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Estimations of Measurement System Variability and PTR under Non-normal Measurement Error  

Chang, Mu-Seong (Department of Industrial and Systems Engineering, Changwon National University)
Kim, Sang-Boo (Department of Industrial and Systems Engineering, Changwon National University)
Publication Information
Journal of Korean Society for Quality Management / v.35, no.1, 2007 , pp. 10-19 More about this Journal
Abstract
ANOVA is widely, used for measurement system analysis. It assumes that the measurement error is normally distributed, which nay not be seen in some industrial cases. In this study the estimates of the measurement system variability and PTR (precision-to-tolerance ratio) are obtained by using weighted standard deviation for the case where the measurement error is non-normally distributed. The Standard Bootstrap method is used foy estimating confidence intervals of measurement system variability and PTR. The point and confidence interval estimates for the cases with normally distributed measurement error are compared to those with non-normally distributed measurement errors through computer simulation.
Keywords
Nonnormal Measurement Error; Measurement System Analysis; Precision-to-tolerance Ratio;
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1 Burdick, R. K., Borror, C. M., and Montgomery, D. C.(2003), 'A Review of Methods for Measurement Systems Capability Analysis', Journal of Quality Technology, Vol. 35, No. 4, pp. 342-354   DOI
2 Daniels, L., Burdick, R. K., and Quiroz, J. (2005), 'Confidence Intervals in a Gauge R&R Study with Fixed Operators', Journal of Quality Technology, Vol. 37, No.3, pp. 179-185   DOI
3 Montgomery, D. C. and Runger, G. C.(1993-94a), 'Gauge Capability and Designed Experiments Part 1 : Basic Methods', Quality Engineering, Vol. 6, No. 1, pp. 115-135   DOI   ScienceOn
4 Pan, J. N.(2004), 'Determination of the optimal allocation of parameters for gauge repeatability and reproducibility study', The International Journal of Quality & Reliability Management, Vol. 21, No.6, pp. 672-682   DOI   ScienceOn
5 Tsui, K. W. and Weerahandi, S.(1989), 'Generalized p-values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters', Journal of the American Statistical Association, Vol. 84, No. 406, pp. 602-607   DOI
6 Gong, L., Burdick, R. K., and Quiroz, J. (2005), 'Confidence Intervals for Unbalanced Two-factor Gauge R&R Studies', Quality and Reliability Engineering International, Vol. 21, No.8, pp. 727-741   DOI   ScienceOn
7 Wang, F. K. and Li, E. Y.(2003), 'Confidence Intervals in Repeatability and Reproducibility using the Bootstrap method', Total Quality Management, Vol. 14, No.3, pp. 341-354   DOI   ScienceOn
8 Barrentine, L. B.(1991), Concepts for R&R Studies, ASQ Quality Press, Milwaukee, WI
9 Burdick, R. K., and Larsen, G. A.(1997), 'Confidence Intervals on Measures of Variability in R&R Studies', Journal of Quality Technology, Vol. 29, No.3, pp, 261-273   DOI
10 Senoglu, B. and Tiku, M. L.(2001), 'Analysis of Variance in Experimental Design with Nonnormal Error Distributions', Communications in Statistics - Theory and Methods, Vol. 30, No.7, pp. 1335-1352   DOI   ScienceOn
11 Efron, B. and Tibshirani, R.(1986), 'Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy', Statistical Science, Vol. 1, No.1, pp. 54-75   DOI
12 Lohr, S. L. and Divan, M.(1997), 'Comparison of Confidence Intervals for Variance Components with Unbalanced data', Journal of statistical computation and simulation, Vol. 58, No. 1, pp. 83-97   DOI   ScienceOn
13 Borror, C. M., Montgomery, D. C., and Runger, G. C.(1997), 'Confidence intervals for Variance Components from Gauge Capability Studies', Quality and Reliability Engineering International, Vol. 13, No.6, pp. 361-369   DOI   ScienceOn
14 Dolezal, K. K., Burdick, R. K., and Birch, N. J.(1998), 'Analysis of a Two-Factor R&R Study with Fixed Operators', Journal of Quality Technology, Vol. 30, No.2, pp. 163-170   DOI
15 Weerahandi, S.(1993), 'Generalized Confidence Intervals', Journal of the American Statistical Association, Vol. 88, No. 423, pp. 899-905   DOI
16 Chiang, A. K. L.(2001), 'A Simple General Method for Constructing Confidence Intervals for Functions of Variance Components', Technometrics, Vol. 43, No.3, pp. 356-367   DOI   ScienceOn
17 Hamada, M. and Weerahandi, S.(2000), 'Measurement System Assessment Via Generalized Inference', Journal of Quality Technology, Vol. 32, No.3, pp. 241-253   DOI
18 Chang, Y. S., Choi, I. S. and Bai, D. S. (2002), 'Process Capability Indices for Skewed Populations', Quality and Reliability Engineering International, Vol. 18, No.5, pp. 383-393   DOI   ScienceOn
19 Burdick, R. K. and Graybill F. A.(l992), Confidence Intervals on Variance Components, Marcel Dekker, New York
20 Lai, Y. W. and Chew, E. P.(2000-01), 'Gauge Capability Assessment for High-yield Manufacturing Processes with Truncated Distribution', Quality Engineering, Vol. 13, No.2, pp. 203-210   DOI   ScienceOn
21 Montgomery, D. C. and Runger, G. C.(1993-94b), 'Gauge Capability and Designed Experiments Part 2 : Experimental Design Models and Variance Component Estimation', Quality Engineering, Vol. 6, No.2, pp, 289-305   DOI   ScienceOn
22 Graybill, F. A. and Wang, C. M.(1980), 'Confidence Intervals on Nonnegative Linear Combinations of Variances', Journal of the American Statistical Association, Vol. 75, No. 372, pp. 869-873   DOI
23 Chiang, A. K. L.(2002), 'Improved Confidence Intervals for a Ratio in an R&R Study', Communications in Statistics-Simulation & Computation, Vol. 31, No.3, pp. 329-344   DOI   ScienceOn