SPC methods for time-dependent processes of counts—A literature review

References

• Acosta-Mejia, C. A. (1999). Improved p charts to monitor process quality. IIE Transactions, 31, 509–516.
   Web of Science ®Google Scholar
• Al-Osh, M. A., & Alzaid, A. A. (1987). First-order integer-valued autoregressive (INAR(1)) process. Journal of Time Series Analysis, 8, 261–275.
   Google Scholar
• Alwan, L. C. (1992). Effects of autocorrelation on control chart performance. Communications in Statistics - Theory and Methods, 21, 1025–1049.
   Web of Science ®Google Scholar
• Alwan, L. C. (1995). The problem of misplaced control limits. Journal of the Royal Statistical Society C, 44, 269–278.
   Web of Science ®Google Scholar
• Alwan, L. C., Champ, C. W., & Maragah, H. D. (1994). Study of average run lengths for supplementary runs rules in the presence of autocorrelation. Communications in Statistics - Simulation and Computation, 23, 373–391.
   Web of Science ®Google Scholar
• Alwan, L. C., & Roberts, H. V. (1988). Time series modeling for statistical process control. Journal of Business & Economic Statistics, 6, 87–95.
   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
• Borges, W., & Ho, L. L. (2001). A fraction defective based capability index. Quality and Reliability Engineering International, 17, 447–458.
   Web of Science ®Google Scholar
• Brook, D., & Evans, D. A. (1972). An approach to the probability distribution of CUSUM run length. Biometrika, 59, 539–549.
   Web of Science ®Google Scholar
• Celano, G. (2011). On the constrained economic design of control charts: A literature review. Produ\c{c}ão, 21, 223–234.
   Google Scholar
• Chen, N., & Zhou, S. (2015). CUSUM statistical monitoring of M/M/1 queues and extensions. Technometrics, 57, 245–256.
   Web of Science ®Google Scholar
• Davoodi, M., Niaki, S. T. A., & Torkamani, E. A. (2015). A maximum likelihood approach to estimate the change point of multistage Poisson count processes. International Journal of Advanced Manufacturing Technology, 77, 1443–1464.
   Web of Science ®Google Scholar
• Du, J.-G., & Li, Y. (1991). The integer-valued autoregressive (INAR(p)) model. Journal of Time Series Analysis, 12, 129–142.
   Google Scholar
• Epprecht, E. K., Costa, A. F. B., & Mendes, F. C. T. (2003). Adaptive control charts for attributes. IIE Transactions, 35, 567–582.
   Web of Science ®Google Scholar
• Ferland, R., Latour, A., & Oraichi, D. (2006). Integer-valued GARCH processes. Journal of Time Series Analysis, 27, 923–942.
   Web of Science ®Google Scholar
• Franke, J., Kirch, C., & Kamgaing, J. T. (2012). Changepoints in times series of counts. Journal of Time Series Analysis, 33, 757–770.
   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, 248–261.
   Web of Science ®Google Scholar
• Hawkins, D. M., & Olwell, D. H. (1998). Cumulative sum charts and charting for quality improvement. New York, NY: Springer-Verlag.
   Google Scholar
• Heinen, A. (2003). Modelling time series count data: An autoregressive conditional Poisson model ( CORE Discussion Paper No. 2003-63). Belgium: University of Louvain.
   Google Scholar
• Hudecov\’a, \v{S}, Hu\v{s}kov\’a, M., & Meintanis, S. (2015). Detection of changes in INAR models. In A. Steland, E. Rafaj{\l}owicz, & K. Szajowski (Eds.), Stochastic models, statistics and their applications, Springer proceedings in mathematics & statistics (Vol. 122, pp. 11–18). Springer.
   Google Scholar
• Jazi, M. A., Jones, G., & Lai, C.-D. (2012). First-order integer valued AR processes with zero inflated Poisson innovations. Journal of Time Series Analysis, 33, 954–963.
   Web of Science ®Google Scholar
• Jensen, W. A., Jones-Farmer, L. A., Champ, C. W., & Woodall, W. H. (2006). Effects of parameter estimation on control chart properties: a literature review. Journal of Quality Technology, 32, 395–409.
   Google Scholar
• Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate discrete distributions (3rd ed.). Hoboken, NJ: Wiley.
