多重品質特性下量測重複性/再現性信賴區間之實證研究

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研究生：	陳鴻麟 Horng-lin Chern
論文名稱：	多重品質特性下量測重複性/再現性信賴區間之實證研究 Confidence intervals for a GR&R study with multiple characteristics
指導教授：	王福琨 Fu-Kwun Wang
口試委員:	郭瑞祥 none 徐世輝 none 許總欣 none 歐陽超 none
學位類別：	博士 Doctor
系所名稱：	管理學院 - 工業管理系 Department of Industrial Management
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	77
中文關鍵詞：	量測重複性與再現性研究、多重品質特性、多變量分析、主成分分析、複式抽樣法、信賴區間
外文關鍵詞：	GR&R study, Multiple characteristics, MANOVA, Principal Component Analysis, Bootstrap method, confidence interval
相關次數：	點閱：313 下載：1
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量測技術與科技發展、工業升級實互為因果關係，首先要有精確的量測技術與方法，組織方能達成追求品質改善的目標，否則必將事倍功半，甚至徒勞無功。在工業實務上有關量測重複性與再現性(Gauge Reproducibility and Repeatability；GR&R)研究中，通常呈現出具有多重品質特性與特性間彼此具相關性等性質，惟目前研究文獻仍大多侷限於單一品質特性之研究，倘若將前述多重品質特性問題逕以單一品質特性問題處理，而忽略品質特性間彼此相關性，恐將錯估量測變異程度，造成整體量測能力誤判。
有鑑於此，本研究嘗試藉由統計學上常用的多變量分析（Multivariate Analysis of Variance； MANOVA）及主成分分析（Principal Component Analysis；PCA）等相關理論之應用，以評估多重品質特性下量測變異分析與量測能力。
研究中首先針對單一個別品質特性之變異情形加以定義、分析，並以精密度/規格公差比（Precision to Tolerance Ratio；PTR Ratio）、%R&R與訊號/雜訊比（Signal to Noise Ratio；SNR Ratio）等三種單一特性量測指標作為衡量依據，以瞭解單一個別品質特性之量測能力；接著並再利用前述多變量統計相關觀念，嘗試建構完成三種多重品質特性下量測指標，例如； (Precision to Tolerance Ratio for Multivariate)、與 (Signal to Noise Ratio for Multivariate)等綜合量測指標，以作為比較、評估整體量測程序適宜性之依據。
我們並在研究中清楚地描述複式抽樣法(Bootstrap)理論與方法原理及修正大樣本法(Modified Large-sample；MLS) 方法，以建構完成出多重品質特性量測指標（例如；、及）之信賴區間；經由變異數-共變異數矩陣成分（Variance-covariance matrix component）及樣本大小（sample size）等參數之模擬設計，並透過複式抽樣法實際運算結果，已確認不論在目標量測值的涵蓋率（coverage proportion）及信賴區間寬度（width of confidence interval）等各方面，皆可適用於大多數模擬情境。
最後，則藉由二個實際案例，以逐步驗證本研究建議方法之實地應用，研究結論顯示多重品質特性資料不論以多變量分析或主成分分析處理，其結果皆優於以變異數分析（Analysis of Variance；ANOVA）處理單一品質特性方式者，故業已彰顯本研究所提出之多變量分析與主成分分析等兩種方法適合處理針對類似多重品質特性之量測重複性與再現性(GR&R)相關研究。

Causal relationships exist between technological developments and industry upgrades/metrology quality. To obtain quality improvements, an accurate measurement is needed. Otherwise, strenuous effort will yield little or no success. The majority of industrial gauge reproducibility and repeatability (GR&R) related studies involve multiple quality interdependent characteristics. However, most current statistical studies focus on single quality characteristics. Because the multiple quality characteristic problems are typically treated as a single quality, dependent features are regarded as independent and the relationships between the quality characteristics are neglected. Erroneous measurement assessment is the likely outcome of this treatment.
The multiple characteristics of GR&R manufacturing tests usually have multivariate normal distribution. This dissertation presents an evaluation of multivariate measurement capability using multivariate analysis of variance (MANOVA) and principal component analysis (PCA). The adequacy of the measurement process is evaluated by three multivariate performance measures—precision to tolerance ratio for multivariate (PTRm ), %R&Rm, and signal to noise ratio for multivariate ( SNRm)—which are combined from all quality characteristics.
In this study, the Bootstrap method and the modified large-sample (MLS) method are used to construct the confidence interval of the measured quantity for multivariate measurement criteria. Factors simulated to validate performance include: the variance-covariance matrix component and sample size. The simulation results show that the Bootstrap method can cover the stated nominal coefficient in most scenarios. The coverage proportion is not significantly affected by variance-components. Also, the width of confidence interval for the measures quantity and coverage proportion is not significantly affected by sample size.
The proposed methodology is applied to two real examples. The results show that both multivariate methods are applicable to GR&R studies with multiple characteristics.

