Evaluation of the Robustness of Statistical Software for Warranty Analysis

Abstract

Warranty data with an implicit censoring at the end of the warranty period is often used in combination with commercially available “Weibull Analysis” software to estimate the rate of product failure after the end of the warranty period. Warranty databases frequently contain some “goodwill” or other special type of claims that are made after the end of the warranty period. Inclusion of such after warranty claims with the usual commercial software violates the assumption of independence of the time-to-failure process and the censoring process. This independence assumption is built into the algorithms used by Reliasoft Weibull++, Win SMITH, and SAS. The research reported here uses Monte Carlo simulation to investigate the robustness (i.e. whether or not the accuracy and precision of the estimation algorithms are maintained) when the independence assumption is violated. The proportion of after warranty claims which are included in the analysis, while censoring non-failed product at the end of the warranty, and the distance between the end of the warranty and the product age for the relevant projection for the failure rate will determine the magnitude of the bias of the projected failure rates. The magnitude of the bias is characterized here as the percent of projection estimates that are at or above the actual failure rate at the relevant age. A method for including after warranty claims along with other information about after warranty failures, e.g. part sales, is proposed and found to be less biased than simply including after warranty claims with no modeling of the censoring process that produced the after warranty claims.