Statistical Models: Propagation of Uncertainty and Monte Carlo Modeling

This chapter presents numerical and statistical methods to support corrosion science analyses. The first section is devoted to Monte Carlo methods for numerical propagation of uncertainty, covering basic concepts such as random sampling and correlated sampling. Examples are presented to examine propagation of uncertainties in water chemistry, the corrosion potential, and the repasivation potential, to quantify the probability of initiation of localized corrosion in metals. The second section presents a summary of extreme value theory, which defines a single general function for the description of tails of any regular distribution, useful to predict extreme corrosion damage based on limited information. Examples of uses of extreme value theory are provided, including uncertainty intervals on extreme damage conditions. The third section presents Markov Chains applied to the description of propagation of pitting corrosion, or corrosion fronts in general, with time. The method is promising, but exploratory in nature because parameters are selected to match average empirical trends and not necessarily based on corrosion mechanisms. Equations are provided for Markov Chain corrosion propagation models that honor average empirical corrosion depths versus time, such as power laws, accounting for random initiation of pitting.