SciELO - Scientific Electronic Library Online

vol.11 issue5Cropping Resilient Watermarking Based on Histogram Modification author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • Have no similar articlesSimilars in SciELO


Journal of applied research and technology

On-line version ISSN 2448-6736Print version ISSN 1665-6423

J. appl. res. technol vol.11 n.5 México Oct. 2013


Using the Monte Carlo Simulation Methods in Gauge Repeatability and Reproducibility of Measurement System Analysis


Tsu-Ming Yeh*, Jia-Jeng Sun


Department of Industrial Engineering and Management, Dayeh University, Taiwan. *



Measurements are required to maintain the consistent quality of all finished and semi-finished products in a production line. Many firms in the automobile and general precision industries apply the TS 16949:2009 Technical Specifications and Measurement System Analysis (MSA) manual to establish measurement systems. This work is undertaken to evaluate gauge repeatability and reproducibility (GR & R) to verify the measuring ability and quality of the measurement frame, as well as to continuously improve and maintain the verification process. Nevertheless, the implementation of GR & R requires considerable time and manpower, and is likely to affect production adversely. In addition, the evaluation value for GR & R is always different owing to the sum of man-made and machine-made variations. Using a Monte Carlo simulation and the prediction of the repeatability and reproducibility of the measurement system analysis, this study aims to determine the distribution of % GR & R and the related number of distinct categories (ndc). This study uses two case studies of an automobile parts manufacturer and the combination of a Monte Carlo simulation, statistical bases, and the prediction of the repeatability and reproducibility of the measurement system analysis to determine the probability density function, the distribution of % GR & R, and the related number of distinct categories (ndc). The method used in this study could evaluate effectively the possible range of the GR & R of the measurement capability, in order to establish a prediction model for the evaluation of the measurement capacity of a measurement system.

Keywords: measurement system analysis, monte carlo simulation, gauge repeatability and reproducibility.





[1] Al-Refaie, A., Bata, N., Evaluating measurement and process capabilities by GR&R with four quality measures, Measurement, Vol.43, No.6, 2010, pp.842-851        [ Links ]

[2] Stevens, N. T., Browne, R., Steiner, S. H., Mackay, R. J., Augmented Measurement System Assessment, Journal of Quality Technology, Vol.42, No.4, 2010, pp.388-399        [ Links ]

[3] Pan, J. N., Determination of the Optimal Allocation of Parameters for Gauge Repeatability and Reproducibility, International Journal of Quality & Reliability Management, Vol.21, No.6, 2004, pp.672-682        [ Links ]

[4] Pan, J. N., Evaluating the Gauge Repeatability and Reproducibility for Different Industries, Quality & Quantity, Vol.40, No.4, 2006, pp.499-518        [ Links ]

[5] Wang, F.K., Chien, T.W., Process-oriented basis representation for a multivariate gauge study, Computers & Industrial Engineering, Vol.58, 2010, pp.143-150        [ Links ]

[6] Montgomery, D. C., Runger, G. C., Gauge Capability and Designed Experiments Part I: Basic Methods, Quality Engineering, Vol.6, No.1, 1993, pp.115-135.         [ Links ]

[7] ISO, "ISO/IEC17025 General requirements for the competence of testing and calibration laboratories", 2nd Edition, 2005.         [ Links ]

[8] Automotive Industry Action Group (AIAG), Statistical Process Control (SPC) Reference Manual, Second Edition, Southfield, MI, 2005.         [ Links ]

[9] Chen, K. S., Wu, C. H., Chen, S. C., Criteria of Determining the P/T Upper Limits of GR&R in MSA, Quality & Quantity, Vol.42, No.1, 2008, pp.23-33        [ Links ]

[10] Kappele, W. D., Raffaldi, J., Gage R&R for Destructive Measurement Systems, Quality Magazine, Vol.5, 2010, pp.32-34.         [ Links ]

[11] Fang, J. J., Wang, P. S., Lee, Y. L., The Study of Gauge Repeatability and Reproducibility, Proceeding of the 10th Conference on Interdisciplinary and Multifunctional Business Management, 2006, pp.288-297        [ Links ]

[12] Automotive Industry Action Group (AIAG), Measurement Systems Analysis (MSA) Reference Manual, 4th Edition, Chrysler, Ford, GM, 2010.         [ Links ]

