Extrapolation of Extreme Pit Depths in Space and Time

Abstract

A four parameter model is proposed for data collected on maximum pit depths enabling simultaneous extrapolation into the future and over large areas of exposed metal. This model is based on the generalized extreme value distribution whose use in this context is here justified mainly on statistical, rather than metallurgical, reasoning. Those aspects of the model which allow for extrapolation in time rely on reported power law dependencies for mean pit depths. Use of the model for predicting means, standard deviations, percentiles, bounds, order statistics, hole counts, and size of perforated areas, is demonstrated, both in general and for a particular data set. Comparisons are made with other reported techniques.

Application of extreme-value statistics to corrosion

“…Evans, however, did not check another possibility using the type Hi distribution which has an upper limit. Recently Laycock et al [24] discussed that usefulness of the generalized extreme value (GEV) distribution:…”

Applications of extreme-value theory in corrosion engineering

“…This is consistent with theories of pitting in steel and other metals. See further argument supporting this approach in Ref, [1]. This type of data censoring can arise through built in limits on measurement capabilities or else through deliberate censoring of a given data set, typically a dense time series, so as to isolate the important events.…”

Performance of Ductile Iron Pipes. I: Characterization of External Corrosion Patterns

“…Sheikh et al (1989) proposed a truncated exponential distribution as the underlying distribution for pit depth and Sheikh et al (1990) proposed a probabilistic model to predict time to failure. Laycock et al (1990) used the generalized extreme value statistics to analyze corrosion pit-depth maxima and subsequently extrapolate sample data in time and space. Scarf et al (1992) extended the work of Laycock et al (1990) to consider the r deepest pits in a sample rather than just the single deepest pit.…”

“…Laycock et al (1990) used the generalized extreme value statistics to analyze corrosion pit-depth maxima and subsequently extrapolate sample data in time and space. Scarf et al (1992) extended the work of Laycock et al (1990) to consider the r deepest pits in a sample rather than just the single deepest pit. Katano et al (1995) and Katano et al (2003) found that the log-normal distribution best fitted their pit data and using regression analysis observed that the environmental factors that were found to be the most significant in determining pit depth (for a given exposure time) included soil type, pH, resistivity, redox potential and sulfate ion.…”