COMPARISON OF KERNEL-BASED NONPARAMETRIC ESTIMATION METHODS FOR TREND RENEWAL PROCESSES - Saito, Yasuhiro; Dohi, Tadashi (International Journal of Industrial Engineering: Theory, Applications and Practice, 2019)
Trend renewal process (TRP) is a generalized stochastic point processwith two elements of a nonhomogeneous Poisson process (NHPP) and a renewal process (RP), and plays a significant role to represent a sub-class of general repair models. Nonparametric estimation of TRPs receives considerable concern in estimating the statistical properties of repairable systems under uncertainty, when the parametric forms of NHPP and/or RP cannot be known in advance. In this paper, we provide an alternative nonparametric kernel-based approach of the TRP for a given trend function which is equivalent to the intensity function of NHPP. In details, we estimate the TRPs with the kernel-based estimator and apply two bandwidth estimation methods which are based on the cross-validation technique. We evaluate effectiveness of our proposed kernel estimation algorithms throughout simulation experiments and, show application examples for a preventive maintenance problem of repairable systems.