Reliability Estimation of Critical Infrastructure Segment Backed up by the Circular Data Analysis

In this paper, we present a novel statistical approach to assess and model data of water distribution network (WDN) failures which contain only few pieces of information, namely the number of failures in a month. The applied statistical method is known as the circular (directional) statistics. It concerns with angular/cyclical data in degrees or radians. The sample space is typically a circle or a sphere and due to the nature of the circular data, they cannot be analysed with commonly used statistical techniques. Circular data approaches can be adapted to analyse time-of-year data and year cycles. Using the methods of descriptive and inferential statistics for circular data, we show that the WDN failure data show a deviation from the uniform model and cannot be modelled by the parametric models. Therefore, we apply the nonparametric circular kernel density estimates to assess and model the data and predict the expected numbers of failures in the respective months of a year.