“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. slip and fall extreme value statistics human locomotion friction slipperiness Weibull reliability

Factors associated with worker slipping in limited-service restaurants

“…The COF measures in the current study could document the friction status only at the time of measurement, but COF can vary over time, partly based on the contamination level on the floor 24 44 45. The risk of slipping was ascertained in the previous 4 weeks.…”

Early Heelstrike Kinetics Are Indicative of Slip Potential During Walking Over a Contaminated Surface

“…The results for heel displacement and ground kinetics in the current study are in good agreement with existing slip literature. Slips have generally been characterized by large heel displacements (>10 mm; Brady, Pavol, Owings, & Grabiner, 2000;, 2002DiDomenico, McGorry, & Chang, 2007;Grönqvist, 1999;Leamon & Li, 1990;Perkins, 1978;Strandberg, 1983). Meanwhile, GRFs were reduced for the contaminated condition, a finding presented by other authors (Cham & Redfern, 2002;Strandberg, 1983).…”

“…It is apparent that for shear forces greater than 30 N, displacements stabilize to less than 30 mm, a displacement that is considered safe (Cham & Redfern, 2002;Leamon & Li, 1990;Perkins, 1978). Although displacements stabilize for UCoF as well, the threshold is rather high at approximately 0.95, which is well above values for UCoF that have been previously considered "safe" (i.e., a required CoF between 0.13 and 0.50, found for a wide range of surface conditions; Barnett, 2002;Brungraber, 1976;Cham & Redfern, 2002;Cooper, PrebeauMenezes, Butcher, & Bertram, 2008;Francis & Zozula, 1990;James, 1980;Perkins, 1978;Redfern et al, 2001;Strandberg, 1983;Strandberg & Lanshammar, 1981). Given previous thinking on what is "safe," it seems as though our current understanding of UCoF is insufficient to explain this result.…”

A comparative evaluation of floor slip resistance test methods

“…Floor slipperiness is one of the most influential parameters affecting the life safety of users, and therefore, many researchers worldwide have sought to establish test methods for floor slipperiness [1][2][3][4]. To date, more than 100 different types of test methods and apparatus have been proposed [5][6][7][8], some of which are used in setting national standards.…”