• 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.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.449-461
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• 2009

Higher sigma quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. The process capability indices and the sigma level $Z_{st}$ ave been widely used in six sigma industries to assess process performance. Most evaluations on process capability indices focus on statistical estimation under normal process which may result in unreliable assessments of process performance. In this paper, we consider statistical estimation for bivariate VPCI(Vector-valued Process Capability Index) $C_{pkl}=(C_{pklx},\;C_{pklx})$ under Marshall and Olkin (1967)'s bivariate exponential process. First, we derive some limiting distribution for statistical inference of bivariate VPCI $C_{pkl}$. And we propose two asymptotic normal confidence regions for bivariate VPCI $C_{pkl}$. The proposed method may be very useful under bivariate exponential process. A numerical result based on our proposed method shows to be more reliable.

• Journal of Distribution Science
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• v.15 no.12
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• pp.95-102
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• 2017

Purpose - This study aims to develop diagnostic indices for managerial performance of agro-food distribution corporations. In particular, weights of diagnostic indices were estimated using the AHP method. Management diagnosis on agro-food distribution corporations is expected to increase their competitiveness in the domestic market as well as in international markets. Research design, data, and methodology - It develops weights or importance of the diagnostic indices based upon the survey of 21 experts in food distribution management. The survey was carried out using e-mail. Management diagnostic indices were developed based upon four BSC(Balanced Scorecard) perspectives of finance, learning/growth/leadership, customer, and internal process/technology. Results - Diagnostic indices on financial perspective consist on profitability, productivity, growth, stability and activity. Learning and leadership perspective indices consist of management will, CEO leadership, level of learning, innovation, and level of management information system. Customer perspective indices are branding, customer and channel management and internal process/technology indices consist of fourteen sub-indices representing technologies, efficiency, and dynamics. It was estimated that the weight of financial perspective index was 0.3, internal process/technology perspective index 0.248, customer category index 0.247, and learning, growth and leadership perspective index 0.205. This study also estimates weights of sub-indices for managerial diagnosis by four different perspectives. Estimated weight of profitability (0.085) is the greatest among financial perspective indices, followed by stability (0.072), growth (0.053), productivity (0.051), and activity (0.038). While estimated weights of leadership, capability, and information indices are 0.100, 0.061, and 0.044 respectively, weights of marketing, customer management, and quality and service indices are 0.104, 0.093, and 0.051, respectively. Among internal process/technology perspective, estimated weights of efficiency, technology, and innovation indices are 0.106, 0.088, and 0.054, respectively. Conclusions - The diagnostic indices for managerial performance of agro-food distribution corporations would be utilized by agro-food distribution corporations themselves, extension service institutions, and consultants. It is also expected that central and local governments use diagnostic indices developed in this study for the purpose of evaluating the effects of governmental support programs for agro-food distribution corporations. Futhermore researchers and consultants would modify diagnostic indices developed in this study, reflecting characteristics and situation of types of agro-food distribution corporations.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.399-422
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• 2003

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 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, some vector-valued ${PCI}_p$ ${C}_p$=(${C}_{px}$, ${C}_{py}$),${C}_{pk}$=(${C}_{pkx}$, ${C}_{pky}$) and ${C}_{pm}$=(${C}_{pmx}$, ${C}_{pmy}$) considering univariate PCIs ${C}_p$,${C}_{pk}$ and ${C}_{pm}$ are studied. First, we propose some asymptotic confidence regions of our vector-valued PCIs with bootstrap. And we examine the performance of asymptotic confidence regions of our vector-valued PCIs ${C}_p$ and ${C}_{pk}$ under the assumption of bivariate normal distribution BN($\mu_{x}$, $\mu_{y}$, $\sigma_{x}^{2}$, $\sigma_{y}^{2}$, $\rho$) and bivariate chi-square distribution Bivariate $x^2$(5,5,$\rho$).

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.1
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• pp.151-157
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• 2019

This study is about the process capability index (PCI). In this study, we introduce several indices including the index $C_{PR}$ and present the characteristics of the $C_{PR}$ as well as its validity. The difference between the other indices and the $C_{PR}$ is the way we use to estimate the standard deviation. Calculating the index, most indices use sample standard deviation while the index $C_{PR}$ uses range R. The sample standard deviation is generally a better estimator than the range R. But in the case of the panel process, the $C_{PR}$ has more consistency than the other indices at the point of non-conforming ratio which is an important term in quality control. The reason why the $C_{PR}$ using the range has better consistency is explained by introducing the concept of 'flatness ratio'. At least one million cells are present in one panel, so we can't inspect all of them. In estimating the PCI, it is necessary to consider the inspection cost together with the consistency. Even though we want smaller sample size at the point of inspection cost, the small sample size makes the PCI unreliable. There is 'trade off' between the inspection cost and the accuracy of the PCI. Therefore, we should obtain as large a sample size as possible under the allowed inspection cost. In order for $C_{PR}$ to be used throughout the industry, it is necessary to analyze the characteristics of the $C_{PR}$. Because the $C_{PR}$ is a kind of index including subgroup concept, the analysis should be done at the point of sample size of the subgroup. We present numerical analysis results of $C_{PR}$ by the data from the random number generating method. In this study, we also show the difference between the $C_{PR}$ using the range and the $C_P$ which is a representative index using the sample standard deviation. Regression analysis was used for the numerical analysis of the sample data. In addition, residual analysis and equal variance analysis was also conducted.

• Journal of Applied Reliability
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• v.1 no.1
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• pp.55-63
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• 2001

In this paper, we utilize the asymptotic variance of $C_{pk}$ to propose a two-sided confidence interval based on percentile-t bootstrap method. This confidence interval is compared with the ones based on the standard and percentile bootstrap methods. Simulation results show that percentile-t bootstrap method is preferred to other methods for constructing the confidence interval.l.

• Journal of Korean Society for Quality Management
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• v.27 no.4
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• pp.256-265
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• 1999

In this paper, we Present the implementation of statistical process control software by using XLISP-STAT which is a kind of object oriented language under Windows environment. This software can be used to generate the graphic objects for various control charts, histogram and plots using the full-down menu system. This software can also be used to calculate control limits, process capability indices and test procedures for normality.

• 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 of Industrial and Systems Engineering
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• v.23 no.55
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• pp.13-24
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• 2000

6 sigma movement is the most prominent quality improvement methodology in practice. Measurement plays an important role in helping any organization improve quality. Therefore, the measurement systems analysis is the first step for the quality improvement of manufacturing process in 6 sigma movement. In this study, we investigate the effect of Gage Repeatability and Reproducibility(Gage R&R) in view of defect rate and process capability indices, and provide guidelines for acceptance of gage repeatability and reproducibility(%R&R) for six sigma quality.

• Journal of Korean Society for Quality Management
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• v.42 no.4
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• pp.607-616
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• 2014

Purpose: This paper reviews popular measurement system indices and proposes a procedure for assessing a measurement system using two parameters with intraclass correlation and a factor for process capability. Methods: Gage Repeatability and Reproducibility(GR&R), precision-to-tolerance ratio(PTR), number of distinct categories, producer's and consumer's risks are employed to assess the measurement capabilities and discuss the relationships between measurement system metrics. Results: Two-dimensional plot by two parameters is presented to assess adequacy of the measurement system and process capability. A numerical example and previously studied case study are provided for illustration. Conclusion: The procedure proposed in this paper using two-dimension parameters provides a valuable procedure and helpful guidelines to quality and production managers in assessing the capabilities of a measurement system and choosing the needed actions to be the most benefit.