Nonparametric Estimation of Lifetime Distributions from a Record of Failures and Follow-ups

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Abstract
This article deals with the estimation problem of the survival function of an industrial product in which the real operating time is different from its actual calendar time. In an observational study of the product, sometimes only the time until failure is observable from the repair requests made by the owner, but nonfailure times themselves are not. The generalized maximum likelihood estimator of the survival function is presented, and its consistency, asymptotic normality, and variance are given. Operating times of construction machines and lifetimes of Channing House men are used to illustrate the method.

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