Auto warranty and driving patterns

Abstract

Automobile warranty coverage is typically limited by age as well as mileage. However, the age is known for all sold vehicles at all times, but mileage is only observed for a vehicle with a claim and only at the time of the claim. We study the relationship between the expected number/cost of warranty claims and the driving patterns. Within a nonparametric framework, we account for the rate of mileage accumulation and propose a measure for the variability of this rate over a vehicle's observable life. We illustrate the ideas with real warranty data and comment on the relationship between the expected number/cost of warranty claims and the driving patterns using results adjusted/unadjusted for withdrawals from the warranty coverage due to mileage accumulation.

Introduction

Understanding the occurrence of warranty claims is of significant interest to manufacturers for two reasons: first, they are a liability incurred at the time of sale and represent the cost of doing business, and second, they allow engineers to assess the reliability of the sold products. Nowadays, the product warranty is considered as an attribute of the product and it is used by manufacturers as a competitive tool in the market place. For example, increasing warranty coverage may attract more buyers, but at the same time, could increase the related servicing costs. See Blischke and Murthy [1] for more discussion on these general points.

Typically, automotive warranties offer a free repair subject to age and mileage limitations. Usually the age of a vehicle is measured from the time of sale to the current time. In this study the limits for “bumper-to-bumper” coverage are 36 months or 36 000 miles, whichever comes first. Some manufacturers offer longer warranties across the board, others offer longer warranties only on their luxury models or for selected components such as powertrain, as for example, the Korean car manufacturer Kia.

Vehicles’ ages are known at all times because sales records are available. On the other hand, the mileage is available only for vehicles that generate warranty claims—this mileage is 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, here the warranty claims are modeled as recurrent events from a repairable system. Also, we use a nonparametric approach because our 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 double censoring in our dataset: the incomplete mileage information and the fact that claims made beyond the warranty database cut off date are not part of the database.

This modeling approach and data structure has been discussed extensively in the past. The model and estimation procedure are based on the ”robust estimator” discussed by Hu and Lawless [5], [4]. The consideration of the number of units at risk due to mileage limitations and based on incomplete mileage information extends Nelson [12] standard estimator. Lawless et al. [9] also dealt with the incomplete data problem and specify a simple linear mileage accumulation model, which is generalized in this study. The general survey paper by Lawless [8] includes a discussion of the bias caused by reporting delay, which was analyzed earlier in Lawless and Nadeau [10] and Kalbfleisch et al. [6].

Recently Rai and Singh [13], Majeske [11], Kleyner and Sanborn [7] and Wu and Akbarov [15] have proposed possible approaches to warranty prediction. Also, see [14] for more on reliability analysis with warranty data.

Chukova and Robinson [3] adopted the robust estimator and linear mileage accumulation model to estimate the number of units at risk at any given time from the incomplete mileage data. This information was used to provide explicit expressions for the estimated mean cumulative number of claims per vehicle with or without adjustments for reporting delay. Christozov and Robinson [2] relax the linearity assumption for the mileage accumulation, proposing instead a piece-wise linear model with nodes occurring at the observed claim times and mileage. In Chukova and Robinson [3] only the last warranty claim was used to estimate a vehicle's mileage accumulation rate whereas for the piece-wise model, all claims in the database were used to characterize the mileage accumulation. In Christozov and Robinson [2], using strata approach, the variability of mileage accumulation rates is defined and comparison between the mean cumulative functions based on this approach with the more basic one given in Chukova and Robinson [3] is provided. Also, an interesting conjecture, that a higher variability in the driving pattern may lead to a higher expected warranty cost (or higher expected number of claims) per vehicle, is formulated. This conjecture is the main focus of this study.

This paper sets out to test whether there is a relationship between the variability of the driving pattern of the vehicle and the frequency and size of the warranty claims made against it.

The content of this paper is as follows. Section 2 outlines the framework and the data that are used in this study. Section 3 introduces the idea of vehicle's “observable life”. In Section 4 the measure for the variability of the driving pattern is proposed. Results for the subset of vehicles with two or more claims are given in Section 5. Vehicles without claims are reintroduced in Section 6. Section 7 specifies the measures of warranty performance and Section 8 summarizes the results for these measures. The direction of causality is discussed in 9 Causality, 10 Conclusions concludes our study.