   Google Scholar
• Jones-Farmer, L. A., Woodall, W. H., Steiner, S. H., & Champ, C. W. (2014). An overview of phase I analysis for process improvement and monitoring. Journal of Quality Technology, 46, 265–280.
   Web of Science ®Google Scholar
• Kang, J., & Lee, S. (2014). Parameter change test for Poisson autoregressive models. Scandinavian Journal of Statistics, 41, 1136–1152.
   Web of Science ®Google Scholar
• Kang, J., & Song, J. (2015). Robust parameter change test for Poisson autoregressive models. Statistics and Probability Letters, 104, 14–21.
   Web of Science ®Google Scholar
• Kedem, B., & Fokianos, K. (2002). Regression models for time series analysis. Hoboken, NJ: Wiley.
   Google Scholar
• Kenett, R. S., & Pollak, M. (2012). On assessing the performance of sequential procedures for detecting a change. Quality and Reliability Engineering International, 28, 500–507.
   Web of Science ®Google Scholar
• Kim, H.-Y., & Park, Y. (2008). A non-stationary integer-valued autoregressive model. Statistical Papers, 49, 485–502.
   Web of Science ®Google Scholar
• Kirch, C., & Kamgaing, J. T. (2015). On the use of estimating functions in monitoring time series for change points. Journal of Statistical Planning and Inference, 161, 25–49.
   Web of Science ®Google Scholar
• Knoth, S. (2006). The art of evaluating monotoring schemes---How to measure the performance of control charts? In H.-J. Lenz & P.-T. Wilrich (Eds.), Frontiers in statistical quality control 8 (pp. 74–99). Heidelberg: Physica Verlag.
   Google Scholar
• Knoth, S. (in press). The case against the use of synthetic control charts. Journal of Quality Technology.
   Web of Science ®Google Scholar
• Knoth, S., & Schmid, W. (2004). Control charts for time series: A review. In H. J. Lenz & P. T. Wilrich (Eds.), Frontiers in statistical quality control 7 (pp. 210–236). Heidelberg: Physica-Verlag.
   Google Scholar
• Koutras, M. V., Bersimis, S., & Maravelakis, P. E. (2007). Statistical process control using Shewhart control charts with supplementary runs rules. Methodology and Computing in Applied Probability, 9, 207–224.
   Web of Science ®Google Scholar
• Li, C., Wang, D., & Zhu, F. (in press). Effective control charts for monitoring the NGINAR(1) process. Quality and Reliability Engineering International.
   Web of Science ®Google Scholar
• McKenzie, E. (1985). Some simple models for discrete variate time series. Water Resources Bulletin, 21, 645–650.
   Google Scholar
• Montgomery, D. C. (2009). Introduction to statistical quality control (6th ed.). New York, NY: Wiley.
   Google Scholar
• Morais, M. C., & Pacheco, A. (in press). On hitting times for Markov time series of counts with applications to quality control. RevStat.
   PubMed Web of Science ®Google Scholar
• Mousavi, S., & Reynolds, Jr., M. R., (2009). A CUSUM chart for monitoring a proportion with autocorrelated binary observations. Journal of Quality Technology, 41, 401–414.
   Web of Science ®Google Scholar
• Page, E. (1954). Continuous inspection schemes. Biometrika, 41, 100–115.
   Web of Science ®Google Scholar
• Perakis, M., & Xekalaki, E. (2005). A process capability index for discrete processes. Journal of Statistical Computation and Simulation, 75, 175–187.
   Web of Science ®Google Scholar
• Psarakis, S., & Papaleonida, G. E. A. (2007). SPC procedures for monitoring autocorrelated processes. Quality Technology & Quantitative Management, 4, 501–540.
   Google Scholar
• Ristić, M. M., Bakouch, H. S., & Nastić, A. S. (2009). A new geometric first-order integer-valued autoregressive (NGINAR(1)) process. Journal of Statistical Planning and Inference, 139, 2218–2226.
   Web of Science ®Google Scholar
• Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1, 239–250.
   Google Scholar
• Saha, M., & Maiti, S. S. (2015). Trends and practices in process capability studies. arXiv:1503.06885v1 [stat.AP].
   Google Scholar
• Schweer, S., & Wei{\ss}, C. H. (2014). Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion. Computational Statistics & Data Analysis, 77, 267–284.
   Web of Science ®Google Scholar
• Schweer, S., & Wichelhaus, C. (2015). Queueing systems of INAR(1) processes with compound Poisson arrivals. Stochastic Models, 31, 618–635.
