• Journal of Korean Society for Quality Management
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• v.30 no.4
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• pp.44-57
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• 2002

In this paper we study two vector-valued process capability indices $C_{p}$＝($C_{px}$, $C_{py}$ ) and $C_{pk}$＝( $C_{pkx}$, $C_{pky}$) considering process capability indices $C_{p}$ and $C_{pk}$. First, we derive two asymptotic distributions of plug-in estimators (equation omitted) and (equation omitted) under. some proper. conditions. Second, we examine the performance of asymptotic confidence regions of our process capability indices $C_{p}$＝( $C_{px}$ , $C_{py}$ ) and $C_{pk}$＝( $C_{pkx}$, $C_{pky}$) under BN($\mu$$_{x}$, $\mu$$_{y}$, $\sigma$$^2$$_{x}$, $\sigma$$^2$$_{y}$,$\rho$)$\rho$)EX>)EX>)EX>)

• Journal of Korean Society for Quality Management
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• v.25 no.2
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• pp.102-111
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• 1997

In this paper I discuss a method of constructing the confidence region for the logistic response surface model. The construction involves a, pp.ication of a general fitting procedure because the log odds is linear in its parameters. Estimation of parameters of the logistic response surface model can be accomplished by maximum likelihood, although this requires iterative computational method. Using the asymptotic results, asymptotic covariance of the estimators can be obtained. This can be used in the construction of confidence regions for the parameters and for the logistic response surface model.

• Journal of the Korean Statistical Society
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• v.18 no.1
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• pp.46-61
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• 1989

This paper is concerned with the development of a nonparametric procedure for the statistical inference about the nonlinear regression parameters. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both under the null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.198-212
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• 1995

This study provides a nonparametric procedure for the statistical inference of the parameters in stationary autoregressive processes. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both underthe null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.399-422
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• 2003

In actual manufacturing industries, process capability analysis often entails characterizing or assessing processes or products based on more than one engineering specification or quality characteristic. Since these characteristics are related, it is a risky undertaking to represent variation of even a univariate characteristic by a single index. Therefore, the desirability of using vector-valued process capability index(PCI) arises quite naturally. In this paper, some vector-valued ${PCI}_p$ ${C}_p$=(${C}_{px}$, ${C}_{py}$),${C}_{pk}$=(${C}_{pkx}$, ${C}_{pky}$) and ${C}_{pm}$=(${C}_{pmx}$, ${C}_{pmy}$) considering univariate PCIs ${C}_p$,${C}_{pk}$ and ${C}_{pm}$ are studied. First, we propose some asymptotic confidence regions of our vector-valued PCIs with bootstrap. And we examine the performance of asymptotic confidence regions of our vector-valued PCIs ${C}_p$ and ${C}_{pk}$ under the assumption of bivariate normal distribution BN($\mu_{x}$, $\mu_{y}$, $\sigma_{x}^{2}$, $\sigma_{y}^{2}$, $\rho$) and bivariate chi-square distribution Bivariate $x^2$(5,5,$\rho$).

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.127-139
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• 1995

This paper is concerned with the asymptotic properties of the least absolute deviation estimators for nonlinear regression models. The simple and practical sufficient conditions for the strong consistency and the asymptotic normality of the least absolute deviation estimators are given. It is confirmed that the extension of these properties to wide class of regression functions can be established by imposing some condition on the input values. A confidence region based on the least absolute deviation estimators is proposed and some desirable asymptotic properties including the asymptotic relative efficiency also discussed for various error distributions. Some examples are given to illustrate the application of main results.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.6B
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• pp.723-729
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• 2008

Confidence intervals of growth curves are calculated to assess the uncertainty of index flood method as a regional frequency analysis. The asymptotic variance of quantile estimator for the generalized logistic distribution is introduced to evaluate confidence intervals. In addition, the variances of at-site frequency estimator and regional frequency estimator are used to evaluate an efficiency index. The efficiency indexes for 14 homogeneous regions based on 378 stations show that index flood method estimators are more efficient than at-site frequency estimators. It is shown that the number of sites in a region needs to be limited for regional gain.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.205-216
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• 1996

The bootstrap calibration method for empirical likelihood is considered to make a confidence region for the regression coefficients. Asymptotic properties are studied regarding the coverage probability. Small sample simulation results reveal that the bootstrap calibration works quite well.

• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.377-389
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• 2011

A higher quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The third generation index $C_{pmk}$ is more powerful than two useful indices $C_p$ and $C_{pk}$ that have been widely used in six sigma industries to assess process performance. In actual manufacturing industries, process capability analysis often entails characterizing or assessing processes or products based on more than one engineering specification or quality characteristic. Since these characteristics are related, it is a risky undertaking to represent the variation of even a univariate characteristic by a single index. Therefore, the desirability of using vector-valued process capability index(PCI) arises quite naturally. In this paper, we consider more powerful vector-valued process capability index $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$ that consider the univariate process capability index $C_{pmk}$. First, we examine the process capability index $C_{pmk}$ and plug-in estimator $\hat{C}_{pmk}$. In addition, we derive its asymptotic distribution and variance-covariance matrix $V_{pmk}$ for the vector valued process capability index $C_{pmk}$. Under the assumption of bivariate normal distribution, we study asymptotic confidence regions of our vector-valued process capability index $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.449-461
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• 2009

Higher sigma quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The process capability indices and the sigma level $Z_{st}$ ave been widely used in six sigma industries to assess process performance. Most evaluations on process capability indices focus on statistical estimation under normal process which may result in unreliable assessments of process performance. In this paper, we consider statistical estimation for bivariate VPCI(Vector-valued Process Capability Index) $C_{pkl}=(C_{pklx},\;C_{pklx})$ under Marshall and Olkin (1967)'s bivariate exponential process. First, we derive some limiting distribution for statistical inference of bivariate VPCI $C_{pkl}$. And we propose two asymptotic normal confidence regions for bivariate VPCI $C_{pkl}$. The proposed method may be very useful under bivariate exponential process. A numerical result based on our proposed method shows to be more reliable.