Statistical Analysis of Defects for Fatigue Strength Prediction and Quality Control of Materials

Beretta, S.; Murakami, Yukitaka

doi:10.1046/j.1460-2695.1998.00104.x

Cited by 168 publications

(76 citation statements)

References 11 publications

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“…Takahashi and Sibuya (1996 consider inference under the assumption of a generalized gamma distribution for the sizes of spherical inclusions. Similar considerations from a more conventional extreme value viewpoint were made by Murakami (1994) and Beretta and Murakami (1998), who assumed a Gumbel distribution for the inclusion diameters. Most recently, Anderson and Coles (2002) proposed a fully Bayesian analysis of the problem, enabling a quantification of estimation precision through the posterior distribution.…”

Section: Introductionmentioning

confidence: 80%

Inference for Stereological Extremes

Bortot

Coles

Sisson

2007

Journal of the American Statistical Association

124

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: 80%

Inference for Stereological Extremes

Bortot

Coles

Sisson

2007

Journal of the American Statistical Association

124

164

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“…Based on numerical simulations, Takahashi 6) has reported that the correlation coefficient of EVD increased with an increased number of inclusions on the unit area. Furthermore, Beretta and Murakami 7) have clarified that the maximum likelihood (ML) method is a reliable method to determine the accurate regression line from EVD. However, the reasons of lower linearity of EVD for inclusions in samples from different stages of steel making process have not been fully understood.…”

Section: Introductionmentioning

confidence: 99%

“…In this method, a relatively small area of steel sample is examined by using light optical microscopy (LOM) for prediction of the maximum size of inclusions in a larger given area (or volume) of steel. [1][2][3][4][5][6][7] For improvement of the accuracy of this estimation method, several studies were carried out. [3][4][5][6][7] The probable largest inclusion can be determined by using a linear regression formula obtained for extreme value distribution (EVD).…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7] For improvement of the accuracy of this estimation method, several studies were carried out. [3][4][5][6][7] The probable largest inclusion can be determined by using a linear regression formula obtained for extreme value distribution (EVD). Based on numerical simulations, Takahashi 6) has reported that the correlation coefficient of EVD increased with an increased number of inclusions on the unit area.…”

Section: Introductionmentioning

confidence: 99%

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Application of Statistics of Extreme Values for Inclusions in Stainless Steel on Different Stages of Steel Making Process

et al. 2011

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A statistics of extreme values was applied to determine the largest inclusion sizes in the Type 304 stainless steel. The samples taken from a tundish, slab and hot rolled steel in one heat were examined by using a two dimensional observation of inclusions on a metal cross section. It was found that the molten steel sample contained two different types of inclusions, which were deoxidation products (SiO2-CaOMgO-Al2O3) and reoxidation products (SiO2-MnO-Cr2O3). As a result, the extreme value distribution (EVD) for different types of inclusions in the melt has two different slopes. Meanwhile, the inclusions in the slab sample provided a good linearity in one EVD. Moreover, the correlation coefficients of the regression lines for both the slab and rolled steel samples increased significantly with an increased number of measurements from 40 to 80 unit areas. It was found also that the EVD data for fractured inclusions on a parallel cross section of rolled steel agreed satisfactorily well with that for the initial spherical inclusions in the slab sample. Based on the geometrical considerations of inclusion deformation and fracture during hotrolling, the maximum length of fractured inclusions in rolled steel can be estimated reasonably well from the EVD for initial undeformed inclusions in the slab sample.

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“…Murakami and coauthors used the Gumbel plot to estimate a large size inclusion in steel. [6][7][8] Anderson et al proposed a threshhold method using a generalized Pareto or other distributions as a 3DSD. 9,10) These methods are useful in the point of analyzing the measurement data graphical.…”

Section: Introductionmentioning

confidence: 99%

Simulation of the Estimation of the Maximum Inclusion Size from 2-Dimensional Observation Data on the Basis of the Extreme Value of Statistics

Takahashi

2009

ISIJ Int.

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It is well known that the large-scale inclusions in steel act as the destruction starting point of the material. The labor is extremely necessary for investigating the maximum inclusions that have been distributed in the matrix of a large volume. The statistics of extreme value method is an excellent technique that can be applied for that case. When a material such as steel is opaque to visible light, the electron beam, and so on, the evaluation of the internal inclusions as three-dimensional (3D) information is presumed from the two-dimensional (2D) information observed under a microscope in respect of sample cross section. It is expected that this presumption error margin is large. It is almost impossible to verify 2D data by 3D one in a real material because the true value is uncertain, especially concerning the information of the tail of the size distribution. The purpose of the present work is to offer statistical information necessary to presume 3D characteristic value from 2D measurement data with respect to the maximum extreme value. The simulation whose 3D characteristic value is already-known is effective to this. Some 3D size distributions such as the exponential, log-normal, pseudo-normal, and Rayleigh distribution is set here, and how the 2D maximum extreme-value distribution (MED) changes into the measured number of sections is shown. The result gives a number of sections necessary to gather data with few error margins directly. Further, some findings of the relation between 3D-MED and 2D-MED are given. The overarching point is a type of the MED and conversion of the dimension.

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Statistical Analysis of Defects for Fatigue Strength Prediction and Quality Control of Materials

Cited by 168 publications

References 11 publications

Inference for Stereological Extremes

Inference for Stereological Extremes

Application of Statistics of Extreme Values for Inclusions in Stainless Steel on Different Stages of Steel Making Process

Simulation of the Estimation of the Maximum Inclusion Size from 2-Dimensional Observation Data on the Basis of the Extreme Value of Statistics

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