   Web of Science ®Google Scholar
• Steutel, F. W., & van Harn, K. (1979). Discrete analogues of self-decomposability and stability. Annals of Probability, 7, 893–899.
   Web of Science ®Google Scholar
• Torkamani, E. A., Niaki, S. T. A., Aminnayeri, M., & Davoodi, M. (2014). Estimating the change point of correlated Poisson count processes. Quality Engineering, 26, 182–195.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H. (2007). Controlling correlated processes of Poisson counts. Quality and Reliability Engineering International, 23, 741–754.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H. (2008a). Thinning operations for modelling time series of counts---A survey. Advances in Statistical Analysis, 92, 319–341.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H. (2008b). Serial dependence and regression of Poisson INARMA models. Journal of Statistical Planning and Inference, 138, 2975–2990.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H. (2009a). Monitoring correlated processes with binomial marginals. Journal of Applied Statistics, 36, 399–414.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H. (2009b). EWMA monitoring of correlated processes of Poisson counts. Quality Technology and Quantitative Management, 6, 137–153.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H. (2009c). Controlling jumps in correlated processes of Poisson counts. Applied Stochastic Models in Business and Industry, 25, 551–564.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H. (2009d). Group inspection of dependent binary processes. Quality Reliability Engineering International, 25, 151–165.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H. (2011a). Detecting mean increases in Poisson INAR(1) processes with EWMA control charts. Journal of Applied Statistics, 38, 383–398.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H. (2011b). The Markov chain approach for performance evaluation of control charts---A tutorial. In S. P. Werther (Ed.), Process control: Problems, techniques and applications (pp. 205–228). New York, NY: Nova Science.
   Google Scholar
• Wei{\ss}, C. H. (2012a). Continuously monitoring categorical processes. Quality Technology and Quantitative Management, 9, 171–188.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H. (2012b). Process capability analysis for serially dependent processes of Poisson counts. Journal of Statistical Computation and Simulation, 82, 383–404.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H., & Kim, H.-Y. (2013). Parameter estimation for binomial AR(1) models with applications in finance and industry. Statistical Papers, 54, 563–590.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H., & Testik, M. C. (2009). CUSUM monitoring of first-order integer-valued autoregressive processes of Poisson counts. Journal of Quality Technology, 41, 389–400.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H., & Testik, M. C. (2011). The Poisson INAR(1) CUSUM chart under overdispersion and estimation error. IIE Transactions, 43, 805–818.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H., & Testik, M. C. (2012). Detection of abrupt changes in count data time series: Cumulative sum derivations for INARCH(1) models. Journal of Quality Technology, 44, 249–264.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H., & Testik, M. C. (2015a). Residuals-based CUSUM charts for Poisson INAR(1) processes. Journal of Quality Technology, 47, 30–42.
   Web of Science ®Google Scholar
• Wei{\ss}, C. H., & Testik, M. C. (2015b). On the phase I analysis for monitoring time-dependent count processes. IIE Transactions, 47, 294–306.
   Web of Science ®Google Scholar
• Woodall, W. H. (1997). Control charts based on attribute data: Bibliography and review. Journal of Quality Technology, 29, 172–183.
   Web of Science ®Google Scholar
• Woodall, W. H. (2000). Controversies and contradictions in statistical process control. Journal of Quality Technology, 32, 341–350.
   Web of Science ®Google Scholar
• Woodall, W. H., & Montgomery, D. C. (2014). Some current directions in the theory and application of statistical process monitoring. Journal of Quality Technology, 46, 78–94.
   Web of Science ®Google Scholar
• Yontay, P., Wei\ss, C. H., Testik, M. C., & Bayindir, Z. P. (2013). A two-sided CUSUM chart for first-order integer-valued autoregressive processes of Poisson counts. Quality and Reliability Engineering International, 29, 33–42.
   Web of Science ®Google Scholar
• Zhang, M., Nie, G., He, Z., & Hou, X. (2014). The Poisson INAR(1) one-sided EWMA chart with estimated parameters. International Journal of Production Research, 52, 5415–5431.
   Web of Science ®Google Scholar
• Zucchini, W., & MacDonald, I. L. (2009). Hidden Markov models for time series: An introduction using R. London: Chapman & Hall/CRC.
   Google Scholar