One-sided precedence monitoring schemes for unknown shift sizes using generalized 2-of-(h+1) and w-of-w improved runs-rules

References

• Acosta-Mejia, C. A. 2007. Two sets of runs rules for the X¯ chart. Quality Engineering 19 (2):129–36. doi:10.1080/17513470701263641.
   Google Scholar
• Albers, W., and W. C. M. Kallenberg. 2008. Minimum control charts. Journal of Statistical Planning and Inference 138 (3):539–51. doi:10.1016/j.jspi.2006.10.004.
   Web of Science ®Google Scholar
• Antzoulakos, D. L., and A. C. Rakitzis. 2007. The revised m-of-k runs rule. Quality Engineering 20 (1):75–81. doi:10.1080/08982110701636401.
   Google Scholar
• Balakrishnan, N., C. Paroissin, and J. C. Turlot. 2015. One-sided control charts based on precedence and weighted precedence statistics. Quality and Reliability Engineering International 31 (1):113–34. doi:10.1002/qre.1750.
   Web of Science ®Google Scholar
• Balakrishnan, N., I. S. Triantafyllou, and M. V. Koutras. 2010. A distribution-free control chart based on order statistics. Communications in Statistics - Theory and Methods 39 (20):3652–77. doi:10.1080/03610920903324858.
   Web of Science ®Google Scholar
• Chakraborti, S., and M. A. Graham. 2019. Nonparametric (Distribution-free) control charts: An updated overview and some results. Quality Engineering 31 (4):523–44. doi:10.1080/08982112.2018.1549330.
   Web of Science ®Google Scholar
• Chakraborti, S., and M. A. Van de Wiel. 2008. A nonparametric control chart based on the Mann-Whitney statistic. IMS Collections. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of. Professor Pranab K. Sen 1:156–72. doi:10.1214/193940307000000112.
   Google Scholar
• Chakraborti, S., and S. Eryilmaz. 2007. A nonparametric Shewhart-type signed-rank control chart based on runs. Communications in Statistics - Simulation and Computation 36 (2):335–56. doi:10.1080/03610910601158427.
   Web of Science ®Google Scholar
• Chakraborti, S., P. Van der Laan, and M. A. Van de Wiel. 2004. A class of distribution-free control charts. Journal of the Royal Statistical Society. Series C: Applied Statistics 53 (3):443–62. doi:10.1111/j.1467-9876.2004.0d489.x.
   Web of Science ®Google Scholar
• Chakraborti, S., S. Eryilmaz, and S. W. Human. 2009. A phase II nonparametric control chart based on precedence statistics with runs-type signaling rules. Computational Statistics & Data Analysis 53 (4):1054–65. doi:10.1016/j.csda.2008.09.025.
   Web of Science ®Google Scholar
• Chakraborti, S., S. W. Human, and M. A. Graham. 2009. Phase I statistical process control charts: An overview and some results. Quality Engineering 21 (1):52–62. doi:10.1080/08982110802445561.
   Web of Science ®Google Scholar
• Chew, X. Y., K. W. Khaw, and W. C. Yeong. 2020. The efficiency of run rules schemes for the multivariate coefficient of variation: A Markov chain approach. Journal of Applied Statistics 47 (3):460–80. doi:10.1080/02664763.2019.1643296.
   PubMed Web of Science ®Google Scholar
• Fu, J. C., and W. Y. W. Lou. 2003. Distribution theory of runs and patterns and its applications: A finite Markov Chain imbedding approach. Singapore: World Scientific Publishing.
   Google Scholar
• Gibbons, J. D., and S. Chakraborti. 2003. Nonparametric statistical inference. 4th ed. New York: Marcel Dekker.
   Google Scholar
• Graham, M. A., A. Mukherjee, and S. Chakraborti. 2017. Design and implementation issues for a class of distribution-free Phase II EWMA exceedance control charts. International Journal of Production Research 55 (8):2397–430. doi:10.1080/00207543.2016.1249428.
   Web of Science ®Google Scholar
• Human, S. W., S. Chakraborti, and C. F. Smit. 2010. Nonparametric Shewhart-type sign control charts based on runs. Communications in Statistics - Theory and Methods 39 (11):2046–62. doi:10.1080/03610920902969018.
