The precision of methods using the statistics of extremes for the estimation of the maximum size of inclusions in clean steels

Anderson, C. W.; Shi, G.; Atkinson, Helen V.; Sellars, C. M.

doi:10.1016/s1359-6454(00)00281-0

Cited by 51 publications

(38 citation statements)

References 21 publications

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“…The more specific task of making inference on the extremes of objects that are observed only stereologically has only been considered much more recently. Direct extreme value analysis without explicit reference to stereological aspects of the problem has been considered by Shi et al (1999aShi et al ( , 1999b and Anderson et al (2000). Taking account of the stereology that generates the data, and assuming spherical inclusions, Drees and Reiss (1992) derived from first principles asymptotic families for the distributions of observed diameters.…”

Section: Introductionmentioning

confidence: 99%

Inference for Stereological Extremes

Bortot

Coles

Sisson

2007

Journal of the American Statistical Association

128

164

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In the production of clean steels the occurrence of imperfections -so-called inclusions -is unavoidable. Furthermore, the strength of a clean steel block is largely dependent on the size of the largest imperfection it contains, so inference on extreme inclusion size forms an important part of quality control. Sampling is generally done by measuring imperfections on planar slices, leading to an extreme value version of a standard stereological problem: how to make inference on large inclusions using only the sliced observations. Under the assumption that inclusions are spherical, this problem has previously been tackled using a combination of extreme value models, stereological calculations, a Bayesian hierarchical model and standard Markov chain Monte Carlo (MCMC) techniques. Our objectives in this article are two-fold: to assess the robustness of such inferences with respect to the assumption of spherical inclusions, and to develop an inference procedure that is valid for non-spherical inclusions. We investigate both of these aspects by extending the spherical family for inclusion shapes to a family of ellipsoids. The issue of robustness is then addressed by assessing the performance of the spherical model when fitted to measurements obtained from a simulation of ellipsoidal inclusions. The issue of inference is more difficult, since likelihood calculation is not feasible for the ellipsoidal model. To handle this aspect we propose a modification to a recently developed likelihood-free MCMC algorithm. After verifying the viability and accuracy of the proposed algorithm through a simulation study, we analyze a real inclusion dataset, comparing the inference obtained under the ellipsoidal inclusion model with that previously obtained assuming spherical inclusions.

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Section: Introductionmentioning

confidence: 99%

Inference for Stereological Extremes

Bortot

Coles

Sisson

2007

Journal of the American Statistical Association

128

164

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“…24,25) The peak value of the inclusion diameter appears in the diameter of less than 10 μm. [26][27][28] The concentration of the inclusion in steel is in between 10 ) before refining when the total oxygen is high.…”

Section: Inclusion Concentrationmentioning

confidence: 99%

Reliability of Inclusion Statistics in Steel by Stereological Methods

Shimasaki

Shoji

et al. 2016

ISIJ Int.

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In this paper, we investigate the reliability of estimating of inclusion size distribution and number density in steel by using stereological methods. The magnitude of the inclusion concentration in steel is evaluated by the total oxygen and the assumed average inclusion sizes. The principles of Schwartz-Saltykov (SS) and modified SS (MSS) methods are introduced. A simulation model is developed to disperse particles with a predefined particle size distribution (PSD) randomly into a three dimensional (3D) space. A series of test planes are generate to measure the two dimensional (2D) PSD and particle number density (PND) on the cross-sections (CS). The SS and MSS methods are applied to investigate the reliability of the translation between the 3D and 2D information of the system, such as the 2D and 3D PSD and PND. The influence of predefined 3D PSD on the reliability of the stereological methods are studied, such as mono sized, lognormal and normal distributions. The effect of the representative group diameters in the discretized groups for SS and MSS methods is investigated as well.

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“…It is not possible to determine the probability of finding such large inclusions using a brute force approach, as the large number of micrographics samples that would need to be examined to have confidence that statistically significant numbers of such particles had been detected would be beyond practical analysis. The size distribution is therefore usually interpreted from a smaller, more manageable, number of micrographs using the statistics of extreme values [18][19][20][21]. There are a number of different approaches to this problem [18].…”

Section: Fatigue Properties Of the Materialsmentioning

confidence: 99%

Fatigue tolerant design of rolling bearings

Gill

Lewis²

2015

Proceedings of the Institution of Mechanical Engineers, Part J:

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A quantitative method for assessing the influence of steel cleanliness on the fatigue life of rolling bearing raceways is presented. The approach systematically accounts for the effect of the highly variable stress state within raceways. Finite element analysis is used to determine the stress state in the bearings. A fracture mechanics model for the safe stress amplitude as a function of inclusion size is employed from Lewis and Tomkins, J Engng Tribology, 226 (5) 389 (2012). The size and number of large inclusions in a large volume of steel are estimated by the Generalised Pareto Distribution. These three elements are combined to determine the failure probability of the raceway in an example rolling bearing. A sensitivity analysis to the various microstructural input parameters is conducted. It is found that the size distribution of the larger inclusions is the most important factor in controlling the fatigue resistance of rolling bearings, and that residual stresses must be considered to produce realistic predictions.

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The precision of methods using the statistics of extremes for the estimation of the maximum size of inclusions in clean steels

Cited by 51 publications

References 21 publications

Inference for Stereological Extremes

Inference for Stereological Extremes

Reliability of Inclusion Statistics in Steel by Stereological Methods

Fatigue tolerant design of rolling bearings

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