Detecting mean increases in Poisson INAR(1) processes with EWMA control charts

References

• Borror , C. M. , Champ , C. W. and Ridgon , S. E. 1998 . Poisson EWMA control charts . J. Qual. Technol. , 30 ( 4 ) : 352 – 361 .
   Web of Science ®Google Scholar
• Borror , C. M. , Montgomery , D. C. and Runger , G. C. 1998 . Robustness of EWMA control chart to non-normality . J. Qual. Technol. , 31 ( 3 ) : 309 – 316 .
   Google Scholar
• Brook , D. and Evans , D. A. 1972 . An approach to the probability distribution of cusum run length . Biometrika , 59 ( 3 ) : 539 – 549 .
   Web of Science ®Google Scholar
• Christensen , A. , Melgaard , H. , Iwersen , J. and Thyregod , P. 2003 . Environmental monitoring based on a hierarchical Poisson–Gamma model . J. Qual. Technol. , 35 ( 3 ) : 275 – 285 .
   Web of Science ®Google Scholar
• Famoye , F. 1994 . Statistical control charts for shifted generalized Poisson distribution . J. Ital. Stat. Soc. , 3 : 339 – 354 .
   Google Scholar
• Freeland , R. K. and McCabe , B. P.M. 2005 . Asymptotic properties of CLS estimators in the Poisson AR(1) model . Stat. Probab. Lett. , 73 : 147 – 153 .
   Web of Science ®Google Scholar
• Friedman , D. J. 1993 . Some considerations in the use of quality control techniques in integrated circuit fabrication . Int. Stat. Rev. , 61 ( 1 ) : 97 – 107 .
   Web of Science ®Google Scholar
• Gan , F. F. 1990 . Monitoring Poisson observations using modified exponentially weighted moving average control charts . Commun. Stat. Simul. Comput. , 19 : 103 – 124 .
   Web of Science ®Google Scholar
• Hawkins , D. M. and Olwell , D. H. 1998 . Cumulative Sum Charts and Charting for Quality Improvement , New York : Springer-Verlag, Inc .
   Google Scholar
• He , B. , Xie , M. , Goh , T. N. and Tsui , K. L. 2006 . On control charts based on the generalized Poisson model . Qual. Technol. Quant. Manage. , 3 ( 4 ) : 383 – 400 .
   Google Scholar
• Heimann , P. A. 1996 . Attributes control charts with large sample sizes . J. Qual. Technol. , 28 ( 4 ) : 451 – 459 .
   Web of Science ®Google Scholar
• Jung , R. C. , Ronning , G. and Tremayne , A. R. 2005 . Estimation in conditional first order autoregression with discrete support . Stat. Pap. , 46 : 195 – 224 .
   Web of Science ®Google Scholar
• Knoth , S. and Schmid , W. 2004 . “ Control charts for time series: A review ” . In Frontiers in Statistical Quality Control 7 , Edited by: Lenz , H.-J. and Wilrich , P.-T. 210 – 236 . Heidelberg : Physica–Verlag .
   Google Scholar
• Lucas , J. M. 1985 . Counted data CUSUM's . Technometrics , 27 ( 2 ) : 129 – 150 .
   Web of Science ®Google Scholar
• Mason , R. L. and Young , J. C. 2008 . It depends – the effect of dependent observations on process control . Qual. Prog. , : 70 – 72 .
   Google Scholar
• McKenzie , E. 1985 . Some simple models for discrete variate time series . Water Resour. Bull. , 21 ( 4 ) : 645 – 650 .
   Google Scholar
• Montgomery , D. C. 2005 . Introduction to Statistical Quality Control , 5 , New York : John Wiley & Sons, Inc .
   Google Scholar
• Montgomery , D. C. and Mastrangelo , C. M. 1991 . Some statistical process control methods for autocorrelated data . J. Qual. Technol. , 23 ( 3 ) : 179 – 193 .
   Web of Science ®Google Scholar
• Nishina , K. 2007 . “ Sampling in implementation of statistical process control ” . In Encyclopedia of Statistics in Quality and Reliability , Edited by: Ruggeri , F. , Kenett , R. and Faltin , F. W. 1723 – 1729 . New York : John Wiley & Sons Ltd .
   Google Scholar
• Paroli , R. , Redaelli , G. and Spezia , L. Poisson hidden Markov models for time series of overdispersed insurance counts . ASTIN Colloquium International Actuarial Association . Brussels, Belgium. pp. 461 – 474 .
   Google Scholar
• Poortema , K. 1999 . On modelling overdispersion of counts . Stat. Neerlandica , 53 ( 1 ) : 5 – 20 .
   Web of Science ®Google Scholar
• Psarakis , S. and Papaleonida , G. E.A. 2007 . SPC procedures for monitoring autocorrelated processes . Qual. Technol. Quant. Manage. , 4 ( 4 ) : 501 – 540 .
   Google Scholar
• Steutel , F. W. and van Harn , K. 1979 . Discrete analogues of self-decomposability and stability . Ann. Probab. , 7 ( 5 ) : 893 – 899 .
   Web of Science ®Google Scholar
• Weiß , C. H. 2007 . Controlling correlated processes of Poisson counts . Qual. Reliab. Eng. Int. , 23 ( 6 ) : 741 – 754 .
   Web of Science ®Google Scholar
• Weiß , C. H. 2008 . Thinning operations for modelling time series of counts – a survey . Adv. Stat. Anal. , 92 ( 3 ) : 319 – 341 .
   Web of Science ®Google Scholar
• Weiß , C. H. 2009 . EWMA monitoring of correlated processes of Poisson counts . Qual. Technol. Quant. Manage. , 6 ( 2 ) : 137 – 153 .
   Web of Science ®Google Scholar
• Weiß , C. H. and Testik , M. C. 2009 . CUSUM monitoring of first-order integer-valued autoregressive processes of Poisson counts . J. Qual. Technol. , 41 ( 4 ) : 389 – 400 .
   Web of Science ®Google Scholar
• Woodall , W. H. 1997 . Control charts based on attribute data: bibliography and review . J. Qual. Technol. , 29 ( 2 ) : 172 – 183 .
   Web of Science ®Google Scholar
• Zhang , N. F. and Pollard , J. F. 1994 . Analysis of autocorrelations in dynamic processes . Technometrics , 36 ( 4 ) : 354 – 368 .
   Google Scholar