   Web of Science ®Google Scholar
• Jensen, W. A., L. A. Jones-Farmer, C. W. Champ, and W. H. Woodall. 2006. Effects of parameter estimation on control chart properties: A literature review. Journal of Quality Technology 38 (4):349–64. doi:10.1080/00224065.2006.11918623.
   Web of Science ®Google Scholar
• Jones-Farmer, L. A., W. H. Woodall, S. H. Steiner, and C. W. Champ. 2014. An overview of phase I analysis for process improvement and monitoring. Journal of Quality Technology 46 (3):265– 80. doi:10.1080/00224065.2014.11917969.
   Web of Science ®Google Scholar
• Khilare, S. K., and D. T. Shirke. 2010. A nonparametric synthetic control chart using sign statistic. Communications in Statistics - Theory and Methods 39 (18):3282–93. doi:10.1080/03610920903249576.
   Web of Science ®Google Scholar
• Khilare, S. K., and D. T. Shirke. 2015. Steady-state behavior of nonparametric control charts using sign statistic. Production 25 (4):739–49. doi:10.1590/0103-6513.113112.
   Google Scholar
• Khoo, M. B. C., and K. N. Ariffin. 2006. Two improved runs rules for Shewhart X¯ control chart. Quality Engineering 18 (2):173–8. doi:10.1080/08982110600567517.
   Google Scholar
• Knoth, S. 2016. The case against the use of synthetic control charts. Journal of Quality Technology 48 (2):178–95. doi:10.1080/00224065.2016.11918158.
   Web of Science ®Google Scholar
• Koutras, M. V., and I. S. Triantafyllou. 2018. A general class of nonparametric control charts. Quality and Reliability Engineering International 34 (3):427–35. doi:10.1002/qre.2263.
   Web of Science ®Google Scholar
• Kritzinger, P., S. W. Human, and S. Chakraborti. 2014. Improved Shewhart-type runs-rules nonparametric sign charts. Communications in Statistics - Theory and Methods 43 (22):4723–48. doi:10.1080/03610926.2012.729637.
   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. doi:10.1080/00949655.2013.766737.
   Web of Science ®Google Scholar
• Machado, M. A. G., and A. F. B. Costa. 2014. A side-sensitive synthetic chart combined with an X¯ chart. International Journal of Production Research 52 (11):3404–16. doi:10.1080/00207543.2013.879221.
   Web of Science ®Google Scholar
• Malela-Majika, J. C., and E. M. Rapoo. 2017. Distribution-free synthetic and runs-rules control charts combined with a Mann-Whitney chart. International Journal of Quality Engineering and Technology 6 (4):219–48. doi:10.1504/IJQET.2017.094305.
   Google Scholar
• Malela-Majika, J. C., E. M. Rapoo, A. Mukherjee, and M. A. Graham. 2019. Distribution-free precedence schemes with a generalized runs-rule for monitoring unknown location. Communications in Statistics - Theory and Methods. Advance online publication. doi:10.1080/03610926.2019.1612914.
   Google Scholar
• Malela-Majika, J. C., S. Chakraborti, and M. A. Graham. 2016a. Distribution-free Phase II Mann-Whitney control charts with runs-rules. The International Journal of Advanced Manufacturing Technology 86 (1–4):723–35. doi:10.1007/s00170-015-8083-1.
   Web of Science ®Google Scholar
• Malela-Majika, J. C., S. Chakraborti, and M. A. Graham. 2016b. Distribution-free precedence control charts with improved runs-rules. Applied Stochastic Models in Business and Industry 32 (4):423–39. doi:10.1002/asmb.2159.
   Web of Science ®Google Scholar
• Malela-Majika, J.-C., S. K. Malandala, and M. A. Graham. 2018. Shewhart control schemes with supplementary 2-of-(h + 1) side-sensitive runs-rules under the Burr-type XII distribution. Quality and Reliability Engineering International 34 (8):1800–17. doi:10.1002/qre.2373.
   Web of Science ®Google Scholar
• Mehmood, R., M. H. Lee, S. Hussain, and M. Riaz. 2019. On efficient construction and evaluation of runs rules based X¯ control chart for known and unknown parameters under different distributions. Quality and Reliability Engineering International 35 (2):582–99. doi:10.1002/qre.2423.
