A new exponentially weighted moving average control chart to monitor count data with applications in healthcare and manufacturing

References

• Weiß C. An introduction to discrete-valued time series. Hoboken (NJ): John Wiley & Sons; 2018.
   Google Scholar
• Coxe S, West SG, Aiken LS. The analysis of count data: a gentle introduction to Poisson regression and its alternatives. J Pers Assess 2009;91(2):121–136. DOI:10.1080/00223890802634175
   PubMed Web of Science ®Google Scholar
• Sim SZ, Gupta RC, Ong SH. Zero-inflated Conway-Maxwell Poisson distribution to analyze discrete data. Int J Biostat 2018;14(1):1–12. DOI:10.1515/ijb-2016-0070
   Google Scholar
• Montgomery DC. Introduction to statistical quality control. Hoboken (NJ): Wiley; 2013.
   Google Scholar
• Lucas JM. Counted data Cusum’s. Technometrics. 1985;27(2):129–144. DOI:10.1080/00401706.1985.10488030
   Web of Science ®Google Scholar
• Gan FF. Monitoring Poisson observations using modified exponentially weighted moving average control charts. Commun Stat Simul Comput 1990;19(1):103–124. DOI:10.1080/03610919008812847
   Web of Science ®Google Scholar
• Kaminsky FC, Benneyan JC, Davis RD, et al. Statistical control charts based on a geometric distribution. J Qual Technol 1992;24(2):63–69. DOI:10.1080/00224065.1992.12015229
   Web of Science ®Google Scholar
• Famoye F. Statistical control charts for shifted generalized Poisson distribution. J Ital Stat Soc. 1994;3(3):339–354. DOI:10.1007/BF02589023
   Google Scholar
• Shen X, Zou C, Jiang W, et al. Monitoring poisson count data with probability control limits when sample sizes are time varying. Nav Res Logist 2013;60(8):625–636. DOI:10.1002/nav.21557
   Web of Science ®Google Scholar
• Urbieta P, Lee L, Alencar A. Cusum and EWMA control charts for negative binomial distribution. Qual Reliab Eng Int 2017;33(4):793–801. DOI:10.1002/qre.2057
   Web of Science ®Google Scholar
• Alencar AP, Ho LL, Albarracin OYE. CUSUM control charts to monitor series of Negative Binomial count data. Stat Methods Med Res 2017;26(4):1925–1935. DOI:10.1177/0962280215592427
   PubMed Web of Science ®Google Scholar
• Boaventura LL, Ferreira PH, Fiaccone RL. New statistical process control charts for overdispersed count data based on the Bell distribution; 2020.
   Google Scholar
• Bourguignon M, Medeiros RMR, Fernandes FH, et al. Simple and useful statistical control charts for monitoring count data. Qual Reliab Eng Int 2021;37(2):541–566. DOI:10.1002/qre.2748
   Web of Science ®Google Scholar
• Sellers KF. A generalized statistical control chart for over- or under-dispersed data. Qual Reliab Eng Int 2012;28(1):59–65. DOI:10.1002/qre.1215
   Web of Science ®Google Scholar
• Saghir A, Lin Z, Abbasi SA, et al. The use of probability limits of COM-poisson charts and their applications. Qual Reliab Eng Int 2013;29(5):759–770. DOI:10.1002/qre.1426
   Web of Science ®Google Scholar
• Saghir A, Lin Z. A flexible and generalized exponentially weighted moving average control chart for count data. Qual Reliab Eng Int 2014;30(8):1427–1443. DOI:10.1002/qre.1564
   Web of Science ®Google Scholar
• Aslam M, Saghir A, Ahmad L, et al. A control chart for COM-Poisson distribution using a modified EWMA statistic. J Stat Comput Simul 2017;87(18):3491–3502. DOI:10.1080/00949655.2017.1373114
   Web of Science ®Google Scholar
• Saghir A, Lin Z. Cumulative sum charts for monitoring the COM-Poisson processes. Comput Ind Eng 2014;68(1):65–77. DOI:10.1016/j.cie.2013.12.004
   Web of Science ®Google Scholar
• Aslam M, Ahmad L, Jun CH, et al. A control chart for COM–poisson distribution using multiple dependent state sampling. Qual Reliab Eng Int 2016;32(8):2803–2812. DOI:10.1002/qre.1965
   Web of Science ®Google Scholar
• Aslam M, Al-Marshadi AH. Design of a control chart based on COM-poisson distribution for the uncertainty environment. Complexity. 2019;2019. DOI:10.1155/2019/8178067
   PubMed Web of Science ®Google Scholar
• Rao GS, Aslam M, Rasheed U, et al. Mixed EWMA–CUSUM chart for COM-Poisson distribution. J Stat Manag Syst 2020;23(3):511–527. DOI:10.1080/09720510.2019.1639947
   Web of Science ®Google Scholar
• Adeoti OA, Malela-Majika JC, Shongwe SC, et al. A homogeneously weighted moving average control chart for Conway–Maxwell Poisson distribution. J Appl Stat 2022;49(12):3090–3119. DOI:10.1080/02664763.2021.1937582
   PubMed Web of Science ®Google Scholar
