Estimation of Lifetime Parameters From Incomplete Field Data

When automobile failures occur within the automotive warranty period, a manufacturer can develop a record of mileages to failure from owners' requests for repair. When no failures occur during the warranty period the owner naturally will not report mileages, and it may be inferred that “no record of failures” means “no failures.” By using a follow-up survey or postal reply cards, data can be acquired to include a partial record of nonfailures. A method of estimating lifetime parameters is proposed for analyzing this kind of data. Assuming a Weibull and an exponential lifetime distribution under the random censoring model, I derive a consistent estimator that can be applied to any censoring distribution.