• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.869-878
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• 2007

In this paper a new process capability index $C_{psks}$ is introduced for non-normal process. $C_{psks}$ that is proposed by transformation of the $C_{psks}$ incorporates an additional skewness correction factor in the denominator of $C_{psks}$. The use of each technique is illustrated by reference to a distribution system which includes the Pearson and Johnson functions. Accordingly, $C_{psks}$ is proposed as the process capability measure for non-normal process.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.937-943
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• 2007

In this paper a new process incapability index $C^*_{psks}$ is introduced for non-normal process. $C^*_{psks}$ is proposed by transformation of the $C^*_{psks}$. The use of each technique is illustrated by reference to a distribution system which includes the Pearson and Johnson functions. Accordingly, $C^*_{psks}$ is proposed as the process capability measures for non-normal process.

• Proceedings of the Safety Management and Science Conference
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• 2000.05a
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• pp.249-263
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• 2000

This paper considers an algorithm using Johnson transformation to calculate process capability index for non-normal distribution. Johnson transformation is well known as one of methods transforming the data with non-normal distribution to normal data.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.159-173
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• 1998

Quality characteristics on the properties of process capability indices (PCIs) are often required to be normally distributed. But, if a characteristic is not normally distributed, serious errors can result from normal-based techniques. In this case, we may well consider the use of new PCIs specially designed to be robust for non-normality. In this paper, a newly proposed measure of process capability is introduced and compared with existing PCIs using the simulated non-normal data.

• 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 $C_{psk}$, $C_{pmk}$, ${C^*}_{psk}$,$C_{pm}$, $C_{pk}$, $C_{p}$.

• Journal of Korean Society for Quality Management
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• v.44 no.1
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• pp.167-180
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• 2016

Purpose: The problem for the traditional control chart is that it is unable to monitor the very small fraction of nonconforming and the underlying distribution is the normal distribution. $Z_p$ control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the $Z_p$ control chart in order to use under non-normal process. Methods: $Z_p$ is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal $Z_p$ control chart is designed based on ${\alpha}$-risk calculated by cumulative distribution function of Burr distribution. ${\beta}$-risk, which is for performance evaluation, obtains in the Burr distribution's cumulative distribution function and control limit. Results: The control limit for non-normal $Z_p$ control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal $Z_p$ control chart is able to control not only the very small fraction of nonconforming, but it is also useful when $Z_p$ distribution is non-normal distribution.

• Proceedings of the Korean Reliability Society Conference
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• 2001.06a
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• pp.311-319
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• 2001

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. Therefore, $C_{s}$ is proposed which extends the most useful index to date, the Pearn-Kotz-Johnson $C_{pmk}$, by not only taking into account that the process mean may not lie midway between the specification limits and incorporating a penalty when the mean deviates from its target, but also incorporating a penalty for skewness. Therefore we propose, a new process capability index $C_{psk}$( WV) applying the weighted variance control charting method for non-normally distributed. The main idea of the weighted variance method(WVM) is to divide a skewed or asymmetric distribution into two normal distribution from its mean to create two new distributions which have the same mean but different standard distributions. In this paper we propose an example, a distribution generated from the Johnson family of distributions, to demonstrate how the weighted variance-based process capability indices perform in comparison with another two non-normal methods, namely the Clements and the Wright methods. This example shows that the weighted valiance-based indices are more consistent than the other two methods In terms of sensitivity to departure to the process mean/median from the target value for non-normal process.s.s.s.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.373-391
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• 2022

The distribution of observations in most econometric studies with spatial heterogeneity is skewed. Usually, a single transformation of the data is used to approximate normality and to model the transformed data with a normal assumption. This assumption is however not always appropriate due to the fact that panel data often exhibit non-normal characteristics. In this work, the normality assumption is relaxed in spatial mixed models, allowing for spatial heterogeneity. An inference procedure based on Bayesian mixed modeling is carried out with a multivariate skew-elliptical distribution, which includes the skew-t, skew-normal, student-t, and normal distributions as special cases. The methodology is illustrated through a simulation study and according to the empirical literature, we fit our models to non-life insurance consumption observed between 1998 and 2002 across a spatial panel of 103 Italian provinces in order to determine its determinants. Analyzing the posterior distribution of some parameters and comparing various model comparison criteria indicate the proposed model to be superior to conventional ones.

• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.803-811
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• 2012

For credit evaluation models, we extend the study of discriminatory power based on AUC obtained from a ROC curve when the number of defaults is small and distribution functions of the defaults and non-defaults are normal distributions. Since distribution functions do not satisfy normality in real world, the distribution functions of the defaults and non-defaults are assumed as normal mixture distributions based on results that the normal mixture could be better fitted than other distribution estimation methods for non-normal data. By using several AUC statistics, the discriminatory power under such a circumstance is explored and compared with those of normal distributions.

• Journal of Korean Society on Water Environment
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• v.24 no.6
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• pp.676-681
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• 2008

The evaluation of the effluent water quality of sewage treatment plant is one of the most important factor in calculating total maximum daily loads (TMDLs). Current method to calculate 95% upper limit of effluent water quality of sewage treatment plant assuming normal distribution of data needs to be implemented in case of non-normal distribution. We have investigated the applicability of percentile ranking method as a non-parametric statistical analysis in case of non-normal distribution of data.