JSM 2004 - Toronto

Abstract #301003

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Activity Number: 48
Type: Contributed
Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
Sponsor: Section on Physical and Engineering Sciences
Abstract - #301003
Title: A Bivariate Treatment of Truncated Warranty Data
Author(s): Jeffrey A. Robinson*+ and Stefanka Chukova
Companies: General Motors R&D Center and Victoria University
Address: Mail Code 480-106-256, Warren, MI, 48090-9055,
Keywords: warranty ; bivariate ; survivor
Abstract:

This article deals with a type of truncation that occurs with typical automotive warranties. Warranty coverage and the resulting claims data are limited by mileage as well as age. 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, i.e., the data are zero-truncated with respect to mileage. An unknown number of vehicles leave coverage due to the mileage constraint, and the number of vehicles eligible to generate a claim at any age-mileage combination is subject to uncertainty. We focus on bivariate treatments of this problem. We review briefly nonparametric procedures for estimating the bivariate cumulative hazard function or related bivariate survivor function. In this context these functions describe the distribution of the age or mileage to the first warranty claim, say, of a given type. We compare the bivariate analyses with univariate results for both age and mileage and discuss the practical similarities and differences between them. Real data examples illustrate the ideas.

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