• Alevizakos V, Koukouvinos C. A progressive mean control chart for COM-Poisson distribution. Commun Stat Simul Comput 2022;51(3):849–867. DOI:10.1080/03610918.2019.1659361
   Web of Science ®Google Scholar
• Xie M, He B, Goh TN. Zero-inflated poisson model in statistical process control. Comput Stat Data Anal 2001;38(2):191–201. DOI:10.1016/S0167-9473(01)00033-0
   Web of Science ®Google Scholar
• He H, Tang W, Wang W, et al. Structural zeroes and zero-inflated models. Shanghai Arch Psychiatry. 2014;26(4):236–242. DOI:10.3969/j.issn.1002-0829.2014.04.008
   PubMedGoogle Scholar
• Chen N, Zhou S, Chang TS, et al. Attribute control charts using generalized zero-inflated poisson distribution. Qual Reliab Eng Int 2008;24(7):793–806. DOI:10.1002/qre.928
   Web of Science ®Google Scholar
• Fatahi AA, Noorossana R, Dokouhaki P, et al. Zero inflated Poisson EWMA control chart for monitoring rare health-related events. J Mech Med Biol 2012;12(4):1–14. DOI:10.1142/S0219519412500650
   Web of Science ®Google Scholar
• Chananet C, Sukparungsee S, Areepong Y. The ARL of EWMA chart for monitoring ZINB model using Markov chain approach. Int J Appl Phys Math. 2014;4(4):236–239. DOI:10.7763/IJAPM.2014.V4.290
   Google Scholar
• Alevizakos V, Koukouvinos C. Monitoring of zero-inflated binomial processes with a DEWMA control chart. J Appl Stat 2021;48(0):1319–1338. DOI:10.1080/02664763.2020.1761950
   PubMed Web of Science ®Google Scholar
• Alevizakos V, Koukouvinos C. Monitoring of zero-inflated Poisson processes with EWMA and DEWMA control charts. Qual Reliab Eng Int 2020;36(1):88–111. DOI:10.1002/qre.2561
   Web of Science ®Google Scholar
• Gupta RC, Ong SH. Analysis of long-tailed count data by Poisson mixtures. Commun Stat Theory Methods. 2005;34(3):557–573. DOI:10.1081/STA-200052144
   Web of Science ®Google Scholar
• Green JA. Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression. Heal Psychol Behav Med. 2021;9(1):436–455. DOI:10.1080/21642850.2021.1920416
   PubMed Web of Science ®Google Scholar
• Faddy MJ, Pettitt AN. Comparisons of statistical distributions for cluster sizes in a developing pandemic. BMC Med Res Methodol 2022;22(1):1–7. DOI:10.1186/s12874-022-01517-9
   PubMed Web of Science ®Google Scholar
• Imoto T. A generalized Conway-Maxwell-Poisson distribution which includes the negative binomial distribution. Appl Math Comput 2014;247:824–834. DOI:10.1016/j.amc.2014.09.052
   Web of Science ®Google Scholar
• Borror CM, Champ CW, Rigdon SE. Poisson EWMA control charts. J Qual Technol 1998;30(4):352–361. DOI:10.1080/00224065.1998.11979871
   Web of Science ®Google Scholar
• Somerville SE, Montgomery DC, Runger GC. Filtering and smoothing methods for mixed particle count distributions. Int J Prod Res 2002;40(13):2991–3013. DOI:10.1080/00207540210140040
   Web of Science ®Google Scholar
• Schaffer JR, Kim MJ. Number of replications required in control chart Monte Carlo simulation studies. Commun Stat Simul Comput 2007;36(5):1075–1087. DOI:10.1080/03610910701539963
   Web of Science ®Google Scholar
• R Core Team. R: a language and environment for statistical computing. [Online]. Available: https://www.r-project.org/
   Google Scholar
• Chan LK, Zhang J. Some issues in the design of EWMA charts. Commun Stat Part B Simul Comput. 2000;29(1):201–217. DOI:10.1080/03610910008813610
   Web of Science ®Google Scholar
• Feng CX. A comparison of zero-inflated and hurdle models for modeling zero-inflated count data. J Stat Distrib Appl 2021;8(1). DOI:10.1186/s40488-021-00121-4
   PubMedGoogle Scholar
• Lord D, Washington S, Ivan JN. Further notes on the application of zero-inflated models in highway safety. Accid Anal Prev 2007;39(1):53–57. DOI:10.1016/j.aap.2006.06.004
   PubMed Web of Science ®Google Scholar
• Campbell H. The consequences of checking for zero-inflation and overdispersion in the analysis of count data. Methods Ecol Evol. 2021;12(4):665–680. DOI:10.1111/2041-210X.13559
   Web of Science ®Google Scholar
• Perla RJ, Provost SM, Little K, et al. Understanding variation in reported covid-19 deaths with a novel Shewhart chart application. Int J Qual Health Care. 2021;33(June 2020):1–8. DOI:10.1093/intqhc/mzaa069
   PubMed Web of Science ®Google Scholar
• He S, Huang W, Woodall WH. CUSUM charts for monitoring a zero-inflated poisson process. Qual Reliab Eng Int 2012;28(2):181–192. DOI:10.1002/qre.1228
   Web of Science ®Google Scholar
• Turner H, Murdoch D, Firth D, et al. Package ‘vcdExtra’; 2021.
   Google Scholar