EWMA Charts for Multivariate Output: Some Stochastic Ordering Results

References

• Fuchs , C. , Kenett , R. S. ( 1998 ). Multivariate Quality Control: Theory and Applications . New York : Marcel Dekker, Inc .
   Google Scholar
• Hotelling , H. ( 1947 ). Multivariate quality control–illustrated by the air testing of sample bombsights . In: Eisenhart , C. , Hastay , M. W. , Wallis , W. A. , eds. Techniques of Statistical Analysis New York : McGraw-Hill , pp. 111 – 184 .
   Google Scholar
• Johnson , N. L. , Kotz , S. , Balakrishnan , N. ( 1995 ). Continuous Univariate Distributions . Vol. 2 . , 2nd ed . New York : John Wiley & Sons .
   Google Scholar
• Johnson , R. A. , Wichern , D. W. ( 1982 ). Applied Multivariate Statistical Analysis . Englewood Cliffs , NJ : Prentice Hall, Inc .
   Google Scholar
• Lowry , C. A. , Woodall , W. H. , Champ , C. W. , Rigdon , S. E. ( 1992 ). A multivariate exponentially weighted moving average control chart . Technometrics 34 : 46 – 53 .
   Web of Science ®Google Scholar
• Montgomery , D. C. ( 1991 ). Introduction to Statistical Quality Control. , 2nd ed . Chichester : John Wiley & Sons .
   Google Scholar
• Morais , M. C. ( 2002 ). Stochastic Ordering in the Performance Analysis of Quality Control Schemes. Ph.D. thesis, Department of Mathematics, IST–TU Lisbon .
   Google Scholar
• Morais , M. C. , Pacheco , A. ( 2001 ). Some stochastic properties of upper one-sided and EWMA charts for μ in the presence of shifts in σ . Sequent. Anal. 20 : 1 – 12 .
   Google Scholar
• Morais , M. C. , Okhrin , Y. , Pacheco , A. , Schmid , W. ( 2006 ). On the stochastic behavior of the run length of EWMA control schemes for the mean of correlated output in the presence of shifts in σ . Statist. Decis. 24 : 1001 – 1018 .
   Google Scholar
• Muirhead , R. J. ( 1982 ). Aspects of Multivariate Statistical Theory . New York : John Wiley & Sons .
   Google Scholar
• Rosołowski , M. , Schmid , W. ( 2003 ). EWMA charts for monitoring the mean and the autocovariances of stationary Gaussian processes . Sequent. Anal. 22 : 257 – 285 .
   Google Scholar
• Shaked , M. , Shanthikumar , J. G. ( 1994 ). Stochastic Orders and Their Applications . Boston : Academic Press, Inc .
   Google Scholar
• Słiwa , P. , Schmid , W. ( 2005 ). Monitoring the cross-covariances of a multivariate time series . Metrika 61 : 89 – 11 .
   Web of Science ®Google Scholar
• Wittmann , B. ( 1994 ). Die Anwendung multivariater Regelkarten und Systeme univariater Regelkarten unter besonderer Berücksichtigung einer modifizierten multivariaten EWMA-Regelkarte. Akademischer Verlag München .
   Google Scholar