Inferences on non-parametric methods for the estimation of the reliability function with multiply censored data

Abstract

In today’s highly competitive business environment, the role of reliability management for improving product performance becomes crucial. Indeed, reliability considerations should be included as vital elements within modern management and business practices. Reliability management is indeed complex because it involves a number of different activities and responsibilities that take place throughout the life-cycle of product and /or services. In reliability practice, the description and study of data, which are often incomplete (censored) is facilitated through the estimation of specific density distribution functions. Although a number of quite efficient modeling techniques have been made available in the literature, the ones prevail and thus widely employed are the non-parametric methods where reliability estimates are obtained directly from the data. In this paper three such inference techniques are reviewed (i.e. the Kaplan-Meier, the Cumulative-Hazard and the Piecewise Exponential Estimator) and the numerical differences when all three are employed for the same data set are analytically established. Furthermore, a study regarding the finite sample behavior in terms of estimated mean squared error based on Monte Carlo Simulations is presented.