A Bias-Corrected Kaplan-Meier Estimator

The Kaplan-Meier estimator (KME) is a classical non-parametric reliability estimator for incomplete data; and it underestimates the reliability. Few estimators have been developed to correct its bias. This paper aims to fill this gap by proposing a bias-corrected estimator. The proposed estimator is a weighted average of two KME-related simple estimators. One is the arithmetic mean of reliability estimates obtained from the KME at two successive failure or censored times; and the other is the KME obtained by adding one to the sample size. The bias-corrected estimator is defined for incomplete data and its performance is quantitatively evaluated for complete data. The theoretical analysis and numerical examples show that the proposed estimator is almost unbiased, can be conveniently implemented in an Excel spreadsheet program, and hence is useful to reliability analysts and practitioners.