• Tunnel and Underground Space
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• v.2 no.2
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• pp.251-264
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• 1992

In this study, the size effect in measuring the fracture toughness of rock was investigated using the ISRM Suggested Method for Fracture toughness using Chevron Bend Specimens. Total 58 specimens were prepared with 4 different diameters, 29, 42, 54, 68mm and center cut-chevron notch. In addition to this, to evaluated the effect of anisotropy of Jecheon granite, which is the sample for this study, core drilling direction was adjusted perpendicular(short transverse) and parallel(arrester) to the rift plane in the sample and the measured fracture toughness for each direction were compared. Important results obtained from this study are as follows. Level ll test condition is more adequate than l, because of low data scattering and precision and corrected fracture toughness of Jechoen granite measured and 2.2MPa{{{{ SQRT { m} }}}} for arrester direction with minimum initial crack length 0.7cm. From the relationship between core diameter and initial crack length presented in the ISRM testing method, the specimen diameter should be bigger than 47mm. The fracture toughnesses measured for arrester and short transverse directon show 10% difference. This is to the anisotropy of Jecheon granite possessing rift plane.

• Proceedings of the KSR Conference
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• 2011.10a
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• pp.1115-1122
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• 2011

Reinforced-Roadbed materials are usually composed of crushed stones. Repeated load application can induce deformation in the reinforced-roadbed layer so that it causes irregularity of track. Thus it is important to develop a prediction model of elastic modulus based on stress-strain relation under repeatitive load in order to investigate behavior of reinforced roadbed. The prediction model of elastic modulus of the material can be obtained from repeated triaxial test. However, a proper size of the sample for the test must be used. In this study, a large repeatitive triaxial test apparatus with the sample size of diameter of 30 cm and height of 60cm was adapted for performing test of the crushed stone reinforced-roadbed considering large particle size to get resilient modulus Mr. The obtained resilient modulus was compared to shear modulus obtained from mid size resonant column test. The sample size effect is somewhat large enough so that it is required to design a scale factor based on similarity law in order to use smaller samples for getting elastic modulus of the crushed stone reinforced-roadbed material. A scale factor could be obtained from this study.

• Journal of Korean Society for Quality Management
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• v.23 no.4
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• pp.28-41
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• 1995

We consider the problem of identifying multiple outliers in linear model. The available regression diagnostic methods often do not succeed in detecting multiple outliers because of the masking and swamping effect. Recently, among the various robust estimator of reducing the effect of outliers, LMS(Least Meadian Square) estimator has been to be a suitable method proposed to expose outliers and leverage points. However, as you know it, the data analysis method with LMS estimator is to be taken the median of the squared residuals in the sample which is extracted the sample space. Then this model causes the trouble, for the number of the chosen sample is nCp, i.e. as the size of sample space n is increasing, the number is increasing fastly. And the covariance matrix may be the singular matrix, so that matrix is approching collinearity. Thus we propose a procedure ELMS for the resampling in LMS method and study the size of the effective elementary set in this algorithm.

• Elastomers and Composites
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• v.58 no.3
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• pp.103-111
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• 2023

The abrasion resistances of silica-filled styrene-butadiene rubber (SBR) compounds prepared with and without dicyclopentadiene resin (SBR-R and SBR-0, respectively) were studied using four different abrasion testers, namely cut and chip (CC), Lambourn, DIN, and laboratory abrasion tester (LAT100). The effect of the resin on the abrasion behavior was elucidated by analyzing the morphologies and size distributions of wear particles. All the wear particles had rough surfaces, but those obtained in the Lambourn abrasion test exhibited relatively smooth surfaces. The size distributions of the wear particles showed different trends depending on the abrasion tester and the rubber compound; however, most of the wear particles were larger than 1000 ㎛. The SBR-R sample showed a wide range of particle sizes (from 63 ㎛) in the LAT100 abrasion test and majority of the wear particles were 500-1000 ㎛, whereas the SBR-0 sample had the most distribution of larger than 1000 ㎛. The abrasion rates of SBR-0 sample were lower than those of the SBR-R sample for the CC and LAT100 abrasion tests, but the Lambourn abrasion test result showed the opposite trend. Addition of the resin influenced the abrasion behavior, however the effect varied depending on the type of abrasion tests.

• Asian-Australasian Journal of Animal Sciences
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• v.22 no.12
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• pp.1620-1624
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• 2009

This study aimed to clarify the effect of mobile bag size and ratio of sample size to bag surface area on intestinal digestibility of forage in sheep. Four Suffolk ewes fitted with ruminal and proximal duodenal cannulae were fed second-cut Italian ryegrass (Lolium multiflorum Lam.) hay twice daily, and the same forage was used to measure intestinal digestibility. The forage samples were incubated in the rumen for 16 h and then in pepsin-HCl solution for 3 h before intestinal incubation. The incubated forage samples were placed in a nylon mobile bag. The bag sizes used were either 20 mm${\times}$20 mm (small bag size; SBS) or 30 mm${\times}$30 mm (large bag size; LBS) and the ratio of the sample size to the surface area of the bag was either 5.5 $mg/cm^{2}$ (low ratio; LR) or 11.0 $mg/cm^{2}$ (high ratio; HR) resulting in four different treatment conditions: SBS-LR, SBS-HR, LBS-LR and LBS-HR. Eight bags per animal were inserted through the duodenal cannulae at 15-min intervals and were subsequently collected from the feces of the animal. The mean intestinal bag transition time did not differ significantly between animals, but ranged from 23.2 to 27.0 h. The intestinal digestibility of dry matter (IDDM) ranged from 0.162${\pm}$0.019 g/g in the SBS-HR treatment group to 0.195${\pm}$0.018 g/g in the SBS-LR treatment. The intestinal digestibility of crude protein (IDCP) ranged from 0.610${\pm}$0.031 g/g in the LBS-LR treatment to 0.693${\pm}$0.018 g/g in the SBS-LR treatment. There was no difference in the IDDM and IDCP between different treatments. It was therefore concluded that the size of the mobile bag and the ratio of the sample size to the bag surface area did not influence the intestinal digestibility of forage. Future studies should use bags with high ratios of sample size to surface area in order to obtain sufficient residue for further analysis.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.297-310
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• 2002

