An Alternative to the Bivariate Control Chart for Process Dispersion

REFERENCES

• Alt , F. B. ( 1985 ). Multivariate quality control . In: Johnson , N. L. , Kotz , S. Eds. Encyclopedia of Statistical Sciences , New York : Wiley , Vol. 6 , pp. 110–122.
   Google Scholar
• Alt , F. B. , Smith , N. D. ( 1988 ). Multivariate process control . In: Krishnaiah , P. R. , Rao , C. R. Eds. Handbook of Statistics: Quality Control and Reliability , Amsterdam : North-Holland , Vol. 7 , pp. 333–351.
   Google Scholar
• Alwan , L. C. ( 2000 ). Statistical Process Analysis . New York : McGraw-Hill International .
   Google Scholar
• Aparisi , F. , Jabaloyes , J. , Carrion , A. ( 1999 ). Statistical properties of the multivariate control chart . Communications in Statistics–Theory and Methods , 28 ( 11 ): 2671 – 2686 .
   Web of Science ®Google Scholar
• Aparisi , F. , Jabaloyes , J. , Carrion , A. ( 2001 ). Generalized variance chart design with the adaptive sample sizes. The bivariate case . Communications in Statistics–Simulation and Computation , 30 ( 4 ): 931 – 948 .
   Web of Science ®Google Scholar
• Bersimis , S. , Psarakis , S. , Panaretos , J. ( 2007 ). Multivariate statistical process control charts: An overview . Quality and Reliability Engineering International , 23 : 517 – 543 .
   Web of Science ®Google Scholar
• David , H. A. ( 1968 ). Gini's mean difference rediscovered . Biometrika , 55 : 573 – 575 .
   Web of Science ®Google Scholar
• Does , R. J. M. M., Roes , K. C. B. , Trip , A. ( 1999 ). Handling multivariate problems with univariate control charts (with discussion) . Journal of Chemometrics , 13 : 353 – 378 .
   Web of Science ®Google Scholar
• Gnanadesikan , M. , Gupta , S. S. ( 1970 ). A selection procedure for multivariate normal distributions in terms of the generalized variances . Technometrics , 12 : 103 – 117 .
   Web of Science ®Google Scholar
• Hawkins , D. M. , Maboudou , E. M. ( 2007 ). Self-starting multivariate exponentially weighted moving average control charting . Technometrics , 49 ( 2 ): 199 – 209 .
   Web of Science ®Google Scholar
• Hillier , F. S. ( 1969 ). and R chart control limits based on a small number of subgroups . Journal of Quality Technology , 1 : 17 – 26 .
   Google Scholar
• Hotelling , H. ( 1947 ). Multivariate quality control . In: Eisenhart, C. M. , Hastay, W. , Wallis, W. A. , Eds. Techniques of Statistical Analysis , New York : McGraw-Hill , pp. 111–184.
   Google Scholar
• Khoo , M. B. C. , Quah , S. H. ( 2004 ). Alternative to the multivariate control charts for process dispersion . Quality Engineering , 16 ( 3 ): 423 – 435 .
   Google Scholar
• Lomnicki , Z. A. ( 1952 ). The standard error of Gini's mean difference . The Annals of Mathematical Statistics , 23 ( 4 ): 636 – 637 .
   Google Scholar
• Lowry , C. A. , Montgomery , D. C. ( 1995 ). A review of multivariate control charts . IIE Transactions , 27 : 800 – 810 .
   Web of Science ®Google Scholar
• Mason , R. L. , Young , J. C. ( 2002 ). Multivariate Statistical Process Control with Industrial Applications . Philadelphia : ASA-SIAM .
   Google Scholar
• Menzefricke , U. ( 2007 ). Control charts for the generalized variance based on its predictive distribution . Communications in Statistics–Theory and Methods , 36 : 1031 – 1038 .
   Web of Science ®Google Scholar
• Montgomery , D. C. , Wadsworth , H. M. , Jr. ( 1972 ). Some techniques for multivariate quality control applications. Technical Conference Transactions, American Society for Quality Control (ASQC), Washington, DC .
   Google Scholar
• Nair , U. S. ( 1936 ). The standard error of Gini's mean difference . Biometrika , 28 : 428 – 436 .
   Web of Science ®Google Scholar
• Nelson , L. S. ( 1984 ). The Shewhart control chart—Tests for special causes . Journal of Quality Technology , 21 : 287 – 289 .
   Google Scholar
• Olkin , I. , Yitzhaki , S. ( 1992 ). Gini regression analysis . International Statistical Review , 60 ( 2 ): 185 – 196 .
   Web of Science ®Google Scholar
• Riaz , M. , Saghir , A. ( 2007 ). Monitoring process variability using Gini's mean difference . Quality Technology and Quantitative Management , 4 ( 4 ): 439 – 454 .
   Google Scholar
• Riaz , M. ( 2008 ). Improved and Robust Monitoring in Statistical Process Control. PhD thesis, University of Amsterdam .
   Google Scholar
• Ross , S. M. ( 1990 ). A Course in Simulations . New York : Macmillan .
   Google Scholar
• Runger , G. C. ( 2007 ). Multivariate control charts overview . In: Ruggeri , F. , Kennet, R. S., Faltin, T. W, Eds. Encyclopedia of Statistics in Quality and Reliability , Chichester : Wiley , Vol. 3 , pp. 1196 – 1201 .
   Google Scholar
• Schaffer , J. R. , Kim , M.-J. ( 2007 ). Number of replications in control chart Monte Carlo simulation studies . Communications in Statistics–Simulation and Computation , 36 ( 5 ): 1075 – 1087 .
   Web of Science ®Google Scholar
• Schechtman , E. , Yitzhaki , S. ( 1987 ). A measure of association based on Gini's mean difference . Communications in Statistics–Theory and Methods , 16 : 207 – 231 .
   Web of Science ®Google Scholar
• Vermaat , M. B. , Does , R. J. M. M. ( 2006 ). A semi-Bayesian method for Shewhart individual control charts . Quality Technology and Quantitative Management , 3 ( 1 ): 111 – 125 .
   Google Scholar
• Wierda , S. J. ( 1994 ). Multivariate statistical process control—Recent results and directions for future research . Statistica Neerlandica , 48 : 147 – 168 .
   Google Scholar
• Woodall , W. H. , Ncube , M. M. ( 1985 ). Multivariate CUSUM quality control procedures . Technometrics , 27 ( 3 ): 285 – 292 .
   Web of Science ®Google Scholar
• Yang , C. H. , Hillier , F. S. ( 1970 ). Mean and variance control chart limits based on a small number of subgroup . Journal of Quality Technology , 2 : 9 – 16 .
   Google Scholar
• Yeh , A. B. , Lin , D. K. J. , McGrath , R. N. ( 2006 ). Multivariate control charts for monitoring covariance matrix: A review . Quality Technology and Quantitative Management , 3 ( 4 ): 415 – 436 .
   Google Scholar
• Yitzhaki , S. ( 2003 ). Gini's mean difference: A superior measure of variability for non-normal distributions . International Journal of Statistics , 61 ( 2 ): 285 – 316 .
   Google Scholar