Design and properties of the predictive ratio cusum (PRC) control charts

References

• Al Labadi, L., and M. Evans. 2017. Optimal robustness results for relative belief inferences and the relationship to prior-data conflict. Bayesian Analysis 12 (3):705–28. doi: 10.1214/16-BA1024.
   Web of Science ®Google Scholar
• Berger, J. O., J. M. Bernardo, and D. Sun. 2009. The formal definition of reference priors. Annals of Statistics 37:905–38.
   Web of Science ®Google Scholar
• Bernardo, J. M. 1979. Reference posterior distributions for Bayesian inference. Journal of the Royal Statistical Society Series B (Methodological) 41 (2):113–28. doi: 10.1111/j.2517-6161.1979.tb01066.x.
   Web of Science ®Google Scholar
• Bourazas, K., F. Sobas, and P. Tsiamyrtzis. 2023. Predictive Ratio Cusum (PRC): A Bayesian approach in online change point detection of short runs. Journal of Quality Technology, online advance. doi: 10.1080/00224065.2022.2161434.
   Web of Science ®Google Scholar
• Bousquet, N. 2008. Diagnostics of prior-data agreement in applied Bayesian analysis. Journal of Applied Statistics 35 (9):1011–29. doi: 10.1080/02664760802192981.
   Web of Science ®Google Scholar
• Brook, D., and D. A. Evans. 1972. An approach to the probability distribution of CUSUM run length. Biometrika 59 (3):539–49. doi: 10.1093/biomet/59.3.539.
   Web of Science ®Google Scholar
• Deming, W. E. 1986. Out of Crisis. Cambridge, MA: The MIT Press.
   Google Scholar
• Dong, Y., A. S. Hedayat, and B. K. Sinha. 2008. Surveillance strategies for detecting change point in incidence rate based on exponentially weighted moving average methods. Journal of the American Statistical Association 103 (482):843–53. doi: 10.1198/016214508000000166.
   Web of Science ®Google Scholar
• Dunn, O. J. 1961. Multiple comparisons among means. Journal of the American Statistical Association 56 (293):52–64. doi: 10.1080/01621459.1961.10482090.
   Web of Science ®Google Scholar
• Egidi, L., F. Pauli, and N. Torelli. 2022. Avoiding prior-data conflict in regression models via mixture priors. Canadian Journal of Statistics 50 (2):491–510. doi: 10.1002/cjs.11637.
   Web of Science ®Google Scholar
• Evans, M., and G. H. Jang. 2011. Weak informativity and the information in one prior relative to another. Statistical Science 26 (3):423–39. doi: 10.1214/11-STS357.
   Web of Science ®Google Scholar
• Evans, M., and H. Moshonov. 2006. Checking for prior-data conflict. Bayesian Analysis 1 (4):893–914. doi: 10.1214/06-BA129.
   Web of Science ®Google Scholar
• Frisén, M. 1992. Evaluations of methods for statistical surveillance. Statistics in Medicine 11 (11):1489–502. doi: 10.1002/sim.4780111107.
   PubMed Web of Science ®Google Scholar
• Hawkins, D. M. 1987. Self-starting CUSUM charts for location and scale. The Statistician 36 (4):299–315. doi: 10.2307/2348827.
   Google Scholar
• Hawkins, D. M., and D. H. Olwell. 1998. Cumulative Sum Charts and Charting for Quality Improvement. New York, NY: Springer-Verlag.
   Google Scholar
• Huang, W., M. R. Reynolds, Jr, and S. Wang. 2012. A binomial GLR control chart for monitoring a proportion. Journal of Quality Technology 44 (3):192–208. doi: 10.1080/00224065.2012.11917895.
   Web of Science ®Google Scholar
• Ibrahim, J., and M. Chen. 2000. Power prior distributions for regression models. Statistical Science 15:46–60.
   Web of Science ®Google Scholar
• Jeffreys, H. 1961. Theory of Probability. 3rd ed. Oxford, UK: Oxford University Press.
