Estimation Method of Lifetime based on the Record of Failures during the Warranty Period

Abstract

This paper deals with the estimation method of the lifetime of a product in which the real operating time is different from its actual calender operating time. During the warranty period of a product, the manufacturer will only collect failure data from the repair requests by the owners. The manufacturer cannot usually obtain the real operating time of non-failure products.Some manufacturers have data about the usage time of the product during the warranty period : for example, mileage that the automobile will have run during that warranty period. In general these data consist of information about both failure and non-failure products. Two nonparametric MLE's about the reliability function of the product are presented. Estimation (A) uses information taken from both failure and non-failure products. Estimation (B) does not distinguish between them. The precision of these two estimators is compared using their asymptotic variances. Estimation (A) proves to have better precision than estimation (B).