Contents
Abstract (Chinese)…………………………………………………………………………… i
Abstract……………………………………………………………………………………… iii
Acknowledgments (Chinese)………………………………………………………………… v
Contents …………………………………………………………………………………… vi
List of Tables ……………………………………………………………………………… viii
List of Figures ……………………………………………………………………………… x
Chapter 1 Introduction………………………………………………………………………1
1.1 Research Background…………………………………………………………………1
1.2 Research Objectives ………………………………………………………………… 2
1.3 Research Procedures………………………………………………………………… 3
Chapter 2 Literature Reviews……………………………………………………………… 5
2.1 Single Characteristic of GR&R………………………………………………………5
2.2 Multiple Characteristics of GR&R……………………………………………………8
2.3 Performance Measurement and Confidence Intervals of GR&R (Bootstrap and MLS）…………………………………………………………………………………9
Chapter 3 Methodology…………………………………………………………………… 17
3.1 Random Model of Multiple Characteristics for MGR&R ………………………… 17
3.1.1 MANOVA Method ………………………………………………………… 17
3.1.2 PCA Method…………………………………………………………………25
3.2 Bootstrap Method ………………………………………………………………… 28
Chapter 4 Simulation Studies………………………………………………………………31
4.1 Case 1 ……………………………………………………………………………… 33
4.2 Case 2 ……………………………………………………………………………… 37
Chapter 5 Illustrative Examples ………………………………………………………… 42
5.1 Example 1……………………………………………………………………………42
5.2 Example 2……………………………………………………………………………50
Chapter 6 Conclusions and Future Research …………………………………………… 60
6.1 Conclusions……………………………………………………………………………60
6.2 Future Research ……………………………………………………………………… 61
References ………………………………………………………………………………… 63
Appendix  ………………………………………………………………………………… 68


List of Tables
Table 3.1 ANOVA for the random-effect model …………………………………………… 18
Table 3.2 ANOVA for the random-effect reduced model (no interaction effect) ……………19
Table 3.3 Multivariate criteria for multivariate measurement systems………………………24
Table 4.1 Simulation design of case 1 ……………………………………………………… 34
Table 4.2 Simulation results of case 1 in the acceptable situation……………………………34
Table 4.3 Simulation results of case 1 in the moderate acceptable situation…………………35
Table 4.4 Simulation results of case 1 in the incapable situation ……………………………35
Table 4.5 Simulation design of case 2 ……………………………………………………… 38
Table 4.6 Simulation results of case 2 in the acceptable situation……………………………39
Table 4.7 Simulation results of case 2 in the moderately acceptable situation……………… 39
Table 4.8 Simulation results of case 2 in the incapable situation…………………………… 39
Table 5.1 Measurement data for the example 1………………………………………………43
Table 5.2 Results for example 1 using ANOVA………………………………………………46
Table 5.3 Results of approval criteria for example 1 using ANOVA…………………………46
Table 5.4 Analysis results of MANOVA for example 1………………………………………47
Table 5.5 Results of approval criteria for example 1 using MANOVA………………………47
Table 5.6 Analysis results of PCA for example 1…………………………………………… 48
Table 5.7 Results for example 1 using PCA method………………………………………… 49
Table 5.8 Approval criteria for example 1 estimated from PCA …………………………… 49
Table 5.9 Measurement data for the example 2………………………………………………51
Table 5.10 Results for example 2 using ANOVA ……………………………………………55
Table 5.11 Results of approval criteria for example 2 using ANOVA ……………………… 55
Table 5.12 Analysis results of MANOVA for example 2 …………………………………… 56
Table 5.13 Results of approval criteria for example 2 using MANOVA …………………… 56
Table 5.14 Analysis results of PCA for example 2……………………………………………57
Table 5.15 Results for example 2 using PCA ……………………………………………… 57
Table 5.16 Approval criteria for example 2 estimated from PCA…………………………… 58
Table 5.17 Comparisons among ANOVA, MANOVA, and PCA estimates for illustrative example 1 and 2………………………………………………………………… 59

List of Figures
Figure 1.1 Research framework ………………………………………………………………4
Figure 4.1 Flowchart for constructing the confidence interval using the Bootstrap method…32
Figure 4.2 Scatter plot of   and   under the simulation scenarios of
case 1 …………………………………………………………………………… 36
Figure 4.3 Scatter plot of   and   under the simulation scenarios of
case 2 …………………………………………………………………………… 40
Figure 5.1 Box plots of the measurement data (T0) for example 1………………………… 44
Figure 5.2 Box plots of the measurement data (T1) for example 1………………………… 44
Figure 5.3 Box plots of the measurement data (Fmax) for example 1……………………… 45
Figure 5.4 Box plots of the measurement data (M1) for example 2………………………… 52
Figure 5.5 Box plots of the measurement data (M2) for example 2………………………… 52
Figure 5.6 Box plots of the measurement data (M3) for example 2………………………… 53
Figure 5.7 Box plots of the measurement data (M4) for example 2………………………… 53

