The Poisson INAR(1) CUSUM chart under overdispersion and estimation error

References

• Borror , C. M. , Champ , C. W. and Rigdon , S. E. 1998 . Poisson EWMA control charts. . Journal of Quality Technology , 30 ( 4 ) : 352 – 361 .
   Web of Science ®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. . Journal of Quality Technology , 35 ( 3 ) : 275 – 285 .
   Web of Science ®Google Scholar
• Famoye , F. 1994 . Statistical control charts for shifted generalized Poisson distribution. . Journal of the Italian Statistical Society , 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. . Statistics and Probability Letters , 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. . International Statistical Review , 61 ( 1 ) : 97 – 107 .
   Web of Science ®Google Scholar
• Gan , F. F. 1990 . Monitoring Poisson observations using modified exponentially weighted moving average control charts. . Communications in Statistics –Simulation and Computation , 19 : 103 – 124 .
   Web of Science ®Google Scholar
• Hawkins , D. M. 1993 . Robustification of cumulative sum charts by Winsorization. . Journal of Quality Technology , 25 ( 4 ) : 248 – 261 .
   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 .
   Google Scholar
• He , B. , Xie , M. , Goh , T. N. and Tsui , K. L. 2006 . On control charts based on the generalized Poisson model. . Quality Technology & Quantitative Management , 3 ( 4 ) : 383 – 400 .
   Google Scholar
• Heimann , P. A. 1996 . Attributes control charts with large sample sizes. . Journal of Quality Technology , 28 ( 4 ) : 451 – 459 .
   Web of Science ®Google Scholar
• Jensen , W. A. , Jones-Farmer , L.A. , Champ , C. W. and Woodall , W. H. 2006 . Effects of parameter estimation on control chart properties: a literature review. . Journal of Quality Technology , 38 ( 4 ) : 349 – 364 .
   Web of Science ®Google Scholar
• Jung , R. C. , Ronning , G. and Tremayne , A. R. 2005 . Estimation in conditional first order autoregression with discrete support. . Statistical Papers , 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, Germany : Physica-Verlag .
   Google Scholar
• Lucas , J. M. 1985 . Counted data CUSUM’s. . Technometrics , 27 ( 2 ) : 129 – 150 .
   Web of Science ®Google Scholar
• McKenzie , E. 1985 . Some simple models for discrete variate time series. . Water Resources Bulletin , 21 ( 4 ) : 645 – 650 .
   Google Scholar
• Montgomery , D. C. 2005 . Introduction to Statistical Quality Control, fifth edition , New York : John Wiley & Sons .
   Google Scholar
• Montgomery , D. C. and Mastrangelo , C. M. 1991 . Some statistical process control methods for autocorrelated data. . Journal of Quality Technology , 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. 1723 – 1729 . Chichester, UK : John Wiley & Sons .
   Google Scholar
• Paroli , R. , Redaelli , G. and Spezia , L. 2000 . “ Poisson hidden Markov models for time series of overdispersed insurance counts ” . In Proceedings of the ASTIN Colloquium International Actuarial Association , 461 – 474 . Brussels .
   Google Scholar
• Poortema , K. 1999 . On modelling overdispersion of counts. . Statistica Neerlandica , 53 ( 1 ) : 5 – 20 .
   Web of Science ®Google Scholar
• Steutel , F. W. and Van Harn , K. 1979 . Discrete analogues of self-decomposability and stability. . Annals of Probability , 7 ( 5 ) : 893 – 899 .
   Web of Science ®Google Scholar
• Testik , M. C. 2007 . Conditional and marginal performance of the Poisson CUSUM control chart with parameter estimation. . International Journal of Production Research , 45 ( 23 ) : 5621 – 5638 .
   Web of Science ®Google Scholar
• Weiß , C. H. 2007 . Controlling correlated processes of Poisson counts. . Quality and Reliability Engineering International , 23 ( 6 ) : 741 – 754 .
   Web of Science ®Google Scholar
• Weiß , C. H. 2008 . Thinning operations for modelling time series of counts—a survey. . Advances in Statistical Analysis , 92 ( 3 ) : 319 – 341 .
   Web of Science ®Google Scholar
• Weiß , C. H. 2011 . Detecting mean increases in Poisson INAR(1) processes with EWMA control charts . Journal of Applied Statistics , 38 ( 2 ) : 383 – 398 .
   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. . Journal of Quality Technology , 41 ( 4 ) : 389 – 400 .
   Web of Science ®Google Scholar
• Woodall , W. H. 1997 . Control charts based on attribute data: bibliography and review. . Journal of Quality Technology , 29 ( 2 ) : 172 – 183 .
   Web of Science ®Google Scholar