Applications of extreme-value theory in corrosion engineering

Abstract

In the context of corrosion engineering it is often natural to be concerned with extreme events. This is because, firstly, it is these extreme events that often lead to failure and, secondly, it may only be possible to measure the extremes, with much of the underlying measurements by their very nature unobservable Statistical methods relating to extreme value theory can be used to model and predict the statistical behaviour of extremes such as the largest pit, thinnest wall, maximum penetration or similar assessment of a corrosion phenomenon. These techniques can be applied to the single largest value, or to a given number of the largest values, measured over individual areas or coupons; or to all values exceeding a given threshold. The data can be modeled to account for dependence on environmental conditions, surface area examined, and the duration of exposure or of experimentation. The application of a selection of these techniques is demonstrated on data from industry and from laboratory experiments.

Influence of Superheat on Macrosegregation in Continuously Cast Steel Billet from Statistical Maximum Viewpoint

“…14) Murakami 15,16) introduced the SEV method in the estimation of the maximum size of inclusions in metal and the results were used to control the quality of materials and predict a scatter band of fatigue strength. Scarf 17) investigated the application of the extreme value theory into corrosion engineering to predict the maximum pit depth in a certain area, which often fails materials. Sun 18) applied the SEV method and the GPD method to estimate the maximum size of inclusions in ultra-clean GCr15 steel, on this basis, the relationship between the maximum size of inclusions and bearing fatigue life has been explored.…”

Models for Dependent Extremes Using Stable Mixtures

“…A third use is in the theory of rational choice (McFadden, 1978). Below we will also consider a fourth problem, analysis of pitting corrosion measurements (Kowaka, 1994; Scarf & Laycock, 1994).…”

thresholdmodeling: A Python package for modeling excesses over a threshold using the Peak-Over-Threshold Method and the Generalized Pareto Distribution

“…Another package is scipy, which has the genpareto (Scipy, 2019) functions, but this does not provide any Peak-Over-Threshold modeling functions since it is not possible to define a threshold using this package. Moreover, this package brings to the community of scientists, engineers, and any other interested person and programmer, the possibility to conduct an extreme value analysis, using a strong, consolidated and high-level programming language, given the importance of the extreme value theory approach for statistical analysis in corrosion engineering (see Scarf & Laycock (1994) and Tan (2017)), hydrology (see Katz, Parlange, & Naveau (2002)), enviromental data analysis (see Rydman (2018) and Bommier (2014)) and many other fields of natural sciences and engineering. (For a large number of additional applications, see Coles (2001)…”