• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.42
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• pp.73-85
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• 1997

In the product liability age the demand on quality is extremely high and inspection and test are automated. The process capability indices $C_p, {\;}C_{pk}$ and p control chart widely used to provide unitless measure of process performance and process control. Traditional process capability indices $C_p, {\;}C_{pk}$ do not represent the process variation from target value. The convention p chart for control of fraction nonconforming becomes inadequate when the fraction nonconforming becomes very small such as PPM level production system. This paper proposes process performance measure considering quadratic loss function and cumulative counts control chart for control of PPM level production system.

• Journal of Korean Society for Quality Management
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• v.32 no.4
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• pp.229-241
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• 2004

Process capability index is used to determine whether a production process is capable of producing items within a specified tolerance. The index $C_{pmk}$ is the third generation process capability index. This index is more powerful than two useful indices $C_p$ and $C_{pk}$. Whether a process distribution is clearly normal or nonnormal, there may be some questions as to which any process index is valid or should even be calculated. As far as we know, yet there is no result for statistical inference with process capability index $C_{pmk}$. However, asymptotic method and bootstrap could be studied for good statistical inference. In this paper, we propose various bootstrap confidence limits for our process capability Index $C_{pmk}$. First, we derive bootstrap asymptotic distribution of plug-in estimator $C_{pmk}$ of our capability index $C_{pmk}$. And then we construct various bootstrap confidence limits of our capability index $C_{pmk}$ for more useful process capability analysis.

• Journal of Korean Society for Quality Management
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• v.24 no.4
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• pp.90-102
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• 1996

Process incapability index which is intended to evaluate the process capability by measuring process incapability provides more detailed information by dividing information about the process mean and variance. But when the target value is not consistent with the center of specification, it is very difficult to evaluate the process capability accurately. Thus it is necessary to improve the existing process incapability index. The improved process incapability index can identify the variation of the process faster than other process capability indices when applied firstly, to the precision process which can be affected sensitively by the change of the process, secondly, to the ordinary process where cost difference from the change of process is noticeable. By using subindices such as inaccuracy index and imprecision index, it is easier for quality manager to find where the cause of the variation of process is, and to take necessary action in advance.

• Communications for Statistical Applications and Methods
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• v.17 no.3
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• pp.459-471
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• 2010

Higher quality level is generally perceived by customers as improved performance by assigning a correspondingly higher satisfaction score. Usually, the quality level is measured by process capability indices. The index is used to determine whether a production process is capable of producing items within a specified tolerance. The third generation index $C_{pmk}$ is more powerful than two useful indices $C_p$ and $C_{pk}$. which have been widely used in six sigma industries to assess process performance. Most evaluations on process capability indices focus on point estimates, which may result in unreliable assessments of process performance. In this paper, we consider better testing procedure on assessing process capability index $C_{pmk}$ for practitioners to use in determining whether a given process is capable. It is easy to use the proposed method for assessing process capability index $C_{pmk}$. Whether a process is clearly normal or nonnormal, our bootstrap testing procedure could be applied effectively without the complexity of calculation. A numerical result based on our proposed method is illustrated.

• Proceedings of the Korean Society for Quality Management Conference
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• 2004.04a
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• pp.70-75
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• 2004

In actual manufacturing industries, process capability indices(PCI) are used to determine whether a production process is capable of producing items within a specified specification limits. We study some vector-valued PCIs $C_p=(C_{px},\;C_{py})$ and $C_{pk}=(C_{pkx},\; C_{pky})$ in this article. We propose some asymptotic confidence regions of PCIs with bootstrapping and examine the performance of those asymptotic confidence regions under the assumption of bivariate normal distribution.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.133-142
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• 1998

This paper is a brief review of the different procedures that are available for fitting theoretical distributions to data. The use of each technique is illustrated by reference to a distribution system which including the Pearson, Poission approximation of Gamma distribution and Burr functions. These functions can be used to calculate percent out of specification. Therefore, in this paper a new methods for estimating a measure of non-normal process capability for Gamma distributed variable data proposed using the percentage nonconforming. Process capability indices combines with the percentage nonconforming information can be used to evaluate more accurately process capability.

• Journal of Applied Reliability
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• v.13 no.3
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• pp.191-206
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• 2013

Application areas for Lifetime Performance Index(LPI), a kind of process capability index to be frequently used as a means of measuring process performance are illustrated with examples. Statistical properties for maximum likelihood and unbiased estimators of LPI are evaluated and discussed under Weibull distribution with known shape parameter. Furthermore, guidelines for selecting an estimator of LPI are also presented.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.594-609
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• 1998

In this dissertation, 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 seven indices, $C_p,\;C_{pk},\;C_{pm},\;C^{\ast}_{pm},\;C_{pmk},\;C_s,\;C_{psk}$ in terms of sensitivity to departure of the process median from the target value T=M from the most sensitive one up to the least sensitive are $C_{psk},\;C_{s},\;C_{pmk},\;C^{\ast}_{pm},\;C_{pm},\;C_{pk},\;C_p$. i.e, By the criteria adopted for evaluation of PCI's $C_{psk}$ is the most sensitive to the departure of the process median from target and $C_p$ is least

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.365-368
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• 2000

This paper proposes a new heuristic method of constructing process capability indices (PCIs) for skewed populations. It is based on weighted standard deviation (WSD) method which decomposes the standard deviation of a quality characteristic into upper and lower deviations and adjusts the value of PCI using decomposed deviations in accordance with the skewness estimated from sample data. For symmetric populations, the proposed PCIs reduce to standard PCIs. Asymptotic distributions of the estimators of the PCIs are obtained. The performances of the proposed methods are compared with those of the standard and other methods. Numerical comparisons indicate that considerable improvements over existing methods can be achieved by the use of WSD method when the underlying distribution is skewed.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.41
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• pp.213-220
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• 1997

Process capability Indices compare the actual performance of manufacturing process to the desired performance. The relationship between the capability index Cpm and the expected squared error loss provides an intuitive interpretation of Cpm. By putting the loss in relative terms a user needs only to specify the target and the distance from the target at which the product would have zero worth, or alternatively, the loss at the specification limits. Confidence limits for the expected relative loss are discussed, and numerical illustration is given.