Data Visualization in Reliability of Repairable Systems: The SiZer Map Tool

Abstract

In this article, the graphical exploratory tool SiZer Map is constructed for the inference of the rate of occurrences of events that follow a nonhomogeneous Poisson process. SiZer Map is defined considering nonparametric local linear kernel estimators for the rate function and its first derivative. The bandwidth parameter is the viewing scale, and the considered time interval is the localization space. The shape characteristics of the rate function are distinguished from those which are merely an artifact of the sampling variability of the data through confidence intervals for the first derivative. The proposal is illustrated with some real data sets that represent recurrent events in time.