Local Polynomial Fitting in Failure Rate Estimation

The failure rate function is one of the most important functions in reliability analysis as it addresses concepts such as scheduling, maintenance, improved system design, cost analysis, etc. Kernel-based estimation of the failure rate function imposes minimal assumptions on the data, and thus offers large flexibility. Therefore, it is very helpful in reliability analysis where the shape of the failure function is a primary target. However, standard kernel estimates are biased more than usual in the endpoints. Motivated by the advantages that the local linear fitting method provides for estimation of densities near the boundary, we employ the technique to the failure rate setting. We show that it produces estimators that have the same amount of boundary bias as in areas outside the boundary. The mean square error properties of the method are demonstrated, and a practically useful procedure for automatic smoothing parameter selection is developed, and studied both theoretically, and by simulations. The result is displayed graphically by distributional, and real life data.