Robustness to non-normality of the multivariate EWMA control chart

Journal of Quality Technology

Volumn 34, Issue 3, 2002, Pages 260-276

  Stoumbos, Zachary G ^a   Sullivan, Joe H ^b  

^a RUTGERS UNIVERSITY   (United States)

^b MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

Average run length; Exponentially weighted moving average; Multivariate control charts; Multivariate gamma distribution; Multivariate t distribution; Statistical process control; Unbiased average run length

Indexed keywords

GRAPHIC METHODS; MULTIVARIABLE CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); STATISTICAL METHODS; VECTORS;

MEAN VECTOR; MULTIVARIATE EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHART;

QUALITY CONTROL;

EID: 0141632816     PISSN: 00224065     EISSN: None     Source Type: Journal    
DOI: 10.1080/00224065.2002.11980157     Document Type: Article

References (33)

1. Alt, F. B. and Smith, N. D. (1988). "Multivariate Process Control" in Handbook of Statistics, Vol. 7, edited by P. R. Krishnaiah and C. R. Rao, Amsterdam: Elsevier Science.
2. Anderson, T. W. (1984). An Introduction to Multivariate Statistical Analysis 2nd ed. Wiley, New York, NY.
3. Borror, C. M.; Montgomery, D. C.; and Runger, G. C. (1999). "Robustness of the EWMA Control Chart to Non-Normality". Journal of Quality Technology 31, pp. 309-316.
4. Coleman, D. E. (1997). "Individual Contributions" in "A Discussion on Statistically-Based Process Monitoring and Control" edited by D. C. Montgomery and W. H. Woodall, Journal of Quality Technology 29, pp. 148-149.
5. Fang, K.-T., and Zhang, Y.-T. (1990). Generalized Multivariate Analysis. Springer-Verlag, Berlin, Germany.
6. Hotelling H. (1947). "Multivariate Quality Control" in Techniques of Statistical Analysis edited by C. Eisenhart, M. W. Hastay, and W. A. Wallis, McGraw-Hill, New York, NY.
7. Jensen, D. R. (1985). "Multivariate Distributions" in Encyclopedia of Statistical Sciences edited by N. L. Johnson and S. Kotz, Wiley, New York, NY.
8. Jensen, D. R. and Good, I. J. (1981). "Invariant Distributions Associated with Matrix Laws Under Structural Symmetry". Journal of the Royal Statistical Society B 43, pp. 327-332.
9. Johnson, M. E. (1987). Multivariate Statistical Simulation. Wiley, New York, NY.
10. Johnson, N. L. Kotz, S. (1972). Distributions in Statistics, Continuous Multivariate Distributions, Vol. 4. Wiley, New York NY.
11. Krishnaiah, P. R. (1985). "Multivariate Gamma Distributions" in Encyclopedia of Statistical Sciences edited by N. L. Johnson and S. Kotz, Wiley, New York, NY.
12. Linderman, K. and Love, T. E. (2000a). "Economic and Economic Statistical Designs for MEWMA Control Charts". Journal of Quality Technology 32, pp. 410-417.
13. Linderman, K. and Love, T. E. (2000b). "Implementing Economic and Economic Statistical Designs for MEWMA Control Charts". Journal of Quality Technology 32, pp. 457-463.
14. Lowry, C. A. and Montgomery D. C. (1995). "A Review of Multivariate Control Charts". IIE Transactions 27, pp. 800-810.
15. Lowry, C. A.; Woodall, W. H.; Champ, C. W.; and Rigdon, S. E. (1992). "A Multivariate Exponentially Weighted Moving Average Control Chart". Technometrics 34, pp. 46-53.
16. Lucas, J. M. and Saccucci, M. S. (1990). "Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements" (with discussion). Technometrics 32, pp. 1-29.
17. Mardia, K. V.; Kent, J. T.; and Bibby, J. M. (1979) Multivariate Analysis. Academic Press, London, UK.
18. Mason, R. L.; Champ, C. W.; Tracy, N. D.; Wierda, S. J.; Young J. C. (1997). "Assessment of Multivariate Process Control Techniques". Journal of Quality Technology 29, pp. 140-143.
19. Montgomery, D. C. (2001). Introduction to Statistical Quality Control 4th ed. Wiley, New York, NY.
20. Peña, D. and Prieto, F. J. (2001). "Multivariate Outlier Detection and Robust Covariance Matrix Estimation". Technometrics 43, pp. 286-310.
21. Prabhu, S. S. and Runger, G. C. (1997) "Designing a Multivariate EWMA Control Chart". Journal of Quality Technology 29, pp. 8-15.
22. Reynolds, M. R., Jr. and Stoumbos, Z. G. (2002) "Control Charts and the Efficient Allocation of Sampling Resources". Preprint.
23. Rigdon, S. E. (1995). "An Integral Equation for the In-Control Average Run Length of a Multivariate Exponentially Weighted Moving Average Control Chart". Journal of Statistical Computation and Simulation 52, pp. 351-365.
24. Ronning, G. (1977). "A Simple Scheme for Generating Multivariate Gamma Distributions with Non-Negative Covariance Matrix". Technometrics 19, pp. 179-183.
25. Ryan, T. P. (2000). Statistical Methods for Quality Improvement 2nd ed. Wiley, New York, NY.
26. Sivazlian, B. D. (1981). "On a Multivariate Extension of the Gamma and Beta Distributions". SIAM Journal of Applied Mathematics 41, pp. 205-209.
27. Steiner, S. H. (1999). "EWMA Control Charts with Time-Varying Control Limits and Fast Initial Response". Journal of Quality Technology 31, pp. 75-86.
28. Stoumbos, Z. G. and Jones, L. A. (2000). "On the Properties and Design of Individuals Control Charts Based on Simplicial Depth". Nonlinear Studies 7, pp. 147-178.
29. Stoumbos, Z. G.; Jones, L. A.; Woodall, W. H.; and Reynolds, M. R., Jr. (2001). "On Shewhart-Type Nonparametric Multivariate Control Charts Based on Data Depth" in Frontiers in Statistical Quality Control 6, edited by H.-J. Lenz and P.-Th. Wilrich, Heidelberg, Germany: Springer-Verlag, pp. 207-227.
30. Stoumbos, Z. G. and Reynolds, M. R., Jr. (2000). "Robustness to Non-Normality and Autocorrelation of Individuals Control Charts". Journal of Statistical Computation and Simulation 66, pp. 145-187.
31. Stoumbos, Z. G.; Reynolds, M. R., Jr.; Ryan, T. P.; and Woodall W. H. (2000). "The State of Statistical Process Control as We Proceed into the 21st Century". Journal of the American Statistical Association 95, pp. 992-998.
32. Wierda, S. J. (1994). "Multivariate Statistical Process Control - Recent Results and Directions for Future Research". Statistica Neerlandica 48, pp, 147-168.
33. Woodall W. H. and Montgomery, D. C. (1999). "Research Issues and Ideas in Statistical Process Control". Journal of Quality Technology 31, pp. 376-386.