An ARL-Unbiased Modified np-Chart for Autoregressive Binomial Counts

References

[1] M. A. Al-Osh and A. A. Alzaid, Binomial autoregressive moving average models, Comm. Statist. Stochastic Models 7 (1991), no. 2, 261–282. 10.1080/15326349108807188Suche in Google Scholar

[2] M. Anastasopoulou and A. C. Rakitzis, EWMA control charts for monitoring correlated counts with finite range, J. Appl. Stat. 49 (2022), no. 3, 553–573. 10.1080/02664763.2020.1820959Suche in Google Scholar PubMed PubMed Central

[3] D. Brook and D. A. Evans, An approach to the probability distribution of cusum run length, Biometrika 59 (1972), 539–549. 10.1093/biomet/59.3.539Suche in Google Scholar

[4] C. J. Cruz, Cartas com ARL sem viés para processos i.i.d. e AR(1) com marginais binomiais (on ARL-unbiased charts for i.i.d. and binomial AR(1) counts), Master’s thesis, Universidade de Lisboa, 2019. Suche in Google Scholar

[5] C. J. Geyer and G. D. Meeden, An R package for UMP and UMPU tests, 2004, https://CRAN.R-project.org/package=ump. Suche in Google Scholar

[6] E. L. Lehmann, Testing Statistical Hypotheses, John Wiley & Sons, New York, 1959. Suche in Google Scholar

[7] E. McKenzie, Some simple models for discrete variate time series, J. Amer. Water Resources Ass. 21 (1985), no. 4, 6455–650. 10.1111/j.1752-1688.1985.tb05379.xSuche in Google Scholar

[8] D. C. Montgomery, Statistical Quality Control: A Modern Introduction, 6th. ed., Wiley, Hoboken, 2009. Suche in Google Scholar

[9] M. C. Morais, An ARL-unbiased np-chart, Econ. Qual. Control 31 (2016), no. 1, 11–21. 10.1515/eqc-2015-0013Suche in Google Scholar

[10] M. C. Morais, S. Knoth, C. J. Cruz and C. H. Weiß, ARL-unbiased CUSUM schemes to monitor binomial counts, Frontiers in Statistical Quality Control 13, Front. Stat. Qual. Control, Springer, Cham (2021), 77–98. 10.1007/978-3-030-67856-2_6Suche in Google Scholar

[11] M. C. Morais, P. Wittenberg and C. J. Cruz, The np-chart with 3-σ limits and the ARL-unbiased np-chart revisited, Stoch. Qual. Control 37 (2022), no. 2, 107–116. 10.1515/eqc-2022-0032Suche in Google Scholar

[12] F. Pascual, EWMA charts for the weibull shape parameter, J. Qual. Technol. 42 (2010), no. 4, 400–416. 10.1080/00224065.2010.11917836Suche in Google Scholar

[13] S. Paulino, M. C. Morais and S. Knoth, On ARL-unbiased c-charts for INAR(1) Poisson counts, Statist. Papers 60 (2019), no. 4, 1021–1038. 10.1007/s00362-016-0861-9Suche in Google Scholar

[14] J. J. Pignatiello, Jr., C. A. Acosta-Mejía and B. V. Rao, The performance of control charts for monitoring process dispersion, 4th Industrial Engineering Research Conference Proceedings, Institute of Industrial Engineers, Peachtree Corners (1995), 320–328. Suche in Google Scholar

[15] A. C. Rakitzis, C. H. Weiß and P. Castagliola, Control charts for monitoring correlated counts with a finite range, Appl. Stoch. Models Bus. Ind. 33 (2017), no. 6, 733–749. 10.1002/asmb.2275Suche in Google Scholar

[16] I. Silva, Analysis of Discrete-valued Time Series: Some Contributions to Discrete-Valued Time Series, Lambert Academic, Saarbrücken, 2005. Suche in Google Scholar

[17] F. W. Steutel and K. van Harn, Discrete analogues of self-decomposability and stability, Ann. Probab. 7 (1979), no. 5, 893–899. 10.1214/aop/1176994950Suche in Google Scholar

[18] C. H. Weiß, Categorical time series analysis and applications in statistical quality control, PhD thesis, Universität Würzburg, 2009. Suche in Google Scholar

[19] C. H. Weiß, Jumps in binomial AR ⁢ ( 1 ) processes, Statist. Probab. Lett. 79 (2009), no. 19, 2012–2019. 10.1016/j.spl.2009.06.010Suche in Google Scholar

[20] C. H. Weiß, Monitoring correlated processes with binomial marginals, J. Appl. Stat. 36 (2009), no. 3–4, 399–414. 10.1080/02664760802468803Suche in Google Scholar

[21] C. H. Weiß, SPC methods for time-dependent processes of counts—a literature review, Cogent Math. 2 (2015), Art. ID 1111116. 10.1080/23311835.2015.1111116Suche in Google Scholar

[22] C. H. Weiß and H.-Y. Kim, Parameter estimation for binomial AR ⁢ ( 1 ) models with applications in finance and industry, Statist. Papers 54 (2013), no. 3, 563–590. 10.1007/s00362-012-0449-ySuche in Google Scholar

[23] C. H. Weiß and P. K. Pollett, Chain binomial models and binomial autoregressive processes, Biometrics 68 (2012), no. 3, 815–824. 10.1111/j.1541-0420.2011.01716.xSuche in Google Scholar PubMed

[24] C. H. Weiß and M. C. Testik, CUSUM monitoring of first-order integer-valued autoregressive processes of poisson counts, J. Qual. Technol. 41 (2009), no. 4, 389–400. 10.1080/00224065.2009.11917793Suche in Google Scholar

[25] ISO, ISO/IEC 14882:2011 Information technology — Programming languages — C++, International Organization for Standardization, Geneva, 2020. Suche in Google Scholar