Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Estimations of Measurement System Variability and PTR under Non-normal Measurement Error

비정규 측정오차의 경우 측정시스템 변동과 PTR 추정

  • Chang, Mu-Seong (Department of Industrial and Systems Engineering, Changwon National University) ;
  • Kim, Sang-Boo (Department of Industrial and Systems Engineering, Changwon National University)
  • 장무성 (창원대학교 산업시스템공학과) ;
  • 김상부 (창원대학교 산업시스템공학과)
  • Published : 2007.03.31
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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

References

  1. Barrentine, L. B.(1991), Concepts for R&R Studies, ASQ Quality Press, Milwaukee, WI
  2. Burdick, R. K. and Graybill F. A.(l992), Confidence Intervals on Variance Components, Marcel Dekker, New York
  3. 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 https://doi.org/10.1002/(SICI)1099-1638(199711/12)13:6<361::AID-QRE126>3.0.CO;2-2
  4. 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 https://doi.org/10.1080/00224065.2003.11980232
  5. 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 https://doi.org/10.1080/00224065.1997.11979768
  6. 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 https://doi.org/10.1002/qre.489
  7. 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 https://doi.org/10.1198/004017001316975943
  8. 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 https://doi.org/10.1081/SAC-120003845
  9. 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 https://doi.org/10.1080/00224065.2005.11980319
  10. 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 https://doi.org/10.1080/00224065.1998.11979835
  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 https://doi.org/10.1214/ss/1177013815
  12. 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 https://doi.org/10.1002/qre.682
  13. 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 https://doi.org/10.2307/2287174
  14. Hamada, M. and Weerahandi, S.(2000), 'Measurement System Assessment Via Generalized Inference', Journal of Quality Technology, Vol. 32, No.3, pp. 241-253 https://doi.org/10.1080/00224065.2000.11980000
  15. 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 https://doi.org/10.1080/08982110108918642
  16. 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 https://doi.org/10.1080/00949659708811823
  17. 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 https://doi.org/10.1080/08982119308918710
  18. 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 https://doi.org/10.1080/08982119308918725
  19. 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 https://doi.org/10.1108/02656710410542061
  20. 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 https://doi.org/10.1081/STA-100104748
  21. 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 https://doi.org/10.2307/2289949
  22. 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 https://doi.org/10.1080/1478336032000046643
  23. Weerahandi, S.(1993), 'Generalized Confidence Intervals', Journal of the American Statistical Association, Vol. 88, No. 423, pp. 899-905 https://doi.org/10.2307/2290779