• 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 $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$.

• Journal of Korean Society for Quality Management
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• v.32 no.4
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• pp.229-241
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• 2004

Process capability index is used to determine whether a production process is capable of producing items within a specified tolerance. The index $C_{pmk}$ is the third generation process capability index. This index is more powerful than two useful indices $C_p$ and $C_{pk}$. Whether a process distribution is clearly normal or nonnormal, there may be some questions as to which any process index is valid or should even be calculated. As far as we know, yet there is no result for statistical inference with process capability index $C_{pmk}$. However, asymptotic method and bootstrap could be studied for good statistical inference. In this paper, we propose various bootstrap confidence limits for our process capability Index $C_{pmk}$. First, we derive bootstrap asymptotic distribution of plug-in estimator $C_{pmk}$ of our capability index $C_{pmk}$. And then we construct various bootstrap confidence limits of our capability index $C_{pmk}$ for more useful process capability analysis.

• Journal of the Korean Statistical Society
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• v.36 no.4
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• pp.471-477
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• 2007

In this paper, we provide a new proof to correct the asymptotic normality for the estimate $\hat{C}_{pmk}\;of\;C_{pmk}$, which is one of the well-known definitions of the process capability index. Also we comment briefly on the correction of the limiting distribution for $\hat{C}_{pmk}$ and on the use of re-sampling methods for the inference of $C_{pmk}$. Finally we discuss the concept of asymptotic unbiasedness.

• Communications for Statistical Applications and Methods
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• v.17 no.3
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• pp.459-471
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• 2010

Higher quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. Usually, the quality level is measured by process capability indices. The index is used to determine whether a production process is capable of producing items within a specified tolerance. The third generation index $C_{pmk}$ is more powerful than two useful indices $C_p$ and $C_{pk}$. which have been widely used in six sigma industries to assess process performance. Most evaluations on process capability indices focus on point estimates, which may result in unreliable assessments of process performance. In this paper, we consider better testing procedure on assessing process capability index $C_{pmk}$ for practitioners to use in determining whether a given process is capable. It is easy to use the proposed method for assessing process capability index $C_{pmk}$. Whether a process is clearly normal or nonnormal, our bootstrap testing procedure could be applied effectively without the complexity of calculation. A numerical result based on our proposed method is illustrated.

• Journal of the Korea Safety Management & Science
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• v.9 no.4
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• pp.137-142
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• 2007

This paper is to introduce attribute acceptance sampling plan based on statistical inference of binomial proportions such as PPM or PPB. In addition, this paper presents three variable sampling acceptance sampling plans based on $C_{pm},\;C_{pmk}$, and Taguchi's loss function. Producers are able to consider as not only external vendors but also internal customers.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.594-609
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• 1998

In this dissertation, a new process capability index $C_{psk}$ is introduced for non-normal process. The Pearson curve and the Johnson curve are selected for capability index calculation and data modeling the normal-based index $C_{psk}$ is used as the model for non-normal process. A significant result of this research find that the ranking of the seven indices, $C_p,\;C_{pk},\;C_{pm},\;C^{\ast}_{pm},\;C_{pmk},\;C_s,\;C_{psk}$ in terms of sensitivity to departure of the process median from the target value T=M from the most sensitive one up to the least sensitive are $C_{psk},\;C_{s},\;C_{pmk},\;C^{\ast}_{pm},\;C_{pm},\;C_{pk},\;C_p$. i.e, By the criteria adopted for evaluation of PCI's $C_{psk}$ is the most sensitive to the departure of the process median from target and $C_p$ is least

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.49
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• pp.77-87
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• 1999

A simple transformation of the $C^{*}$$_{pm}$, $C_{pp}$ can be regard as a process incapability index, provides an uncontaminated separation between information concerning the process accuracy and precision while this kind of information separation is not available with the $C^{*}$$_{pm}$. Recently, Kyung-seok Shin et. al. introduced an improved process incapability index $C^{*}$$_{pmk}$ by the transformation of the $C_{pmk}$. Accordingly, in this article process incapability index $C^{*}$$_{psk}$ will be proposed by the transformation of the $C_{psk}$. The motivation behind introduction of $C^{*}$$_{psk}$ is that $C_{psk}$ has failed to overcome is that it cannot distinguish process of high conforming output proportions from those of low conforming output proportions. Process incapability index $C^{*}$$_{psk}$ can identify a difference between two things by comparison on $C_{psk}$ and $C^{*}$$_{psk}$.EX>$_{psk}$.EX>$_{psk}$.

