“Slip and Fall” Theory—Extreme Order Statistics

Abstract

Classical "slip and fall" analysis was reformulated in this paper to account for the stochastic nature of friction. As it turned out, the new theory, arising from this analysis, was a precise statement of the distribution function for the smallest value among n independent observations. This made it possible to invoke an important result from the asymptotic theory of extreme order statistics that reduced the theory to a simple and elegant relationship among the probability of slipping, the critical friction criterion, the distance traveled by the walker, and the average, spread and asymmetry of the distribution of friction coefficients. The new theory reveals that short walks lead to fewer falls; low friction floors are sometimes better than high friction ones.