Browsing by Author "Yen, Chia-Ling"

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A MULTIVARIATE CONTROL CHART FOR DETECTING INCREASES IN PROCESS DISPERSION
(2010-10-01)
Yen, Chia-Ling
;
Shiau, Jyh-Jen Horng
;
統計學研究所
;
Institute of Statistics
For signalling alarms sooner when the dispersion of a multivariate process is "increased", a multivariate control chart for Phase II process monitoring is proposed as a supplementary tool to the usual monitoring schemes designed for detecting general changes in the covariance matrix. The proposed chart is constructed based on the one-sided likelihood ratio test (LRT) for testing the hypothesis that the covariance matrix of the quality characteristic vector of the current process, Sigma, is "larger" than that of the in-control process, Sigma(0), in the sense that Sigma - Sigma(0) is positive semidefinite and Sigma not equal Sigma(0). Assuming Sigma(0) is known, the LRT statistic is derived and then used to construct the control chart. A simulation study shows that the proposed control chart indeed outperforms three existing two-sided-test-based control charts under comparison in terms of the average run length. The applicability and effectiveness of the proposed control chart are demonstrated through a semiconductor example and two simulations.
A MULTIVARIATE CONTROL CHART FOR DETECTING INCREASES IN PROCESS DISPERSION
(2010-10-01)
Yen, Chia-Ling
;
Shiau, Jyh-Jen Horng
;
統計學研究所
;
Institute of Statistics
For signalling alarms sooner when the dispersion of a multivariate process is "increased", a multivariate control chart for Phase II process monitoring is proposed as a supplementary tool to the usual monitoring schemes designed for detecting general changes in the covariance matrix. The proposed chart is constructed based on the one-sided likelihood ratio test (LRT) for testing the hypothesis that the covariance matrix of the quality characteristic vector of the current process, Sigma, is "larger" than that of the in-control process, Sigma(0), in the sense that Sigma - Sigma(0) is positive semidefinite and Sigma not equal Sigma(0). Assuming Sigma(0) is known, the LRT statistic is derived and then used to construct the control chart. A simulation study shows that the proposed control chart indeed outperforms three existing two-sided-test-based control charts under comparison in terms of the average run length. The applicability and effectiveness of the proposed control chart are demonstrated through a semiconductor example and two simulations.
Effective Control Charts for Monitoring Multivariate Process Dispersion
(2012-06-01)
Yen, Chia-Ling
;
Shiau, Jyh-Jen Horng
;
Yeh, Arthur B.
;
統計學研究所
;
Institute of Statistics
When monitoring process dispersion, it is common to pay more attention to dispersion increases than to decreases for practical reasons. Nonetheless, it is also important to detect dispersion decreases for two reasons: (i) it deserves further investigations as to why the process has improved; and (ii) if the process has changed, the settings of the control chart would need to be adjusted for effective future monitoring. In this paper, we first propose an effective control chart for detecting multivariate dispersion decreases in phase II process monitoring, which is constructed using the same approach as that of the one-sided likelihood-ratio-test-based multivariate chart proposed recently in the literature for detecting dispersion increases. We then discuss a combined charting scheme by combining these two one-sided charts for detecting either dispersion increases or decreases. Comparative simulation studies show that the proposed combined control charting scheme outperforms several existing two-sided control charts in terms of the average run length when the process dispersion indeed increases or decreases. Two real-life examples are presented to demonstrate the applicability of the proposed charts. Copyright (c) 2011 John Wiley & Sons, Ltd.
The density control chart: a general approach for constructing a single chart for simultaneously monitoring multiple parameters
(2012)
Chen, Hung-Chia
;
Yeh, Arthur B.
;
Yen, Chia-Ling
;
Chen, Lin-An
;
統計學研究所
"The majority of the existing literature on simultaneous control charts, i.e. control charting mechanisms that monitor multiple population parameters such as mean and variance on a single chart, assume that the process is normally distributed. In order to adjust and maintain the overall type-I error probability, these existing charts rely largely on the property that the sample mean and sample variance are independent under the normality assumption. Furthermore, the existing charting procedures cannot be readily extended to non-normal processes. In this article, we propose and study a general charting mechanism which can be used to construct simultaneous control charts for normal and non-normal processes. The proposed control chart, which we call the density control chart, is essentially based on the premise that if a sample of observations is from an in-control process, then another sample of observations is no less likely to be also from the in-control process if the likelihood of the latter is no less than the likelihood of the former. The density control chart is developed for normal and non-normal processes where the distribution of the plotting statistic of the density control chart can be explicitly derived. Real examples are given and discussed in these cases. We also discuss how the density control chart can be constructed in cases when the distribution of the plotting statistic cannot be determined. A discussion of potential future research is also given."
Yield-Related Process Capability Indices for Processes of Multiple Quality Characteristics
(2013-06-01)
Shiau, Jyh-Jen Horng
;
Yen, Chia-Ling
;
Pearn, W. L.
;
Lee, Wan-Tsz
;
統計學研究所
Process capability indices (PCIs) have been widely used in industries for assessing the capability of manufacturing processes. Castagliola and Castellanos (Quality Technology and Quantitative Management 2005, 2(2):201220), viewing that there were no clear links between the definition of the existing multivariate PCIs and theoretical proportion of nonconforming product items, defined a bivariate Cpk and Cp (denoted by BCpk and BCp, respectively) based on the proportions of nonconforming product items over four convex polygons for bivariate normal processes with a rectangular specification region. In this paper, we extend their definitions to MCpk and MCp for multivariate normal processes with flexible specification regions. To link the index to the yield, we establish a reachable' lower bound for the process yield as a function of MCpk. An algorithm suitable for such processes is developed to compute the natural estimate of MCpk from process data. Furthermore, we construct via the bootstrap approach the lower confidence bound of MCpk, a measure often used by producers for quality assurance to consumers. As for BCp, we first modify the original definition with a simple preprocessing step to make BCp scale-invariant. A very efficient algorithm is developed for computing a natural estimator BCp of BCp. This new approach of BCp can be easily extended to MCp for multivariate processes. For BCp, we further derive an approximate normal distribution for BCp, which enables us to construct procedures for making statistical inferences about process capability based on data, including the hypothesis testing, confidence interval, and lower confidence bound. Finally, the proposed procedures are demonstrated with three real data sets. Copyright (c) 2012 John Wiley & Sons, Ltd.