CUSUM Monitoring of First-Order Integer-Valued Autoregressive Processes of Poisson Counts

References

• Al-Osh, M. A. and Alzaid, A. A. (1987). “First-Order Integer-Valued Autoregressive (INAR(1)) Process”. Journal of Time Series Analysis 8 (3), pp. 261–275.
   Google Scholar
• Atienza, O. O.; Tang, L. C.; and Ang, B. (2002). “A CUSUM Scheme for Autocorrelated Observations”. Journal of Quality Technology 34 (2), pp. 187–199.
   Web of Science ®Google Scholar
• Borror, C. M.; Champ, C. W.; and Rigdon, S. E. (1998). “Poisson EWMA Control Charts”. Journal of Quality Technology 30 (4), pp. 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), pp. 539–549.
   Web of Science ®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, pp. 147–153.
   Web of Science ®Google Scholar
• Goldsmith, P. L. and Whitfield, H. (1961). “Average Run Lengths in Cumulative Chart Quality Control Schemes”. Technometrics 3 (1), pp. 11–20.
   Web of Science ®Google Scholar
• Harris, T. J. and Ross, W. H. (1991). “Statistical Process-Control Procedures for Correlated Observations”. Canadian Journal Of Chemical Engineering 69 (1), pp. 48–57.
   Web of Science ®Google Scholar
• Hawkins, D. M. and Olwell, D. H. (1998). Cumulative Sum Control Charts and Charting for Quality Improvement. New York, NY: Springer-Verlag, New York.
   Google Scholar
• Jung, R. C. and Tremayne, A. R. (2003). “Testing for Serial Dependence in Time Series Models of Counts”. Journal of Time Series Analysis 24 (1), pp. 65–84.
   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, pp. 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, Lenz, H.-J. and Wilrich, P.-T. (eds.), pp. 210–236. Heidelberg: Physica-Verlag.
   Google Scholar
• Lambert, D. and Liu, C. (2006). “Adaptive Thresholds: Monitoring Streams of Network Counts”. Journal of American Statistical Association 101, pp. 78–88.
   Web of Science ®Google Scholar
• Lu, C. W. and Reynolds, M. R. (2001). “CUSUM Charts for Monitoring an Autocorrelated Process”. Journal of Quality Technology 33 (3), pp. 316–334.
   Web of Science ®Google Scholar
• McKenzie, E. (1985). “Some Simple Models for Discrete Variate Time Series”. Water Resources Bulletin 21 (4), pp. 645–650.
   Google Scholar
• Montgomery, D. C. (2005). Introduction to Statistical Quality Control, 5th edition. New York, NY: John Wiley and Sons.
   Google Scholar
• Page, E. (1954). “Continuous Inspection Schemes”. Biometrika 41 (1), pp. 100–115.
   Web of Science ®Google Scholar
• Psarakis, S. and Papaleonida, G. E. A. (2007). “SPC Procedures for Monitoring Autocorrelated Processes”. Quality Technology and Quantitative Management 4 (4), pp. 501–540.
   Google Scholar
• Runger, G. C. (2002). “Assignable Causes and Autocorrelation: Control Charts for Observations or Residuals?” Journal of Quality Technology 34 (2), pp. 165–170.
   Web of Science ®Google Scholar
• Runger, G. C.; Willemain, T. R.; and Prabhu, S. (1995). “Average Run Lengths for CUSUM Control Charts Applied to Residuals”. Communications in Statistics–Theory and Methods 24 (1), pp. 273–282.
   Web of Science ®Google Scholar
• Schmid, W. (1997). “CUSUM Control Schemes for Gaussian Processes”. Statistical Papers 38, pp. 191–217.
   Web of Science ®Google Scholar
• Severin, T. and Schmid, W. (1999). “Monitoring Changes in GARCH Processes”. Allgemeines Statistisches Archiv 83, pp. 281–307.
   Google Scholar
• Steutel, F. W. and van Harn, K. (1979). “Discrete Analogues of Self-Decomposability and Stability”. Annals of Probability 7 (5), pp. 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), pp. 5621–5638.
   Web of Science ®Google Scholar
• Weiss, C. H. (2007). “Controlling Correlated Processes of Poisson Counts”. Quality Reliability Engineering International 23 (6), pp. 741–754.
   Web of Science ®Google Scholar
• Weiss, C. H. (2008). “Thinning Operations for Modeling Time Series of Counts–A Survey”. Advances in Statistical Analysis 92 (3), pp. 319–341.
   Web of Science ®Google Scholar
• Yaschin, E. (1993). “Performance of the CUSUM Control Schemes for Serially Correlated Observations”. Technometrics 35 (1), pp. 37–52.
   Web of Science ®Google Scholar
• Ye, N.; Giordano, J.; and Feldman, J. (2001). “A Process Control Approach to Cyber Attack Detection”. Comm. of the ACM 44 (8), pp. 76–82.
   Web of Science ®Google Scholar