Table of Contents
Journal of Quality and Reliability Engineering
Volume 2013, Article ID 542305, 14 pages
http://dx.doi.org/10.1155/2013/542305
Research Article

Robust Control Charts for Monitoring Process Mean of Phase-I Multivariate Individual Observations

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7

Received 22 November 2012; Revised 22 March 2013; Accepted 2 April 2013

Academic Editor: Adiel Teixeira de Almeida

Copyright © 2013 Asokan Mulayath Variyath and Jayasankar Vattathoor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Hotelling, “Multivariate quality control,” in Techniques of Statistical Analysis, C. Eisenhart, H. Hastay, and W. A. Wallis, Eds., pp. 111–184, McGrawHill, New York, NY, USA, 1947. View at Google Scholar
  2. N. D. Tracy, J. C. Young, and R. L. Mason, “Multivariate control charts for individual observations,” Journal of Quality Technology, vol. 24, pp. 88–95, 1992. View at Google Scholar
  3. J. H. Sullivan and W. H. Woodall, “A comparison of multivariate control charts for individual observations,” Journal of Quality Technology, vol. 28, no. 4, pp. 398–408, 1996. View at Google Scholar · View at Scopus
  4. J. A. N. Vargas, “Robust estimation in multivariate control charts for individual observations,” Journal of Quality Technology, vol. 35, no. 4, pp. 367–376, 2003. View at Google Scholar · View at Scopus
  5. W. A. Jensen, J. B. Birch, and W. H. Woodall, “High breakdown estimation methods for phase I multivariate control charts,” Quality and Reliability Engineering International, vol. 23, no. 5, pp. 615–629, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Chenouri, S. H. Steiner, and A. M. Variyath, “A multivariate robust control chart for individual observations,” Journal of Quality Technology, vol. 41, no. 3, pp. 259–271, 2009. View at Google Scholar · View at Scopus
  7. D. L. Donoho and P. J. Huber, “The notion of breakdown point,” in A Festschrift for Erich Lehmann, P. Bickel, K. Doksum, and J. Hodges, Eds., pp. 157–184, Wadsworth, Belmont, Calif, USA, 1983. View at Google Scholar
  8. H. P. Lopuhaä and P. J. Rousseeuw, “Breakdown points of affine equivariant estimators of multivariate location and covariance matrices,” The Annals of Statistics, vol. 19, pp. 229–248, 1991. View at Google Scholar
  9. D. L. Donoho and M. Gasko, “Breakdown properties of location estimates based on halfspace depth and projected outlyingness,” The Annals of Statistics, vol. 20, pp. 1803–1827, 1992. View at Google Scholar
  10. P. L. Davies, “Asymptotic behavior of S-estimates of multivariate location parameters and dispersion matrices,” The Annals of Statistics, vol. 15, pp. 1269–1292, 1987. View at Google Scholar
  11. C. Croux and G. Haesbroeck, “Influence function and efficiency of the minimum covariance determinant scatter matrix estimator,” Journal of Multivariate Analysis, vol. 71, no. 2, pp. 161–190, 1999. View at Publisher · View at Google Scholar · View at Scopus
  12. G. Pison, S. van Aelst, and G. Willems, “Small sample corrections for LTS and MCD,” Metrika, vol. 55, no. 1-2, pp. 111–123, 2002. View at Publisher · View at Google Scholar · View at Scopus
  13. D. L. Woodru and D. M. Rocke, “Computable robust estimation of multivariate location and shape in high dimension using compound estimators,” Journal of American Statistical Association, vol. 89, pp. 888–896, 1994. View at Google Scholar
  14. D. M. Hawkins and D. J. Olive, “Improved feasible solution algorithms for high breakdown estimation,” Computational Statistics and Data Analysis, vol. 30, no. 1, pp. 1–11, 1999. View at Google Scholar · View at Scopus
  15. P. J. Rousseeuw and K. van Driessen, “A fast algorithm for the minimum covariance determinant estimator,” Technometrics, vol. 41, no. 3, pp. 212–223, 1999. View at Google Scholar · View at Scopus
  16. P. J. Rousseeuw and B. C. van Zomeren, “Unmasking multivariate outliers and leverage points,” Journal of American Statistical Association, vol. 85, pp. 633–639, 1990. View at Google Scholar
  17. P. L. Davies, “The asymptotics of Rousseeuw's minimum volume ellipsoid estimator,” The Annals of Statistics, vol. 20, no. 4, pp. 1828–1843, 1992. View at Google Scholar
  18. C. Croux and G. Haesbroeck, “An easy way to increase the finite-sample efficiency of the resampled minimum volume ellipsoid estimator,” Computational Statistics and Data Analysis, vol. 25, no. 2, pp. 125–141, 1997. View at Google Scholar · View at Scopus
  19. V. Torodov, “rrcov: Scalable Robust Estimators with High Breakdown point,” R package version 0.5-03, 2009, http://cran.r-project.org/web/packages/rrcov/.