Approach for Inferring Fractiles of Future Time between Failures

When the data on the time between failures (TBF) are available, a challenging issue is to infer the distribution of future TBFs. The existing approaches to address this issue include varying-parameter normal and Weibull distributions, where the distributional parameters are functions of the number of cumulative failures. Since the distributional parameters are extrapolated from the two fitted models of the distribution parameters, these approaches may be not robust. In this paper, we propose an improved approach. The proposed approach first estimates alpha-fractiles of time to failure from the observed data for multiple alpha values, and then fits the estimates associated with each alpha value to a three-parameter power-law model. The fitted power-law models are used to estimate the fractiles of a certain future TBF, which form an empirical distribution of the future TBF. The empirical distribution can be further fitted to a distribution model. Due to multiple fractiles are estimated, it is expected that the proposed approach is robust. The approach is illustrated by the well-known bus-motor failure data.