Nonparametric Estimation of Time Trend for Repairable Systems Data

Abstract

The trend-renewal-process (TRP) is defined to be a time-transformed renewal process, where the time transformation is given by a trend function λ( ⋅) which is similar to the intensity of a nonhomogeneous Poisson process (NHPP). A nonparametric maximum likelihood estimator of the trend function of a TRP can be obtained in principle in a similar manner as for the NHPP using kernel smoothing. But for a TRP one must consider the simultaneous estimation of the renewal distribution, which is here assumed to belong to a parametric class such as the Weibull-distribution. A weighted kernel estimator for λ( ⋅) is suggested and studied. Other approaches are also briefly discussed.