposes a particular discretisation on the warranty data. The goal of these stratifications is to extract information needed for the evaluation of several warranty characteristics, such as the mean cumulative cost function, the rate of depletion of the warranty resource as well as to detect useful trends in these characteristics.