On exchangeable, causal and cascading failures

Abstract

This paper is addressed to engineers and statisticians working on topics in reliability and survival analysis. It is also addressed to designers of network systems. The material here is prompted by problems of infrastructure assurance and protection. Infrastructure systems, like the internet and the power grid, comprise a web of interconnected components experiencing interacting (or dependent) failures. Such systems are prone to a paralyzing collapse caused by a succession of rapid failures; this phenomenon is referred to as "cascading failures." Assessing the reliability of an infrastructure system is a key step in its design. The purpose of this paper is to articulate on aspects of infrastructure reliability, in particular the notions of chance, interaction, cause and cascading.

Following a commentary on how the term "reliability" is sometimes interpreted, the paper begins by making the argument that exchangeability is a meaningful setting for discussing interaction. We start by considering individual components and describe what it means to say that they are exchangeable. We then show how exchangeability leads us to distinguish between chance and probability. We then look at how entire networks can be exchangeable and how components within a network can be dependent. The above material, though expository, serves the useful purpose of enabling us to introduce and make precise the notions of causal and cascading failures. Classifying dependent failures as being either causal or cascading and characterizing these notions is a contribution of this paper. The others are a focus on networks and their setting in the context of exchangeability.

A simple model for cascading failures closes the paper. A virtue of this model is that it enables us to make the important claim that causal failures are more deleterious to infrastructure reliability than cascading failures. This claim, being contrary to a commonly held perception of network designers and operators, is perhaps the key contribution of this paper.