Statistics seminar
Liverpool University Statistics Division
Time: 2pm, Friday June 4th
Venue: Room 2.11, Maths & Oceanography Building, University of Liverpool
Speaker: Clive Anderson (University of Sheffield)
Title: The Largest Inclusions Within a Piece of Steel
Abstract: Imagine a solid object, homogeneous except for the presence within
it of small particles of foreign material of different sizes. Interest resides
in the size of the largest of these particles, and how that size relates to
the volume of the solid. Direct measurement inside the solid is impossible,
but particles intersecting the surface can be seen in section.
This is a problem with particular relevance to new high quality steels. All
steels contain inclusions -- small particles of impurities -- which affect
fatigue behaviour and other mechanical properties. In the new high quality
steels intended for critical applications (so-called clean steels) the number
and size of inclusions are much reduced, and it becomes crucial for safety and
commercial reasons to know the likely size of the largest. Measurement of the
cross-sections of inclusions exposed in sampled polished surfaces of the steel
can be made reasonably routinely.
Without the emphasis on the largest particles, inference about three-
dimensional particle sizes on the basis of two-dimensional sections is a
standard problem in stereology ('Wicksell's Corpuscle Problem').
The talk will present a development which concentrates specifically on
inferences about large particle sizes, combining modern extreme value
modelling with stereological ideas. The results will be illustrated with data
on clean steels.
Other forthcoming seminars:
Tuesday 21 September
Alexandros Karagregoriou (University of Cyprus)
On asymptotic properties of model identification procedures
Full seminar programme available via http://www.liv.ac.uk/maths/SOR/
Damian Clancy
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