Some theoretical comments regarding the run-length properties of the synthetic and runs-rules X¯ monitoring schemes – part 1: zero-state

References

• Antzoulakos, D. L., & Rakitzis, A. C. (2008). The modified r out of m control chart. Communications in Statistics – Simulation and Computation, 37(2), 396–408.10.1080/03610910701501906
   Web of Science ®Google Scholar
• Benneyan, J. C., Lloyd, R. C., & Plsek, P. E. (2003). Statistical process control as a tool for research and healthcare improvement. Quality and Safety in Health Care, 12(6), 458–464.10.1136/qhc.12.6.458
   PubMed Web of Science ®Google Scholar
• Bourke, P. D. (1991). Detecting a shift in fraction nonconforming using run-length control charts with 100% inspection. Journal of Quality Technology, 23(3), 225–238.
   Web of Science ®Google Scholar
• Chiu, W.-C., & Lu, S.-L. (2015). On the steady-state performance of the Poisson double GWMA control chart. Quality Technology & Quantitative Management, 12(2), 195–208.10.1080/16843703.2015.11673376
   Web of Science ®Google Scholar
• Chiu, W.-C., & Sheu, S.-H. (2008). Fast initial response features for Poisson GWMA control charts. Communications in Statistics – Simulation and Computation, 37(7), 1422–1439.10.1080/03610910801990033
   Web of Science ®Google Scholar
• Davis, R. B., & Woodall, W. H. (2002). Evaluating and improving the synthetic control chart. Journal of Quality Technology, 34(2), 200–208.
   Web of Science ®Google Scholar
• Derman, C., & Ross, S. M. (1997). Statistical aspects of quality control. San Diego, CA: Academic Press.
   Google Scholar
• Fu, J. C., & Lou, W. Y. W. (2003). Distribution theory of runs and patterns and its applications: A finite markov chain imbedding approach. Singapore: World Scientific.10.1142/4669
   Google Scholar
• Haq, A., & Khoo, M. B. C. (2016). A new synthetic control chart for monitoring process mean using auxiliary information. Journal of Statistical Computation and Simulation, 86, 3068–3092.10.1080/00949655.2016.1150477
   Web of Science ®Google Scholar
• Haq, A., Brown, J., & Moltchanova, E. (2013). New synthetic EWMA and synthetic CUSUM control charts for monitoring the process mean. Quality and Reliability Engineering International, 32(1), 269–290.
   Google Scholar
• Huh, I. (2014). Optimal monitoring methods for univariate and multivariate EWMA control charts (Published PhD thesis). School of Graduate Studies McMaster University, Canada.
   Google Scholar
• Khoo, M. B. C. (2013). Recent developments on synthetic control charts. Proceedings of IEEE Symposium on Business, Engineering and Industrial Applications (ISBEIA) (pp. 460–465).
   Google Scholar
• Klein, M. (2000). Two alternatives to the Shewhart X¯ control chart. Journal of Quality Technology, 32(4), 427–431.
   Web of Science ®Google Scholar
• Knoth, S. (2016). The case against the use of synthetic control charts. Journal of Quality Technology, 48(2), 178–195.
   Web of Science ®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(2), 207–224.10.1007/s11009-007-9016-8
   Web of Science ®Google Scholar
• Machado, M. A. G., & Costa, A. F. B. (2014). Some comments regarding the synthetic chart. Communications in Statistics – Theory and Methods, 43(14), 2897–2906.10.1080/03610926.2012.683128
   Web of Science ®Google Scholar
• Machado, M. A. G., & Costa, A. F. B. (2014). A side-sensitive synthetic chart combined with an X¯ chart. International Journal of Production Research, 52(11), 3404–3416.10.1080/00207543.2013.879221
   Web of Science ®Google Scholar
• Montgomery, D. C. (2013). Statistical quality control: A modern introduction (7th ed.). Singapore: Wiley.
   Google Scholar
• Polunchenko, A. S. (2016). A note on efficient performance evaluation of the Cumulative Sum chart and the Sequential Probability Ratio Test. Applied Stochastic Models in Business and Industry, 32(5), 565–573.
   Google Scholar
• Qiu, P. (2014). Introduction to statistical process control. Taylor & Francis Group.
   Google Scholar
• Reynolds, M. R., Jr, & Lou, J. (2010). An evaluation of a GLR control chart for monitoring the process mean. Journal of Quality Technology, 42(3), 287–310.
   Web of Science ®Google Scholar
• Ryu, J.-H., Wan, H., & Kim, S. (2010). Optimal design of a CUSUM chart for a mean shift of unknown size. Journal of Quality Technology, 42(3), 311–326.
   Web of Science ®Google Scholar
• Scariano, S. M., & Calzada, M. E. (2009). The generalized synthetic chart. Sequential Analysis, 28(1), 54–68.10.1080/07474940802619261
   Google Scholar
• Shongwe, S. C., & Graham, M. A. (2017). A modified side-sensitive synthetic chart to monitor the process mean. Quality Technology and Quantitative Management, 1–26. doi:10.1080/16843703.2016.1208939
   Google Scholar
• Wisner, P. S. (2009). Statistical process control for quality improvement finance: The ultimate resource. Bloomsbury Press.
   Google Scholar
• Woodall (1986). Weaknesses of the economical design of control charts. Technometrics, 28, 408–409.
   Web of Science ®Google Scholar
• Wu, Z., & Spedding, T. A. (2000). A synthetic control chart for detecting small shifts in the process mean. Journal of Quality Technology, 32(1), 32–38.
   Web of Science ®Google Scholar
• Zhang, S., & Wu, Z. (2005). Designs of control charts with supplementary runs rules. Computers & Industrial Engineering, 49(1), 76–97.10.1016/j.cie.2005.02.002
   Web of Science ®Google Scholar