                                

References
Al-Refaie, A., Bata, N., Evaluating measurement and process capabilities by GR&R with four quality measures, Measurement, 43, 842-851, 2010.
Anderson T. W., Asymptotic theory for principal component analysis, Annals of Mathematical Statistics, 34, 122-148, 1963.
Automotive Industry Action Group (AIAG). Measurement Systems Analysis: Reference Manual (3rd edition). AIAG: Detroit, MI, 2002.
Awad, M., Erdmann, T. P., Shaushal, Y., Barth, B., A measurement system analysis approach for hard-to-repeat events, Quality Engineering, 21, 300-305, 2009.
Burdick, R. K., Allen, A. E., Larsen, G. A., Comparing variability of two measurement processes using R&R studies, Journal of Quality Technology, 34, 97-105, 2002.
Burdick, R. K., Borror, C. M., Montgomery, D. C., A review of methods for measurement systems capability analysis, Journal of Quality Technology, 35, 342-354, 2003.
Burdick, R. K., Borror, C. M., Montgomery, D. C., Design and Analysis of Gauge R&R Studies: Making Decisions with Confidence Intervals in Random and Mixed ANOVA Models. ASA/SIAM: Philadelphia, 2005a.
Burdick, R. K., Larsen, G. A., Confidence intervals on measures of variability in R&R studies, Journal of Quality Technology, 29, 261-273, 1997.
Burdick, R. K., Park, Y. J., Montgomery, D. C., Borror, C. M., Misclassification rates in gauge R&R studies, Journal of Quality Technology, 37, 294-303, 2005b.
Browne, R. P., Assessment of a measurement system using repeat measurement of failing units, Quality Engineering, 22, 21-29, 2010.
Cadima, J., Jolliffe, I. T., Loading and correlation in the interpretation of principal components, Journal of Applied Statistics, 22, 203-214, 1995.
Chen, C. J., Chen, Y. L., Chang, L. C., Pitch measurement by traceable atomic force microscope, International Journal of Nanoscience, 2, 335-341, 2003.
Chiang, A. K. L., A simple general method for constructing confidence intervals for functions of variance components, Technometrics, 43, 356-367, 2001.
Conors, M., Merrill, K., O’Donnell, B., A comprehensive approach to measurement system evaluation, In ASA Proceeding of the Section on Physical and Engineering Science, 136-138, 1995.
Daniels, L., Burdick, R. K., Quiroz, Confidence intervals in a gauge R&R study with fixed operators, Journal of Quality Technology, 37, 179-185, 2005.
DiCicco, T. J., Efron, B., Bootstrap confidence intervals, Statistical Science, 11, 189-228, 1996.
de Mast, J., van Wieringen, W. N., Modeling and evaluating repeatability and reproducibility of ordinal classifications, Technometrics, 52, 94-106, 2010.
Dolezal, K. K., Burdick, R. K., Birch, N. J., Analysis of a two-factor R&R Study with fixed operators, Journal of Quality Technology, 30, 163-170, 1998.
Efron, B., Bootstrap methods - another look at the jackknife, The Annals of Statistics, 7, 1-26, 1979.
Efron, B., Nonparametric standard errors and confidence intervals, Canadian Journal of Statistics, 9, 139-172, 1981.
Efron, B., Tibshirani, R. J., An Introduction to the Bootstrap. Chapman & Hall: New York, 1993.
Efron, B., Better bootstrap confidence intervals, Journal of American Statistical Association, 82, 171-185, 1987.
Gong, L., Burdick, R. K., Quiroz, Confidence intervals for unbalanced two-factor gauge R&R studies, Quality and Reliability Engineering International, 21, 737-741, 2005.
Hamada, M., Weerahandi, S., Measurement system assessment via generalized inference, Journal of Quality Technology, 32, 241-253, 2000.
Hunag, Z. H., Ni, J., Shih, A. J., Quantitative evaluation of powder spray effects on stereovision measurements, Measurement Science and Technology, 19, 1-11, 2008.
IMSL Inc., IMSL STAT/ LIBRARY. Problem-Solving Software Systems, Version 2.0. IMSL Inc.: Dallas, Texas, 1993.
Johnson, R. A, Wichern, D. W., Applied Multivariate Statistical Analysis. Prentice-Hall: Upper Saddle River, New Jersey, 1998.
Jackson, J. E., Principal component and factor analysis: part I ― principal components, Journal of Quality Technology, 12, 201-213, 1980.
Kao, C. C., Shih, A. J., Form measurements of micro-holes, Measurement Science and Technology, 18, 3603-3611, 2007.