• Journal of Korean Society for Quality Management
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• v.26 no.1
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• pp.48-60
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• 1998

This paper proposes a fourth generation index $C_{psk}$, constructed from $C_{psk}$, by introducing the factor｜$\mu$-T｜ in the numerator as an extra penalty for the departure of the process mean from the preassigned target value T. The motivation behind the introduction of $C_{psk}$ is that when $T\neqM$ process shifts away from target are evaluated without respect to direction. All indices that are now in use assume normally distributed data, and any use of the indices on non-normal data results in inaccurate capability measurements. In this paper, a new process capability index $C_{psk}$ is introduced for non-normal process. The Pearson curve and the Johnson curve are selected for capability index calculation and data modeling the normal-based index $C_{psk}$ is used as the model for non-normal process. A significant result of this research find that the ranking of the six indices, $C_{p}$, $C_{pk}$, $C_{pm}$, ${C^*}_{psk}$, $C_{pmk}$, $C_{psk}$in terms of sensitivity to departure of the process median from the target value from the most sensitive one up to the least sensitive are $C_{psk}$, $C_{pmk}$, ${C^*}_{psk}$,$C_{pm}$, $C_{pk}$, $C_{p}$.

• Toxicological Research
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• v.28 no.1
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• pp.19-24
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• 2012

In the present study, toxicity of silver nanoparticles (AgNPs) was investigated in the nematode, Caenohabditis elegans focusing on the upstream signaling pathway responsible for regulating oxidative stress, such as mitogen-activated protein kinase (MAPK) cascades. Formation of reactive oxygen species (ROS) was observed in AgNPs exposed C.elegans, suggesting oxidative stress as an important mechanism in the toxicity of AgNPs towards C. elegans. Expression of genes in MAPK signaling pathways increased by AgNPs exposure in less than 2-fold compared to the control in wildtype C.elegans, however, those were increased dramatically in sod-3 (gk235) mutant after 48 h exposure of AgNPs (i.e. 4-fold for jnk-1 and mpk-2; 6-fold for nsy-1, sek-1, and pmk-1, and 10-fold for jkk-1). These results on the expression of oxidative stress response genes suggest that sod-3 gene expression appears to be dependent on p38 MAPK activation. The high expressions of the pmk-1 gene 48 h exposure to AgNPs in the sod-3 (gk235) mutant can also be interpreted as compensatory mechanisms in the absence of important stress response genes. Overall results suggest that MAPK-based integrated stress signaling network seems to be involved in defense to AgNPs exposure in C.elegans.

• Journal of Korean Society for Quality Management
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• v.28 no.2
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• pp.103-122
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• 2000

Process capability indices (PCI) $C_p\;C_{pk},\;C_m,\;and\;C_{pmk}$ are widely used to evaluate the process performance. The PCI's have been evolved to consider the 'off targetness' more adequately. However, all of these indices are found to be inconsistent with the proportion of nonconforming items, in some cases. That is, the PCI for a process may result in higher value even when the proportion of defectives increases. For these reasons, we propose a new capability index, $c_{pd}$, which is consistent with the defect rate. The characteristics of the new PCI, $c_{pd}$ are investigated with respect to the existing PCI's. Some statistical properties of an estimator for $c_{pd}$ are also investigated by a Monte Carlo simulation. Sensitivity study under minor deviation from normality is also performed to show the robustness of $c_{pd}$. A good estimator for $c_{pd}$ is under study.