A study on the g and h control charts

References

• Abramowitz, M., and I. A. Stegun. 1964. Handbook of mathematical functions: With formulas, graphs, and mathematical tables. Vol. 55. Washington, DC: National Bureau of Standards Applied Mathematics Series. U.S. Government Printing Office.
   Google Scholar
• Benneyan, J. C. 1999. Geometric-based g-type statistical control charts for infrequent adverse events. In Institute of Industrial Engineers Society for Health Systems Conference Proceeding, 175–85.
   Google Scholar
• Benneyan, J. C. 2001a. Number-between g-type statistical quality control charts for monitoring adverse events. Health Care Management Science 4 (4):305–18. doi:10.1023/a:1011846412909.
   PubMedGoogle Scholar
• Benneyan, J. C. 2001b. Performance of number-between g-type statistical control charts for monitoring adverse events. Health Care Management Science 4 (4):319–36.
   PubMedGoogle Scholar
• Blackwell, D. 1947. Conditional expectation and unbiased sequential estimation. The Annals of Mathematical Statistics 18 (1):105–10. doi:10.1214/aoms/1177730497.
   Google Scholar
• Casella, G., and R. L. Berger. 2002. Statistical inference, 2nd ed. Pacific Grove, CA: Duxbury.
   Google Scholar
• Driver, K. A., and S. J. Johnston. 2006. An integral representation of some hypergeometric functions. Electronic Transactions on Numerical Analysis 25:115–20.
   Web of Science ®Google Scholar
• Dutka, J. 1981. The incomplete beta function – a historical profile. Archive for History of Exact Sciences 24 (1):11–29. doi:10.1007/BF00327713.
   Web of Science ®Google Scholar
• Hankin, R. K. S. 2016. Hypergeo: The Gauss hypergeometric function. https://CRAN.R-project.org/package=hypergeo. R package version 1.2.13 (published on April 7, 2016).
   Google Scholar
• Hogg, R. V., J. W. McKean, and A. T. Craig. 2013. Introduction to mathematical statistics, 7 ed. Boston, MA: Pearson.
   Google Scholar
• Jacquez, G. M., L. A. Waller, R. Grimson, and D. Wartenberg. 1996. The analysis of disease clusters, Part I: State of the art. Infection Control and Hospital Epidemiology 17 (5):319–27. doi:10.2307/30141932.
   PubMed Web of Science ®Google Scholar
• Kaminsky, F. C., J. C. Benneyan, R. D. Davis, and R. J. Burke. 1992. Statistical control charts based on a geometric distribution. Journal of Quality Technology 24 (2):63–9. doi:10.1080/00224065.1992.12015229.
   Web of Science ®Google Scholar
• Lehmann, E. L., and G. Casella. 1998. Theory of point estimation, 2nd ed. New York: Springer-Verlag.
   Google Scholar
• Miller, A. R., and R. B. Paris. 2011. Euler-type transformations for the generalized hypergeometric function r+2fr+1(x). Zeitschrift Für Angewandte Mathematik Und Physik 62:31–45.
   Web of Science ®Google Scholar
• Minitab. 2018. Methods and formulas for g chart. Minitab 18 Support. Accessed November 4, 2021. https://support.minitab.com/en-us/minitab/20/
   Google Scholar
• Miyakawa, M. 1984. Analysis of incomplete data in competing risks model. IEEE Transactions on Reliability R-33 (4):293–6. doi:10.1109/TR.1984.5221828.
   Web of Science ®Google Scholar
• Montgomery, D. C. 2013. Statistical quality control: An modern introduction, 7th ed. Singapore: John Wiley & Sons.
   Google Scholar
• Özarslan, M., and C. Ustaoğlu. 2019. Some incomplete hypergeometric functions and incomplete riemann-liouville fractional integral operators. Mathematics 7 (5):483. doi:10.3390/math7050483.
   Web of Science ®Google Scholar
• Park, C. 2010. Parameter estimation for reliability of load sharing systems. IIE Transactions 42 (10):753–65. doi:10.1080/07408171003670991.
   Web of Science ®Google Scholar
• Park, C., L. Ouyang, and M. Wang. 2021. Robust g-type quality control charts for monitoring nonconformities. Computers & Industrial Engineering 162:107765. doi:10.1016/j.cie.2021.107765.
   Web of Science ®Google Scholar
• Park, C., and M. Wang. 2022. rQCC: Robust quality control chart. https://CRAN.R-project.org/package=rQCC. R package version 2.22.1 (published on January 25, 2022).
   Google Scholar
• Rainville, E. D. 1960. Special functions. New York: Macmillan.
   Google Scholar
• Rao, C. R. 1945. Information and accuracy attainable in the estimation of statistical parameters. Bulletin of the Calcutta Mathematical Society 37:81–91.
   Google Scholar
• Seaborn, J. B. 1991. Hypergeometric functions and their applications. New York: Springer.
   Google Scholar
• Vining, G. 2009. Technical advice: Phase I and Phase II control charts. Quality Engineering 21 (4):478–9. doi:10.1080/08982110903185736.
   Web of Science ®Google Scholar