[13] He, S. G., Wang, G. A., Cook, D. F., Multivariate measurement system analysis in multisite testing: An online technique using principal component analysis, Expert Systems with Applications, Vol.38, 2011, pp.14602-14608.         [ Links ]

[14] Burdick, R. K., Borror, C. M., Montgomery, D. C., A review of methods for measurement systems capability analysis, Journal of Quality Technology, Vol.35, No.4, 2003, pp.342-354.         [ Links ]

[15] Li, M. H., Al-Refaie, A., Improving wooden parts' quality by adopting DMAIC procedure, Quality and Reliability Engineering International, Vol.24, 2008, pp.351-360.         [ Links ]

[16] Barrentine, L. B., Concepts for R&R Studies, ASQC Quality Press, Milwaukee, WI, 1991.         [ Links ]

[17] Automotive Industry Action Group (AIAG), Measurement Systems Analysis, AIAG Reference Manual, Southfield, MI, 1997.         [ Links ]

[18] Mandel, J., Repeatability and Reproducibility, Journal of Quality Technology, Vol.4, No.2, 1972, pp.74-85.         [ Links ]

[19] Montgomery, D. C., Runger, G. C. Gauge Capability Analysis and Designed Experiments Part II: Experimental Design Models and Variance Component Estimation, Quality Engineering, Vol.6, No.2, 1993, pp.289-305        [ Links ]

[20] McNeese, W. H., Klein, R. A., Measurement System Sampling and Process Capability, Quality Engineering, Vol.4, No.1, 1991, pp.21-39.         [ Links ]

[21] Tsai, P., Variable Gauge Repeatability and Reproducibility Study Using The Analysis of Variance, Quality Engineer, Vol.1, No.1, 1998, pp.107-115.         [ Links ]

[22] James, P. D., Finderne, A., Graphical Display of Gauge R&R Data, ASQC Quality Congress Transactions, Milwaukee, 1991, pp.835-839.         [ Links ]

[23] Metropolis, N., Ulam, S., The Monte Carlo Method, Journal of the American Statistical Association, Vol.44, No.247, 1949, pp.335-341.         [ Links ]

[24] García-Alonso, C. R., Arenas-Arroyo, E., Pérez-Alcalá, G. M., macro-economic model to forecast remittances based on Monte-Carlo simulation and artificial intelligence, Expert Systems with Applications, Vol.39, 2012, pp.7929-7937.         [ Links ]

[25] Yeh, W. C., Lin, Y. C., Chung, Y. Y., Performance analysis of cellular automata Monte Carlo Simulation for estimating network reliability, Expert Systems with Applications, Vol.37, 2010, pp.3537-3544        [ Links ]

[26] Robert, C. P., Casella, G., Monte Carlo Statistical Methods, Springer-Verlag, 2nd Edition, 2004.         [ Links ]

[27] Wittwer, J. W., Monte Carlo Simulation Basics, From, June 1, 2004,, 2004.         [ Links ]

[28] Manno, I., Introduction to the Monte Carlo Method, Akademiai Kiado, 1999.         [ Links ]

[29] Chaitin, G. J., Exploring Randomness, Springer-Verlag, 2001.         [ Links ]

[30] Lehmer, D. H., Mathematical methods in large-scale computing units, Proceedings of the Second Symposium on Large Scale Digital Computing Machinery, Harvard University Press, 1951, pp.141-146.         [ Links ]

[31] Law, A. M., Kelton, W. D., Simulation Modeling & Analysis, Third Edition, McGraw-Hill, 2000.         [ Links ]

[32] Wichmann, B. A., Hill, I. D., An efficient and portable pseudo-random number generator, Applied Statistics, Vol.31, No.2, 1982, pp.188-190.         [ Links ]

[33] Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T., Numerical Recipes in FORTRAN 77: The Art of Scientific Computing, Second Edition, Cambridge University Press, 1992.         [ Links ]

[34] Wheeler, D. J., Lyday, R. W., Evaluating the Measurement Process, SPC Press, Inc., Knoxville, Tennessee, 1989.         [ Links ]

[35] ISO, 2008, ISO/IEC Guide 98-3: Uncertainty of measurement - Part3: Guide to the expression of uncertainty in measurement (GUM: 1995).         [ Links ]

[36] ISO, 1994, ISO 5725-1, Accuracy (trueness and precision) of Measurement Methods and Results-Part 1: General Principles and Definitions. ISO: Geneva, Switzerland.         [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License