Assessing Risk of Exceedance Events with Buffered Probability of Exceedance and Superquantiles

Abstract

Many systems, or components of systems, often have associated with them a critical safety threshold. If events then occur that have magnitude larger than such a threshold, such as a weather event or physical stress on a component, critical failures become likely and/or overall system integrity can become critically compromised. Therefore, regulations and risk assessments are often formulated mathematically in terms of Probability of Exceedance (POE). This characteristic, however, can hide important information about the frequency, magnitude, and overall risk of exceedance events. This includes the magnitude of events that do exceed the threshold. Additionally, the frequency and magnitude of near-exceedance events, just below the threshold, are ignored entirely. We overview a new probabilistic characterization of exceedance risk call Buffered Probability of Exceedance (bPOE), also reviewing a closely related concept called the superquantile. We show that bPOE simultaneously assess both the frequency and magnitude of both exceedance events and near-exceedance events. After introducing bPOE and superquantiles, we show how it can be viewed as superior to POE as a measure of exceedance risk. We then present a simple parametric distribution fitting procedure that utilizes bPOE and the superquantile, two characteristics that we see are advantageous to consider when estimation of exceedance risk and tail density are the focus of the fitting procedure.