Local Polynomial Fitting of the Mean Residual Life Function

Abstract

The mean residual life (MRL) function is one of the most important, widely used reliability measures in practice. For example, it is used to design burn-in programs, plan spare provision, and formulate warranty policies. Parametric techniques, which rely on the assumption that the parametric form of the failure time is known, are usually employed in estimating the MRL function. However, this approach could lead to an inconsistent, inaccurate estimator of the MRL function if the assumption is violated. A nonparametric approach in such a setup provides a promising alternative. In this paper, we employ local polynomial regression with fixed design points accompanied by appropriate binning to construct several new estimators for the MRL function. The asymptotic unbiasedness and consistency of the these estimators are proven. We then bring in two popular bandwidth selection methods to select the bandwidth of the proposed MRL estimators. Finally, we evaluate the performance of the estimators using several simulated and real life examples. Results indicate that the proposed estimators perform well in estimating MRL functions, particularly MRL models with constant, bathtub-shaped, and upside-down bathtub-shaped MRL functions.