Estimating residual life distribution from fractile curves of a condition variable

In a condition-based maintenance setting, a challenging issue is to determine the distribution of residual life. In this paper we propose a non-parametric approach to estimate the residual life distribution. The proposed approach starts with several empirical fractile curves of a condition variable. The curves are fitted to power-law models using a weighted least square method (with large weights being assigned to the recent observations), and the times to failure are extrapolated from the fitted power-law models. In such a way, the empirical residual life distribution is obtained. The main advantages of the proposed approach include: (a) it does not need to make assumptions about the degradation process and the distribution family of residual life; (b) the fitted power-law models can reflect recent trend; and (c) the empirical residual life distribution provides more information about the behavior of residual life since a number of fractile curves are used. These advantages make the prediction more accurate. A real-world example is included to illustrate the appropriateness and usefulness of the approach.