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Estimation of embedded particle properties from plane section intercepts

Published online by Cambridge University Press:  01 July 2016

D. A. Evans  and
K. R. Clarke
D. A. Evans
Affiliation:
University of Newcastle upon Tyne
K. R. Clarke
Affiliation:
University of Newcastle upon Tyne
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Abstract

Estimation of the properties of particles embedded in a solid medium via observations on random plane sections is studied. The particular properties considered are those associated with steel inclusions, for example, projected area fraction, total caliper length per unit volume and elongation factor. The approach is general, and with the minimum of assumptions about the particle shape, formulae are obtained for suitable estimators and their variances. Generalised moment relations are derived for the case of given, arbitrary shapes. Estimations of the density of particle centres based upon reciprocal observations are shown to lack robustness to small changes in shape and a more reliable density estimator is discussed. Consideration is given to the case of particles with elliptical profiles and to the use of aggregated results which arise when using automatic scanning equipment. Results are given for the case when there is length-biassing of the intercept distribution due to edge-effects for finite sample areas. Finally, the implication of a positive lower resolution point is discussed.

Keywords

EMBEDDED PARTICLE PROPERTIESCORPUSCLE PROBLEMPOISSON FIELDINCLUSIONSINTERCEPTSEDGE-EFFECTLENGTH-BIASSINGTRUNCATION DUE TO POSITIVE LOWER RESOLUTION POINTDENSITY ESTIMATIONELLIPTICAL PARTICLESQUADRATSSTEREOLOGYQTM (QUANTITATIVE TELEVISION MICROSCOPE)
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 3 , September 1975 , pp. 542 - 560
Copyright
Copyright © Applied Probability Trust 1975 

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References

Delesse, A. (1847) Procédé mécanique pour déterminer la composition des roches. Compt. Rend., 25, 544–545.Google Scholar
Fullman, R. L. (1953) Measurement of particle sizes in opaque bodies. J. Metals 5, 447–452.Google Scholar
Mardia, K. V. (1970) Families of Bivariate Distributions. Griffin, London.Google Scholar
Moran, P. A. P. (1972) The probabilistic basis of stereology. Suppl. Adv. Appl. Prob., 69–91.CrossRefGoogle Scholar
Nicholson, W. L. (1970) Estimation of linear properties of particle size distributions. Biometrika 57, 273–297.CrossRefGoogle Scholar
Plackett, R. L. (1965) A class of bivariate distributions. J. Amer. Statist. Assoc. 60, 516–522.CrossRefGoogle Scholar
Wicksell, S. D. (1925). The corpuscle problem. A mathematical study of a biometric problem. Biometrika 17, 84–99.Google Scholar