Larrosa, A., Lozano, L. J., Katuri, K. P., Head, I., Scott, K., Godinez, C., On the repeatability and reproducibility of experimental two-chambered microbial fuel cells, Fuel, 88, 1852-1857, 2009.
Larsen, G., Measurement system analysis in a production test environment with multiple test parameters, Quality Engineering, 16, 297-306, 2003.
Ledolter, J., Designed experiments in nanotechnology: reviewing the statistical analyses of five studies, Quality Technology & Quantitative Management, 8, 183-209, 2011.
Li, M-H., Al-Refaie, A., Improving Wooden part’s Quality by Adopting DMAIC procedure, Quality and Reliability Engineering International, 24, 351-360, 2008.
Lu, J. C., Jeng, S. L., Wang, K., A review of statistical methods for quality improvement and control in nanotechnology, Journal of Quality Technology, 42, 148-164, 2009.
Mardia, K. V., Tests for univariate and multivariate normality. In: Handbook of Statistics. North-Holland: Amsterdam, 279-320, 1980.
Majeske, K. D., Approval criteria for multivariate measurement systems, Journal of Quality Technology, 40, 140-153, 2008.
Meulen, F. V., Koning, H. D., Mast, J. D., Nonrepeatable gauge R&R studies assuming temporal or patterned object variation, Journal of Quality Technology, 41, 426-439, 2009.
Montgomery, D. C., Runger, G. C., Gauge capability and designed experiments. Part I: basic methods, Quality Engineering, 6, 115-135, 1993a.
Montgomery, D. C., Runger, G. C., Gauge capability analysis and designed experiments. Part Ⅱ: experimental design models and variance component estimation, Quality Engineering, 6, 289-305, 1993b.
Montgomery, D. C., Design and Analysis of Experiments. John Wiley & Sons: New York, 2009.
Osma, A., An assessment of the robustness of gauge repeatability and reproducibility analysis in automotive components, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 225, 895-912, 2011.
Shao, J., Tu, D., The Jacknife and Bootstrap, Springer, New York, 1995.
Stevens, N. T., Browne, R., Steiner, S. H., Mackay, R. J., Augmented measurement system assessment, Journal of Quality Technology, 42, 388-399, 2010.
Stout, G., Measurement put to the test, Quality, 33, 41-48, 1994.
Sweeney, S., Analysis of two-dimensional gage repeatability and reproducibility, Quality Engineering, 19, 29-37, 2007.
Vago, E., Kemeny, S., A model-bases approach for attribute gauge analysis, Quality and Reliability Engineering International, 27, 753-769, 2011.
Voelkel, J. G., Gauge R&R analysis for two-dimensional data with circular tolerances, Journal of Quality Technology, 35, 153-167, 2003.
Wang, C. Y., Pan, S. P., Peng, G. S., Tasi, J. H., A comparison study on the measurement of nanoparticles, Proceedings of SPIE, 5879, 323-328, 2005.
Wang, C. Y., Fu, W. E., Lin, H. L., Peng, G. S., Preliminary study on nanoparticle sizes under the APEC technology cooperative framework, Measurement Science and Technology, 18, 487-495, 2007.
Wang, F. K., Chern, H. L., Confidence intervals for two-dimensional data with circular tolerances in a gauge R&R study, Quality & Quantity, 46, 55-69, 2012a.
Wang, F. K., Chern, H. L., Yu, T. C., A gauge study for dynamic light scattering and differential mobility analyzer instruments, Journal of Testing and Evaluation, 40, 1-6, 2012b.
Wang, F. K., Yang, C. W., Applying principal component analysis to a GR&R study, Journal of the Chinese Institute of Industrial Engineering, 24, 182-189, 2007.
Wang, F. K., Li, E. Y., Confidence intervals in repeatability and reproducibility using bootstrap method, Total Quality Management and Business Excellence, 14, 341-354, 2003.
West, J. E., Standards column, Quality Engineering, 21, 111-116, 2009.
White, T. K., Borror, C. M., Two-dimensional guidelines for measurement system indices, Quality and Reliability Engineering International, 27, 479-487, 2011.
Wilrich, P. T., The determination of precision of qualitative measurement methods by interlaboratory experiments, Accreditation & Quality Assurance, 15, 439-444, 2010.
Woodall, W. H., Borror, C. M., Some relationships between gage R&R criteria, Quality and Reliability Engineering International, 24, 99-106, 2008.

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