• 대한안전경영과학회:학술대회논문집
• /
• 대한안전경영과학회 2004년도 추계학술대회
• /
• pp.69-79
• /
• 2004

Process capability indices are widely used in industries and quality assurance system. When designing the parameter on the multiple quality characteristics, there has been a study for optimization of problems, but there has been few former study on the possible conflicting phenomena in considertion of the correlations among the characteristics. To solve the issue on the optimal design for multiple quality characteristics, the study propose the expected loss function with cross-product terms among the characteristics and derived range of the coefficients of terms. Therefore, the analysis have to be required a multivariate statistical technique. This paper introduces to multivariate capability indices and then selects a multivariate process capability index incorporated both the process variation and the process deviation from target among these indices under the multivariate normal distribution. We propose a new multivariate capability index $MC_{pm}^{++}$ using quality loss function instead of the process variation and this index is compared with the proposed indices when quality characteristics are independent and dependent of each other.

• 대한안전경영과학회지
• /
• 제5권3호
• /
• pp.145-156
• /
• 2003

As we understand it, Process Capability indices are intended to provide single-number assessments of ability to meet specification limits on quality characteristics of interest. As a consequence of the varied ways in which PCIs are used, there have been two natural lines of research work: $\circled1$ studies on the properties of PCIs and their estimators in many different environments; $\circled2$ construction of new PCIs purporting to have better properties in certain circumstances. The most of existing process capability indices are concerned with the single variable. But, in many cases, a quality characteristic is composed with several factors. In that case, we want to know the integrated process capability of a quality characteristic not those of each factor. In this paper, we proposed a new multivariate system process capability index called $MSPCI:SC_{psk}$ which is the geometric mean of performance measure $C_{psk}$'S, and will be used as the criterion to assess multiple response process designs. Numerical illustration is done for $SC_{psk}$, $\overline{C_p}$(f), Cp, Cpk, Cpm, and Cpsk.

• Journal of the Korean Data and Information Science Society
• /
• 제18권4호
• /
• pp.869-878
• /
• 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.

• 산업경영시스템학회지
• /
• 제41권2호
• /
• pp.174-183
• /
• 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.

• 품질경영학회지
• /
• 제30권3호
• /
• pp.66-78
• /
• 2002

Process capability indices are being used as indicators for measurements of process capability for SPC of quality assurance system in industries. In view of the enhancement of customer satisfaction, process capability indices in which loss functions are used to deal with the economic loss In the processes deviated from the target, are in an adequate representation of the customer's perception of quality In this connection, the loss function has become increasingly important in quality assurance. Taguchi uses a modified form of the quadratic loss function to demonstrate the need to consider the proximity to the target while assessing its quality. But this traditional quadratic loss function is inadequate to assessing the quality and quality improvement since different processes have different sets of economic consequences on the manufacturing, Thereby, a flexible approach to the development of the loss function needs to be desired. In this paper, we introduce an easily understood loss function, based on reflection of probability density function of the normal distribution. That is, the Reflected Normal Loss function can be adapted to an asymmetric loss as well as to a symmetric loss around the target. We propose that, instead of the process variation, a new capability index, CpI using the Reflected Normal Loss Function that can accurately reflect the losses associated with the process and a new capability index CpI Is compared with the classical indices as $C_{p}$ , $C_{pk}$, $C_{pm}$ and $C_{pm}$ $^{+}$.>.+/./.

• 산업경영시스템학회지
• /
• 제30권4호
• /
• pp.182-189
• /
• 2007

Process Capability indices(PCIs) have been widely used in manufacturing industries to provide a quantitative measure of process performance. PCIs have been developed to represent process capability more exactly. The traditional process capability indices Cp, Cpk, Cpm, $Cpm^+$ have been used to characterize process performance on the basis of univariate quality characteristics. Cp, Cpk consider the process variation, Cpm considers both the process variation and the process deviation from target and $Cpm^+$ considers economic loss for the process deviation from target In the previous studies, only one designated location on each part is measured. System process capability index even though in single process, multiple measurement locations on each part are required to calculate the reliable process capability. In manufacturing industry, there is growing interest in quantitative measures of process variation under multivariate quality characteristics. The multivariate process capability index incorporates both the process variation and the process deviation from target or considers expected loss caused by the process deviation from target. In this paper, we compare various process capability indices and propose the application method of PCIs.

• Communications for Statistical Applications and Methods
• /
• 제18권3호
• /
• pp.377-389
• /
• 2011

공정능력지수는 공정능력을 측정하고 분석하기 위하여 매우 중요한 역할을 하는 측도로, 품질수준과 밀접한 관계가 있을 뿐만 아니라 보다 높은 품질수준은 고객들에게 더 큰 만족을 가져다 준다. 제3세대 공정 능력지수 $C_{pmk}$는 gms히 6시그마 산업현장에서 공정능력을 평가하기 위하여 유용하게 사용되는 두 가지 지수 $C_p$와 $C_{pk}$보다 이론적으로 강력한 지수이다. 실제로 제조현장에서 두 가지 이상의 서로 연관이 있는 품질특성치들과 제품에 대한 규격한계들을 사용하여 보다 정확한 공정능력 분석이 필요할 것이다. 이러한 경우에 단순히 하나의 일변량 공정능력지수를 통하여 공정능력분석을 하기 보다는 벡터 공정능력지수나 다변량공정능력지수를 통하여 분석을 수행하는 것이 바람직할 것이다. 본 논문에서는 3세대 공정능력지수 $C_{pmk}$를 고려하여 2차원 벡터 공정능력지수 $C_{pmk}$ = ($C_{pmkx}$, $C_{pmky}$)$^t$에 대하여 연구하였다. 우선, $C_{pmk}$에 대한 플러그-인(plug-in) 추정량 $\hat{C}_{pmk}$과 관련하여 핵심내용인 극한 확률분포를 유도하였다. 나아가 이러한 결과를 기초로 이변량 정규분포하에서 공분산 행렬 $V_{pmk}$을 구체적으로 계산하였다. 또한 이 행렬의 추정을 통하여 벡터 공정능력지수 $C_{pmk}$에 대한 근사적인 공동 신뢰영역을 제시함으로써, 본 논문에서의 극한분포 연구결과가 벡터 공정능력지수 $C_{pmk}$에 대한 통계적 추론에 유용하게 활용될 수 있음을 보여주었다.

• 산업경영시스템학회지
• /
• 제42권2호
• /
• pp.18-27
• /
• 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.

• 품질경영학회지
• /
• 제30권1호
• /
• pp.118-132
• /
• 2002

This paper presents a process incapability index to provide manager with various information of process and to reduce cost. The introduced process incapability indices indicate information about mean and variance of manufacturing process and variance of inspection process to evaluate process capability using ratio of variance and difference between target and mean to specification. This model can be used by the scale of six sigma management.

• 산업경영시스템학회지
• /
• 제30권3호
• /
• pp.28-36
• /
• 2007

Process Capability indices (PCIs) have been widely used in manufacturing industries to provide a quantitative measure of process performance. PCIs have been developed to represent process capability more exactly. In the previous studies, only one designated location on each part is measured. But even though in single process, multiple measurement locations on each part are required to calculate the reliable process capability. In this paper, we propose a new process capability index with multiple measurement locations on each part. We showed numerical examples and sensitivity analysis according to the number of measurement locations.