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A New Process Capability Measure for Non-normal Process

  • Jun, Mi-Jung;Cho, Gyo-Young
    • 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.

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A New Process Incapability Measure for Non-normal Process

  • Jun, Mi-Jung;Cho, Gyo-Young
    • 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.

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Implementation of Nonparametric Statistics in the Non-Normal Process (비정규 공정에서 비모수 통계의 적용)

  • Choe, Seong-Un
    • Proceedings of the Safety Management and Science Conference
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    • pp.573-577
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    • 2012
  • Based on latest research, the parametric quality statistics cannot be used in non-normal process with demand pattern of many-variety and small-volume, since it involves extremely small sample size. The research proposes nonparametric quality statistics according to the number of lot or batch in the non-normal process. Additionally, the nonparametric Process Capability Index (PCI) is used with 14 identified non-normal distributions.

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A Study on the Application of CUSUM Control Charts under Non-normal Process (비정규 공정에서의 누적합 관리도 적용에 관한 연구)

  • Kim, Jong-Geol;Eom, Sang-Jun;Choe, Seong-Won
    • Proceedings of the Safety Management and Science Conference
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    • pp.535-549
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    • 2011
  • Control chart is most widely used in SPC(Statistical Process Control), Recently it is a critical issue that the standard control chart is not suitable to non-normal process with very small percent defective. Especially, this problem causes serious errors in the reliability procurement, such as semiconductor, high-precision machining and chemical process etc. Procuring process control technique for non-normal process with very small percent defective and perturbation is becoming urgent. Control chart technique in non-normal distribution become very important issue. In this paper, we investigate on research trend of control charts under non-normal distribution with very small percent defective and perturbation, and propose some variable-transformation methods applicable to CUSUM control charts in non-normal process.

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Statistical Tests for Process Capability Index Cp Based on Mixture Normal Process (혼합 정규공정 하에서의 공정능력지수 Cp에 대한 가설검정)

  • Cho, Joong Jae;Heo, Tae-Young;Jeong, Jun Chel
    • Journal of the Korean Society for Quality Management
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    • v.42 no.2
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    • pp.209-219
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    • 2014
  • Purpose: The purpose of this study is to develop the statistical test for process capability index $C_p$ based on mixture normal process. Methods: This study uses Bootstrap method to calculate the approximate P-value for various simulation conditions under mixture normal process. Results: This study indicates that our proposed method is effective way to test for process capability index $C_p$ based on mixture normal process. Conclusion: This study finds out that statistical test for process capability index $C_p$ based on mixture normal process is useful for real application.

Research Results and Trends Analysis on Process Control Charts for Non-normal Process (비정규 공정을 위한 공정관리도의 연구동향 분석)

  • Kim, Jong-Gurl;Kim, Chang-Su;Um, Sang-Joon;Kim, Hyung-Man;Choi, Seong-Won;Jeong, Dong-Gu
    • Proceedings of the Safety Management and Science Conference
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    • pp.547-556
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    • 2013
  • Control chart is most widely used in SPC(Statistical Process Control), Recently it is a critical issue that the standard control chart is not suitable to non-normal process with very small percent defective. Especially, this problem causes serious errors in the reliability procurement, such as semiconductor, high-precision machining and chemical process etc. Procuring process control technique for non-normal process with very small percent defective and perturbation is becoming urgent. Control chart technique in non-normal distribution become very important issue. In this paper, we investigate on research trend of control charts under non-normal distribution.

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A Study of Technology Trends for Effective Process Control under Non-Normal Distribution (비정규분포하에서의 효과적 공정관리를 위한 기술체계동향 연구)

  • Kim, Jong-Gurl;Um, Sang-Joon;Kim, Young-Sub;Ko, Jae-Kyu
    • Proceedings of the Safety Management and Science Conference
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    • pp.599-610
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    • 2008
  • It is an important and urgent issue to improve process capability in quality control. Process capability refers to the uniformity of the process. The variability in the process is a measure of the uniformity of output. A simple, quantitative way to express process capability, the degree of variability from target in specification is defined by process capability index(PCI). Almost process capability indices are defined under normal distribution. However, these indices can not be applied to the process of non-normal distribution including reliability. We investigate current research on the process of non-normal distribution, and advanced method and technology for developing more reliable and efficient PCI. Finally we suggest the perspective for future study.

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Analysis of Multivariate Process Capability Using Box-Cox Transformation (Box-Cox변환을 이용한 다변량 공정능력 분석)

  • Moon, Hye-Jin;Chung, Young-Bae
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.42 no.2
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    • pp.18-27
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    • 2019
  • The process control methods based on the statistical analysis apply the analysis method or mathematical model under the assumption that the process characteristic is normally distributed. However, the distribution of data collected by the automatic measurement system in real time is often not followed by normal distribution. As the statistical analysis tools, the process capability index (PCI) has been used a lot as a measure of process capability analysis in the production site. However, PCI has been usually used without checking the normality test for the process data. Even though the normality assumption is violated, if the analysis method under the assumption of the normal distribution is performed, this will be an incorrect result and take a wrong action. When the normality assumption is violated, we can transform the non-normal data into the normal data by using an appropriate normal transformation method. There are various methods of the normal transformation. In this paper, we consider the Box-Cox transformation among them. Hence, the purpose of the study is to expand the analysis method for the multivariate process capability index using Box-Cox transformation. This study proposes the multivariate process capability index to be able to use according to both methodologies whether data is normally distributed or not. Through the computational examples, we compare and discuss the multivariate process capability index between before and after Box-Cox transformation when the process data is not normally distributed.

Multivariate Process Capability Index Using Inverted Normal Loss Function (역정규 손실함수를 이용한 다변량 공정능력지수)

  • Moon, Hye-Jin;Chung, Young-Bae
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.41 no.2
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    • pp.174-183
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    • 2018
  • In the industrial fields, the process capability index has been using to evaluate the variation of quality in the process. The traditional process capability indices such as $C_p$, $C_{pk}$, $C_{pm}$ and $C^+_{pm}$ have been applied in the industrial fields. These traditional process capability indices are mainly applied in the univariate analysis. However, the main streams in the recent industry are the multivariate manufacturing process and the multiple quality characteristics are corrected each other. Therefore, the multivariate statistical method should be used in the process capability analysis. The multivariate process indices need to be enhanced with more useful information and extensive application in the recent industrial fields. Hence, the purpose of the study is to develop a more effective multivariate process index ($MC_{pI}$) using the multivariate inverted normal loss function. The multivariate inverted normal loss function has the flexibility for the any type of the symmetrical and asymmetrical loss functions as well as the economic information. Especially, the proposed modeling method for the multivariate inverted normal loss function (MINLF) and the expected loss from MINLF in this paper can be applied to the any type of the symmetrical and asymmetrical loss functions. And this modeling method can be easily expanded from a bivariate case to a multivariate case.

A New Measure of Process Capability for Non-Normal Process : $C_{psk}$ (비정규 공정에 대한 공정능력의 새로운 측도: $C_{psk}$)

  • 김홍준;송서일
    • Journal of the 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 $C_{psk}$, $C_{pmk}$, ${C^*}_{psk}$,$C_{pm}$, $C_{pk}$, $C_{p}$.

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