   Google Scholar
• Kass, R. E., and A. E. Raftery. 1995. Bayes factors. Journal of the American Statistical Association 90 (430):773–95. doi: 10.1080/01621459.1995.10476572.
   Web of Science ®Google Scholar
• Keefe, M. J., W. H. Woodall, and L. A. Jones-Farmer. 2015. The conditional in-control performance of self-starting control charts. Quality Engineering 27 (4):488–99. doi: 10.1080/08982112.2015.1065323.
   Web of Science ®Google Scholar
• Kenett, R. S., and M. Pollak. 2012. On assessing the performance of sequential procedures for detecting a change. Quality and Reliability Engineering International 28 (5):500–7. doi: 10.1002/qre.1436.
   Web of Science ®Google Scholar
• Li, Z., C. Zou, Z. Gong, and Z. Wang. 2014. The computation of average run length and average time to signal: An overview. Journal of Statistical Computation and Simulation 84, 8:1779–802.
   Web of Science ®Google Scholar
• Lucas, J. M., and R. B. Crosier. 1982. Fast initial response for CUSUM quality-control schemes: Give your CUSUM a head start. Technometrics 24 (3):199–205. doi: 10.1080/00401706.1982.10487759.
   Web of Science ®Google Scholar
• Montgomery, D. C. 2009. Introduction to Statistical Quality Control. 6th ed. New York, NY: Wiley.
   Google Scholar
• Moustakides, G. V. 1986. Optimal stopping times for detecting changes in distributions. Annals of Statistics 14 (4):1379–87.
   Web of Science ®Google Scholar
• Pruett, J. M., and H. Schneider. 1993. Essentials of SPC in the Process Industries. Research Triangle Park, NC: Instrument Society of America.
   Google Scholar
• Quesenberry, C. P. 1991. SPC Q Charts for start-up processes and short or long runs. Journal of Quality Technology 23 (3):213–24. doi: 10.1080/00224065.1991.11979327.
   Web of Science ®Google Scholar
• Ritov, Y. A. 1990. Decision theoretic optimality of the CUSUM procedure. The Annals of Statistics 18 (3):1464–9.
   Web of Science ®Google Scholar
• Ryan, A. G., and W. H. Woodall. 2010. Control charts for poisson count data with varying sample sizes. Journal of Quality Technology 42 (3):260–75. doi: 10.1080/00224065.2010.11917823.
   Web of Science ®Google Scholar
• Steiner, S. H. 1999. EWMA control charts with time-varying control limits and fast initial response. Journal of Quality Technology 31 (1):75–86. doi: 10.1080/00224065.1999.11979899.
   Web of Science ®Google Scholar
• West, M. 1986. “ Bayesian model monitoring. Journal of the Royal Statistical Society: Series B (Methodological) 48 (1):70–8.
   Google Scholar
• West, M., and P. J. Harrison. 1986. Monitoring and adaptation in Bayesian forecasting models. Journal of the American Statistical Association 81 (395):741–50. doi: 10.1080/01621459.1986.10478331.
   Web of Science ®Google Scholar
• Zantek, P. F. 2005. Run-length distributions of Q-chart schemes. IIE Transactions 37 (11):1037–45. doi: 10.1080/07408170500232297.
   Web of Science ®Google Scholar
• Zantek, P. F. 2006. Design of cumulative sum schemes for start-up processes and short runs. Journal of Quality Technology 38 (4):365–75. doi: 10.1080/00224065.2006.11918624.
   Web of Science ®Google Scholar
• Zantek, P. F. 2008. A Markov-chain method for computing the run-length distribution of the self-starting cumulative sum scheme. Journal of Statistical Computation and Simulation 78 (5):463–73. doi: 10.1080/00949650601146562.
   Web of Science ®Google Scholar
• Zantek, P. F., and S. T. Nestler. 2009. Performance and properties of Q-Statistic monitoring schemes. Naval Research Logistics (NRL) 56 (3):279–92. doi: 10.1002/nav.20330.
   Web of Science ®Google Scholar