Tid: 8 december 2008 kl 15.15-17.00 .

Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Professor Holger Rootzén, Matematisk statistik, Chalmers Tekniska Högskola/Göteborgs Universitet.

Titel: Pitting Corrosion: analysis of designed experiments with extreme value distributed responses.

Sammanfattning: This talk discusses how Extreme Value Statistics can be used to to validate and improve designed experiments with extremal responses, and how to extrapolate and compare results.

A main motivation is corrosion tests: Localized, or "pitting", corrosion can limit the usefulness of magnesium and other new lightweight materials aimed at reducing weight, and thus CO₂ emissions from cars. It makes judicious choice of alloys and surface treatments necessary. Standard methods to evaluate corrosion test are based on analyzing weight loss by ANOVA. These methods may be misleading in two ways. Usually it is not weight loss but the risk of perforation, i.e. the depth of the deepest pit which is of interest. Further the standard ANOVA assumptions of normality and homogeneity of variances typically are not satisfied by pit depth measurements, and don't give credible extrapolation into extreme tails.

The talk presents a streamlined approach to analysis of such experiments. It consists of

• 1.) a preliminary analysis to check that the experiment has worked out as intended,
• 2.) a separate analysis for each individual experimental condition, and
• 3.) a strategy for pairwise comparisons.

Further, a class of hierarchical random effects models for extreme value data is discussed. The models are obtained by mixing extreme value distributions over positive stable distributions. They open up exciting new possibilities to develop extreme value analogues of normal random effects models.

The big challenge is to develop a full theory of design and analysis of experiments with extreme value distributed responses -- the present results are just an early beginning.

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