An Extreme-Value Statistical Analysis of Maximum Pit Depths and Time to First Perforation

Abstract

This paper demonstrates that if the distribution of pits on a group of corroding samples is such that the sample maximum pit depths are distributed according to the equation Pw=exp[-e-a(w-w)]where Pw is the cumulative probability of occurrence of a pit of depth w and if the characteristic deepest pit depth, W, increases according to the equation W=blogt+cwhere t is the exposure time, then the times-to-first perforation for a group of samples are distributed according to the equation Ps=exp[−(tv)k]where Ps is the survival function or the probability that the first sample perforation will not have occurred at exposure time t. The significance of the characteristic deepest pit depth, W, the characteristic age V and the shape factors a and k, are discussed.