   Web of Science ®Google Scholar
• Montgomery, D. C. 2005. Introduction to statistical quality control. 5th ed. New York: Wiley.
   Google Scholar
• Patil, S. H., and D. T. Shirke. 2017. Economic design of nonparametric sign control chart. Communications in Statistics - Theory and Methods 46 (18):8987–98. doi:10.1080/03610926.2016.1200095.
   Web of Science ®Google Scholar
• Pawar, V. Y., D. T. Shirke, and S. K. Khilare. 2018. Nonparametric moving average control charts using sign and signed-rank statistics. International Journal of Scientific Research in Mathematical and Statistical Sciences 5 (4):171–8. doi:10.26438/ijsrmss/v5i4.171178.
   Google Scholar
• Psarakis, S., A. K. Vyniou, and P. Castagliola. 2014. Some recent developments on the effects of parameter estimation on control charts. Quality and Reliability Engineering International 30 (8):1113–29. doi:10.1002/qre.1556.
   Web of Science ®Google Scholar
• Qiu, P. 2014. Introduction to statistical process control. Boca Raton, FL: CRC Press, Taylor & Francis Group, A Chapman & Hall Book.
   Google Scholar
• Rakitzis, A. C., S. Chakraborti, S. C. Shongwe, M. A. Graham, and M. B. C. Khoo. 2019. An overview of synthetic-type control charts: Techniques and Methodology. Quality and Reliability Engineering International 35 (7):2081–96. doi:10.1002/qre.2491.
   Web of Science ®Google Scholar
• Reynolds, M. R., Jr, and L. Lou. 2010. An evaluation of GLR control chart combined with an X¯ chart. Journal of Quality Technology 42 (3):287–310. doi:10.1080/00224065.2010.11917825.
   Web of Science ®Google Scholar
• Shongwe, S. C. 2020. On the design of nonparametric runs-rules schemes using the Markov chain approach. Quality and Reliability Engineering International 36 (5):1604–21. doi:10.1002/qre.2648.
   Web of Science ®Google Scholar
• Shongwe, S. C., and M. A. Graham. 2016. On the performance of Shewhart-type synthetic and runs-rules charts combined with an X¯ chart. Quality and Reliability Engineering International 32 (4):1357–79. doi:10.1002/qre.1836.
   Web of Science ®Google Scholar
• Shongwe, S. C., J. C. Malela-Majika, and E. M. Rapoo. 2019. One-sided and two-sided w-of-w runs-rules schemes: An overall performance perspective and the unified run-length derivations. Journal of Probability and Statistics 2019:1–20. doi:10.1155/2019/6187060.
   Web of Science ®Google Scholar
• Shongwe, S. C., J. C. Malela-Majika, and T. Molahloe. 2019. One-sided runs-rules schemes to monitor autocorrelated time series data using a first-order autoregressive model with skip sampling strategies. Quality and Reliability Engineering International 35 (6):1973–97. doi:10.1002/qre.2487.
   Web of Science ®Google Scholar
• Tran, K. P., P. Castagliola, and N. Balakrishnan. 2017. On the performance of Shewhart median chart in the presence of measurement errors. Quality and Reliability Engineering International 33 (5):1019–29. doi:10.1002/qre.2087.
   Web of Science ®Google Scholar
• Triantafyllou, I. S. 2018. Nonparametric control charts based on order statistic: Some advances. Communications in Statistics - Simulation and Computation 47 (9):2684–702. doi:10.1080/03610918.2017.1359283.
   Web of Science ®Google Scholar
• Triantafyllou, I. S. 2019. A new distribution-free control scheme based on order statistics. Journal of Nonparametric Statistics 31 (1):1–30. doi:10.1080/10485252.2018.1518524.
   Web of Science ®Google Scholar
• Triantafyllou, I. S. 2020. Simulation-based comparative analysis of nonparametric control charts with runs-type rules. In Control Charts [Working Title]. London: IntechOpen. doi:10.5772/intechopen.91040.
   Google Scholar
• Wu, Z., M. Yang, W. Jiang, and M. B. C. Khoo. 2008. Optimisation designs of the combined Shewhart-CUSUM control charts. Computational Statistics & Data Analysis 53 (2):496–506. doi:10.1016/j.csda.2008.08.032.
   Web of Science ®Google Scholar