Liang and Zeger proposed generalized estimating equations(GEE) for analyzing repeated data which is discrete or continuous. GEE model can be extended to model for repeated categorical data and its estimator has asymptotic multivariate normal distribution in large sample sizes. But GEE is based on large sample asymptotic theory. In this paper, we study the properties of GEE estimators for repeated ordinal data in small sample sizes. We generate ordinal repeated measurements for two groups using two methods. Through Monte Carlo simulation studies we investigate the empirical type 1 error rates, powers, relative efficiencies of the GEE estimators, the effect of unequal sample size of two groups, and the performance of variance estimators for polytomous ordinal response variables, especially in small sample sizes.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1067-1080
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• 2010

A number of methods have been developed to determine sample sizes in clinical trial, and most clinical trial organizations determine sample sizes based on the methods. In contrast, determining sufficient sample sizes needed for experiments using microarray chips is unsatisfactory and not widely in use. In this paper, our objective is to provide a guideline in determining sample sizes, utilizing reproducibility of real microarray data. In the reproducibility comparison, five methods for discovering differential expression are used: Fold change, Two-sample t-test, Wilcoxon rank-sum test, SAM, and LPE. In order to standardize gene expression values, both MAS5 and RMA methods are considered. According to the number of repetitions, the upper 20 and 100 gene accordances are also compared. In determining sample sizes, more realistic information can be added to the existing method because of our proposed approach.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.669-684
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• 2017

Mediation models are widely used in many fields of research and have recently gained attention in epidemiology. The mediation proportion is a standard measure to evaluate what part of the total exposure effect on an outcome may be explained by a particular mediator and to examine how important that pathway is relative to the overall exposure effect. A common question is how large a sample size is needed to achieve high statistical power or, equivalently, what magnitude of effect can be detected. Current power and sample size calculations for mediation analysis are limited and additional research is needed. We therefore propose a computer-intensive power analysis using the mediation proportion. We conduct simulation studies to calculate statistical powers and sample sizes. And then, we illustrate our power analysis using an example from the Adult Health Study of atomic-bomb survivors and demonstrate that the method is relatively straightforward to understand and compute.

• Communications for Statistical Applications and Methods
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• v.26 no.6
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• pp.527-538
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• 2019

This paper considers the issue of obtaining the optimal design in Poisson regression model when the sample size is small. Poisson regression model is widely used for the analysis of count data. Asymptotic theory provides the basis for making inference on the parameters in this model. However, for small size experiments, asymptotic approximations, such as unbiasedness, may not be valid. Therefore, first, we employ the second order expansion of the bias of the maximum likelihood estimator (MLE) and derive the mean square error (MSE) of MLE to measure the quality of an estimator. We then define DM-optimality criterion, which is based on a function of the MSE. This criterion is applied to obtain locally optimal designs for small size experiments. The effect of sample size on the obtained designs are shown. We also obtain locally DM-optimal designs for some special cases of the model.

• Computers and Concrete
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• v.28 no.5
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• pp.521-532
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• 2021

Present paper focuses on the modeling of size effect on the compressive strength of normal concrete with the application of Discrete Element Method (DEM). Test specimens with different size and shape were cast and uniaxial compressive strength test was performed on each sample. Five different concrete mixes were used, all belonging to a different normal strength concrete class (C20/25, C30/37, C35/45, C45/55, and C50/60). The numerical simulations were carried out by using the PFC 5 software, which applies rigid spheres and contacts between them to model the material. DEM modeling of size effect could be advantageous because the development of micro-cracks in the material can be observed and the failure mode can be visualized. The series of experiments were repeated with the model after calibration. The relationship of the parallel bond strength of the contacts and the laboratory compressive strength test was analyzed by aiming to determine a relation between the compressive strength and the bond strength of different sized models. An equation was derived based on Bazant's size effect law to estimate the parallel bond strength of differently sized specimens. The parameters of the equation were optimized based on measurement data using nonlinear least-squares method with SSE (sum of squared errors) objective function. The laboratory test results showed a good agreement with the literature data (compressive strength is decreasing with the increase of the size of the specimen regardless of the shape). The derived estimation models showed strong correlation with the measurement data. The results indicated that the size effect is stronger on concretes with lower strength class due to the higher level of inhomogeneity of the material. It was observed that size effect is more significant on cube specimens than on cylinder samples, which can be caused by the side ratios of the specimens and the size of the purely compressed zone. A limit value for the minimum size of DE model for cubes and cylinder was determined, above which the size effect on compressive strength can be neglected within the investigated size range. The relationship of model size (particle number) and computational time was analyzed and a method to decrease the computational time (number of iterations) of material genesis is proposed.