Network Reliability and Borel's Paradox

Abstract

Borel's paradox is a paradox in probability theory with implications in modeling and inference. The paradox arises when we induce probabilities from a high-dimensional, nondiscrete space to its lower dimensional subspace using conditioning arguments that are ill defined. The purpose of this article is to draw attention to the fact that when assessing the reliability of a network there are circumstances under which the paradox comes into play, and to show the consequences of the paradox on the calculated reliability. In particular, we are able to establish the counter-intuitive result that the reliability of a series system of n components, whose life-lengths are independent, converges to a half (and not to zero), as n increases.