High breakdown estimation methods for phase I multivariate control charts

Quality and Reliability Engineering International

Volumn 23, Issue 5, 2007, Pages 615-629

  Jensen, Willis A ^a   Birch, Jeffrey B ^b   Woodall, William H ^b  

^a W L GORE AND ASSOCIATES   (United States)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Breakdown point; Minimum covariance determinant; Minimum volume ellipsoid; Multivariate outliers; Multivariate statistical process control; Robust estimation

Indexed keywords

COMPUTER SIMULATION; ESTIMATION; QUALITY CONTROL; ROBUST CONTROL; SOFTWARE PACKAGES;

BREAKDOWN ESTIMATION METHODS; BREAKDOWN POINT; CONTROL LIMITS; MINIMUM VOLUME ELLIPSOID;

MULTIVARIABLE CONTROL SYSTEMS;

EID: 34547841587     PISSN: 07488017     EISSN: 10991638     Source Type: Journal    
DOI: 10.1002/qre.837     Document Type: Article

References (34)

1. Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA. Robust Statistics: The Approach Based on Influence Functions. Wiley: New York, 1986.
2. Rousseeuw PJ, Leroy AM. Robust Regression and Outlier Detection. Wiley: New York, 1987.
3. Rocke DM. Robust control charts. Technometrics 1989; 31:173-184.
4. q charts: Robust control charts. Statistician 1992; 41:97-104.
5. Tatum LG. Robust estimation of the process standard deviation for control charts. Technometrics 1997; 39:127-141.
6. Davis CM, Adams BM. Robust monitoring of contaminated data. Journal of Quality Technology 2005; 37:163-174.
7. Wisnowski JW, Simpson JR, Montgomery DC. A performance study for multivariate location and shape estimators. Quality and Reliability Engineering International 2002; 18:117-129.
8. Vargas JA. Robust estimation in multivariate control charts for individual observations. Journal of Quality Technology 2003; 35:367-376.
9. Rocke DM, Woodruff DL. Computation of robust estimates of multivariate location and shape. Statistica Neerlandica 1993; 47:27-42.
10. Rocke DM, Woodruff DL. Identification of outliers in multivariate data. Journal of the American Statistical Association 1996;91:1047-1061.
11. Sullivan JH, Woodall WH. A comparison of multivariate control charts for individual observations. Journal of Quality Technology 1996; 28:398-408.
12. Rousseeuw PJ. Least median of squares regression. Journal of the American Statistical Association 1984; 79:871-880.
13. Rousseeuw PJ, van Zomeren BC. Unmasking multivariate outliers and leverage points. Journal of the American Statistical Association 1990; 85:633-639.
14. Rousseeuw PJ, van Zomeren BC. Robust distance: Simulations and cutoff values. Directions in Robust Statistics and Diagnostics Part II, Stahel W, Weisberg S (eds.). Springer: New York, 1991.
15. Davies PL. Asymptotic behavior of S-estimators of multivariate location parameters and dispersion matrices. The Annals of Statistics 1987; 15:1269-1292.
16. Lopuhaä HP, Rousseeuw PJ. Breakdown points of affine equivariant estimators of multivariate location and covariance matrices. The Annals of Statistics 1991; 19:229-248.
17. Cook RD, Hawkins DM. Discussion of 'Unmasking multivariate outlier and leverage points'. Journal of the American Statistical Association 1990; 85:640-644.
18. Cook RD, Hawkins DM, Weisberg S. Exact iterative computation of the robust multivariate minimum volume ellipsoid estimator. Statistics and Probability Letters 1993; 16:213-218.
19. Woodruff DL, Rocke DM. Heuristic search algorithms for the minimum volume ellipsoid. Journal of Computational and Graphical Statistics 1993; 2:69-95.
20. Hawkins DM. A feasible solution algorithm for the minimum volume ellipsoid estimator in multivariate data. Computational Statistics 1993; 8:95-107.
21. Hawkins DM. The feasible solution algorithm for the minimum covariance determinant estimator in multivariate data. Computational Statistics and Data Analysis 1994; 17:197-210.
22. Agullo J. Exact iterative computation of the multivariate minimum volume ellipsoid estimator with a branch and bound algorithm. Proceedings in Computational Statistics, Prat A (ed.). Physica: Heidelberg, 175-180, 1996.
23. Croux C, Haesbroeck G. An easy way to increase the finite-sample efficiency of the resampled minimum volume ellipsoid estimator. Computational Statistics and Data Analysis 1997; 25:125-141.
24. Croux C, Haesbroeck G. A note on finite-sample efficiencies for the minimum volume ellipsoid. Journal of Statistical Computation and Simulation 2002; 72:585-596.
25. Agullo J. New algorithms for computing the least trimmed squares regression estimator. Computational Statistics and Data Analysis 2001; 36:425-439.
26. Hawkins DM, Olive DJ. Improved feasible solution algorithms for high breakdown estimation. Computational Statistics and Data Analysis 1999; 30:1-11.
27. Rocke DM, Woodruff DL. Robust estimation of multivariate location and shape. Journal of Statistical Planning and Inference 1997; 57:245-255.
28. Rousseeuw PJ, Van Driessen K. A fast algorithm for the minimum covariance determinant estimator. Technometrics 1999; 41:212-223.
29. Mason RL, Young JC. Multivariate Statistical Process Control with Industrial Applications. SIAM: Philadelphia, PA, 2002.
30. Woodruff DL, Rocke DM. Computable robust estimation of multivariate location and shape in high dimension using compound generators. Journal of the American Statistical Association 1994; 89:888-896.
31. Hadi AS. Identifying multiple outliers in multivariate data. Journal of the Royal Statistical Society, Series B 1992; 54:761-777.
32. Hadi AS. A modification of a method for the detection of outliers in multivariate samples. Journal of the Royal Statistical Society, Series B 1994; 56:393-396.
33. Jensen WA, Birch JB, Woodall WH. High breakdown estimation methods for phase I multivariate control charts. Technical Report 05-6, Virginia Polytechnic Institute and State University, Blacksburg, VA, 2005.
34. 2 statistic based on the successive differences covariance matrix estimator. Journal of Quality Technology 2006; 38:217-229.