• The Korean Journal of Applied Statistics
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• v.29 no.2
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• pp.301-308
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• 2016

The process capability index is used to determine whether a production process is capable of producing items within a specified tolerance. Some process capability indices $C_p$, $C_{pk}$ and $C_{pm}$ have been of particular interest as useful management tools for tracking process performance. Most evaluations on process capability indices focus on statistical estimation and test of hypothesis. It is necessary to investigate their asymptotic correlationship among basic estimators ${\hat{C}}_p$, ${\hat{C}}_{pk}$ and ${\hat{C}}_{pm}$ of process capability indices $C_p$, $C_{pk}$ and $C_{pm}$. In this paper, we study their asymptotic correlationship for three process capability indices ${\hat{C}}_p$, ${\hat{C}}_{pk}$ and ${\hat{C}}_{pm}$ under bivariate normal distribution BN(${\mu}_x,{\mu}_y,{\sigma}^2_x,{\sigma}^2_y,{\rho}$). With some nonnormal processes, the asymptotic correlation coefficient of any two respective process capability index estimators could be established.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.2935-2944
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• 2000

Gas tungsten arc(GTA) welding is used to rrpiar the seat ring in swing type check valve in power plant because of its high weld quality. In order to automate the welding process, it is needed to analyze the process of inside pipe girth welding. In this study, the shapes of weld bead on pipe inside and outside were predicted and its validity was investigated. On the assumption that the welding arc had a bivariate gaussian distribution, analytical solution was derived to predict the temperature distribution in pipe weld using mapping under consideration of physical relationships. The size of weld bean could be predicted from this equation and its accuracy was verified by experiments.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.623-632
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• 2014

We shall consider the estimation for the parameter and the right tail probability in a general exponential distribution. We also shall consider the estimation of the reliability P(X < Y ) and the skewness trends of the density function of the ratio X=(X+Y) for two independent general exponential variables each having different shape parameters and known scale parameter. We then shall consider the estimation of the failure rate average and the hazard function for a general exponential variable having the density function with the unknown shape and known scale parameters, and for a bivariate density induced by the general exponential density.

• Journal of Ecology and Environment
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• v.41 no.8
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• pp.223-234
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• 2017

Background: Spatial structure of plants in a population reflects complex interactions of ecological and evolutionary processes. For dioecious plants, differences in reproduction cost between sexes and sizes might affect their spatial distribution. Abiotic heterogeneity may also affect adaptation activities, and result in a unique spatial structure of the population. Thus, we examined sex- and size-related spatial distributions of old-growth forest of dioecious tree Torreya nucifera in extremely heterogeneous Gotjawal terrain of Jeju Island, South Korea. Methods: We generated a database of location, sex, and size (DBH) of T. nucifera trees for each quadrat ($160{\times}300m$) in each of the three sites previously defined (quadrat A, B, C in Site I, II, and III, respectively). T. nucifera trees were categorized into eight groups based on sex (males vs. females), size (small vs. large trees), and sex by size (small vs. large males, and small vs. large females) for spatial point pattern analysis. Univariate and bivariate spatial analyses were conducted. Results: Univariate spatial analysis showed that spatial patterns of T. nucifera trees differed among the three quadrats. In quadrat A, individual trees showed random distribution at all scales regardless of sex and size groups. When assessing univariate patterns for sex by size groups in quadrat B, small males and small females were distributed randomly at all scales whereas large males and large females were clumped. All groups in quadrat C were clustered at short distances but the pattern changed as distance was increased. Bivariate spatial analyses testing the association between sex and size groups showed that spatial segregation occurred only in quadrat C. Males and females were spatially independent at all scales. However, after controlling for size, males and females were spatially separated. Conclusions: Diverse spatial patterns of T. nucifera trees across the three sites within the Torreya Forest imply that adaptive explanations are not sufficient for understanding spatial structure in this old-growth forest. If so, the role of Gotjawal terrain in terms of creating extremely diverse microhabitats and subsequently stochastic processes of survival and mortality of trees, both of which ultimately determine spatial patterns, needs to be further examined.

• The Korean Journal of Applied Statistics
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• v.9 no.2
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• pp.13-23
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• 1996

In this paper, we consider the Marshall and Olkin's bivariate exponential model under random censorship for the distribution of failure times of a system with two components. We propose a bootstrap testing procedure for independence and compare the powers of it with other tests via Monte Carlo simulation.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.795-800
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• 2001

Two evaluation techniques of the tunnel lining concrete using ultra sonic velocity method are developed. Modified linear regression technique is proposed to enhance the corelation between the pulse velocity and the compressive strength of core specimens. And bivariate normal distribution is assumed to evaluate the quality of concrete as a terms of compressive strength. A simple corelation table between the pulse velocity and the compressive strength of core specimens are proposed.

• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.93-104
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• 1996

In this paper, Marshall and Olkin's bivariate exponential distribution is assumed for stress and strength model. We derive the asymptotic distributions and construct some approximate confidence intervals for P(X

• Journal of the Korean Data and Information Science Society
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• v.8 no.1
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• pp.79-83
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• 1997

This paper considers the problem of estimating the model parameters and reliability functions for Freund bivariate exponential distribution. Uniformly minimum variance unbiased estimators for model parameters, joint reliability and marginal reliability functions are obtained in the both case of non-identically distributed marginals and identically distributed marginals.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.297-308
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• 2001

A partial ordering is developed here among conditionally positive quadrant dependent (CPQD) bivariate random vectors. This permits us to measure the degree of CPQD-ness and to compare pairs of CPQD random vectors. Some properties and closure under certain statistical operations are derived.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.2
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• pp.135-139
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• 2001

A process control procedure is suggested when screening inspection is performed with a surrogate variable correlated with the performance variable. Assuming bivariate normal distribution for the performance and screening variable, the procedure is designed on the basis of the time required for detecting process shift.