• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.52
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• pp.69-79
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• 1999

The main objective of this study are to propose two methods that would be a comprehensive measure of evaluation for non-normal process capability with Beta distributions. First method is introduced using process capability index $C_{psk}$ by the Pearson system and Johnson system. The Pearson system and the Johnson System selected for process capability index calculation have a equivalent result of this study that the ranking of the seven indices 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 $C^{*}_{pm}$ , $C_{psk}$ , $C_{s}$ , $C_{pmk}$ , $C_{pm}$ , $C_{pk}$ , $C_{p}$ . Second method show using the percentage nonconforming by the Pearson, Johnson and Burr functions. In thus study, we find that the Pearson system and the Burr system are a reasonable method to estimate percentage nonconforming. But, the exact procedure for deriving this estimate will be based on Beta distribution. Accordingly, if a process is not normally distributed , but normal-based techniques are used serious errors can result.

• The Korean Journal of Applied Statistics
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• v.29 no.2
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• pp.301-308
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• 2016

The process capability index is used to determine whether a production process is capable of producing items within a specified tolerance. Some process capability indices $C_p$, $C_{pk}$ and $C_{pm}$ have been of particular interest as useful management tools for tracking process performance. Most evaluations on process capability indices focus on statistical estimation and test of hypothesis. It is necessary to investigate their asymptotic correlationship among basic estimators ${\hat{C}}_p$, ${\hat{C}}_{pk}$ and ${\hat{C}}_{pm}$ of process capability indices $C_p$, $C_{pk}$ and $C_{pm}$. In this paper, we study their asymptotic correlationship for three process capability indices ${\hat{C}}_p$, ${\hat{C}}_{pk}$ and ${\hat{C}}_{pm}$ under bivariate normal distribution BN(${\mu}_x,{\mu}_y,{\sigma}^2_x,{\sigma}^2_y,{\rho}$). With some nonnormal processes, the asymptotic correlation coefficient of any two respective process capability index estimators could be established.

• Korean Journal of Computational Design and Engineering
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• v.18 no.5
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• pp.359-366
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• 2013

In the lower arm design process, a tolerance optimization of the variance of design variables should be preceded before manufacturing process, since it is very cost-effective compared to a strict management of tolerance of products. In this study, a design of experiment (DOE) based on response surface model (RSM) was carried out to find optimized design variables of the lower arm, which can meet a given requirement of probability constraint for the process capability index (Cpk) of the weight and maximum stress. Then, the design space was explored by using the central composite design method, in which the 2nd order Taylor expansion was applied to predict a standard deviation of the responses. The optimal solutions satisfying the probability constraint of the Cpk were found by considering both of the mean value and the standard deviation of the design variables.

• Journal of Korean Society for Quality Management
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• v.27 no.4
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• pp.114-122
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• 1999

As the rapid growth of Industrial society, many enterprises are inclined to ppm management from the traditional$3\'{o}$ management method. Therefore it is need to extend process capability index for guarantee of quality assurance level to ppm unit. Thus, in this paper, using the probability of standard normal distribution from $ 3\'{o}; to; 6\'{o}$ which was developed by Song(1997), the capability index which is proposed considers the numbers of inspection facility and quality assurance level. Also, quality assurance level is determined by considering the precision of inspection when one and two sided specification limits are given for the probability which is out of the specification limit.

• 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.

• Journal of Korean Society for Quality Management
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• v.27 no.2
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• pp.81-100
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• 1999

Process capability indexes are widely used in industries. Nevertheless, important statistical issues that deal with the appropriate use of process capability indexes have only appeared in the technical literature and are thus unknown to many users. In this paper we will first review various kinds of process capability indexes and then try to understand how much uncertainty is associated with them in relation to the assumption of normal distribution, the estimate of ${\sigma}$, the sampling error, the size of number of observations available and the presence of data correlation. Finally, we will propose a proper use of process capability indexes in an effort to assess a complex process.

• Journal of Korean Society for Quality Management
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• v.47 no.4
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• pp.713-723
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• 2019

Purpose: The purpose of this study is to develop a statistical program for capability analysis of measuring system and measurement process based upon KS Q ISO 22514-7. Methods: R is a powerful open source functional programming language that provides high level graphics and interfaces to other languages. Therefore, in this study, we will develop the statistical program using R language. Results: The R program developed in this study consists of the following five modules. ① Measuring system capability analysis with Type 1 study data: MSCA_Type1.R ② Measuring system capability analysis with Linearity study(Type 4 study) data: MSCA_Type4.R ③ Measurement process capability analysis with Type 1 study & Gage R&R study data: MPCA_T1GRR.R ④ Measurement process capability analysis with Type 4 study & Gage R&R study data: MPCA_T4GRR.R ⑤ Attribute measurement processes capability analysis : AttributeMP.R Conclusion: KS Q ISO 22514-7 evaluates measuring systems and measurement processes on the basis of the measurement uncertainty that was determined according to the GUM(KS Q ISO/IEC Guide 98-3). KS Q ISO 22514-7 offers precise procedures, however, computations are more intensive. The R program of this study will help to evaluate the measurement process.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.543-554
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• 1997

A family of some capability indices { $C_{p}$(.alpha.,.beta.); .alpha..geq.0, .beta..geq.0}, containing the indices $C_{p}$, $C_{{pk}}$, $C_{{pm}}$, and $C_{{pmk}}$, has been defined by Vannman(1993) for the case of two-sided specification interval. By varying the parameters of the family various capability indices with suitable properties are obtained. We derive tha asymptotic distribution of the family { $C_{p}$(.alpha.,.beta.); .alpha..geq.0,.beta..geq.0} under general proper conditions. It is also shown that the bootstrap approximation to the distribution of the estimator $C_{p}$(.alpha., .beta.) is vaild for almost all sample sequences. These asymptotic distributions would be used in constructing some bootstrap confidence intervals.tervals.

• 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>)

• 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.