Nonparametric estimation of the product reliability from grouped warranty data with unknown start-up time

초록

This article presents methods for nonparametric estimation of the lifetime distribution from grouped warranty data comprising the number of production and the number of failures for each period. The start-up time of each failed item is unknown, while its time of production is recorded in the field warranty dataset. This type of dataset is incomplete in the sense that the age of a failed item is unknown. We propose an algorithm for nonparametric maximum likelihood estimation of the product reliability, under the condition that the holding-time distribution is known. We also present an algorithm for estimating the holding-time distribution with additional dataset of sales volume for each period. Examples are presented to illustrate the characteristic of the proposed estimator. Significance: Field reliability data are collected by many production companies in warranty data acquisition systems. The nonparametric estimation technique proposed herein is a realistic approach to solving incomplete data problems in the grouped warranty data.

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