Nonparametric (distribution-free) control charts: An updated overview and some results

References

• Amin, R. W., and O. Widmaier. 1999. Sign control charts with variable sampling intervals. Communications in Statistics: Theory and Methods 28 (8):1961–85. doi:10.1080/03610929908832398.
   Web of Science ®Google Scholar
• Amin, R. W., M. R. Reynolds, Jr., and S. T. Bakir. 1995. Nonparametric quality control charts based on the sign statistic. Communications in Statistics: Theory and Methods 24 (6):1597–623. doi:10.1080/03610929508831574.
   Web of Science ®Google Scholar
• Bakir, S. T. 2004. A distribution-free shewhart quality control chart based on signed-ranks. Quality Engineering 16 (4):613–23. doi:10.1081/QEN-120038022.
   Google Scholar
• Bakir, S. T. 2011. Distribution-free (nonparametric) quality control charts part I.
   Google Scholar
• Bakir, S. T., and M. R. Reynolds. Jr. 1979. A nonparametric procedure for process control based on within-group ranking. Technometrics 21 (2):175–83. doi:10.1080/00401706.1979.10489747.
   Web of Science ®Google Scholar
• Bell, R. C., L. A. Jones-Farmer, and N. Billor. 2014. A distribution-free multivariate phase I location control chart for subgrouped data from elliptical distributions. Technometrics 56 (4):528–38. doi:10.1080/00401706.2013.879264.
   Web of Science ®Google Scholar
• Benjamini, Y., and Y. Hochberg. 1995. Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B (Methodological ) 57 (1):289–300.
   Web of Science ®Google Scholar
• Bennett, B. M. 1964. Non-parametric test for randomness in a sequence of multinomial trials. Biometrics 20 (1):182–90. doi:10.2307/2527626.
   Web of Science ®Google Scholar
• Boone, J. M., and S. Chakraborti. 2012. Two simple shewhart-type multivariate nonparametric control charts. Applied Stochastic Models in Business and Industry 28 (2):130–40. doi:10.1002/asmb.900.
   Web of Science ®Google Scholar
• Capizzi, G., and G. Masarotto. 2013. Phase I distribution-free analysis of univariate data. Journal of Quality Technology 45 (3):273–84. doi:10.1080/00224065.2013.11917938.
   Web of Science ®Google Scholar
• Capizzi, G., and G. Masarotto. 2017. Phase I distribution-free analysis of multivariate data. Technometrics 57 (4):484–95. doi:10.1080/00401706.2016.1272494.
   Google Scholar
• Chakraborti, S., and M. A. Graham. 2007. Nonparametric control charts. In Encyclopedia of statistics in quality and reliability, Vol. 1, 415–429. New York: John Wiley.
   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.
   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 and 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
• Chakraborti, S., S. W. Human, and M. A. Graham. 2011. Nonparametric (distribution-free) quality control charts. In Handbook of methods and applications of statistics: Engineering, Quality control, and physical sciences, ed. N. Balakrishnan, 298–329. New York: John Wiley & Sons.
   Google Scholar
• Chakraborti, S., P. Qiu, and A. Mukherjee. 2015. Introduction to the special issue: Nonparametric statistical process control charts. Quality and Reliability Engineering International 31 (1):1–2. doi:10.1002/qre.1759.
   Web of Science ®Google Scholar
• Chakraborti, S., P. Van der Laan, and S. T. Bakir. 2001. Nonparametric control charts: An overview and some results. Journal of Quality Technology 33 (3):304–15. doi:10.1080/00224065.2001.11980081.
   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
• Chakraborty, N., S. Chakraborti, S. W. Human, and N. Balakrishnan. 2016. A generally weighted moving average signed-rank control chart. Quality and Reliability Engineering International 32 (8):2835–45. doi:10.1002/qre.1968.
   Web of Science ®Google Scholar
• Chen, N., X. Zi, and C. Zou. 2016. A distribution-free multivariate control chart. Technometrics 58 (4):448–59. doi:10.1080/00401706.2015.1049750.
   Web of Science ®Google Scholar
• Cheng, C.-R., and J.-J. H. Shiau. 2015. A distribution-free multivariate control chart for phase I applications. Quality and Reliability Engineering International 31 (1):97–111. doi:10.1002/qre.1751.
   Web of Science ®Google Scholar
• Choi, K., and J. Marden. 1997. An approach to multivariate rank tests in multivariate analysis of variance. Journal of the American Statistical Association 92 (440):1581–90. doi:10.1080/01621459.1997.10473680.
   Web of Science ®Google Scholar
• Chowdhury, S., A. Mukherjee, and S. Chakraborti. 2015. Distribution-free phase II CUSUM control chart for joint monitoring of location and scale. Quality and Reliability Engineering International 31 (1):135–51. doi:10.1002/qre.1677.
   Web of Science ®Google Scholar
• Coelho, M. L. I., M. A. Graham, and S. Chakraborti. 2017. Nonparametric signed-rank control charts with variable sampling intervals. Quality and Reliability Engineering International 33 (8):2181–92. doi:10.1002/qre.2177.
   Web of Science ®Google Scholar
• Dávila, D., S. Runger, G. Tuv. and E. 2014. Public health surveillance with ensemble-based supervised learning. IIE Transactions 46 (8):770–89. doi:10.1080/0740817X.2014.894806.
   Web of Science ®Google Scholar
• Das, N. 2008. Nonparametric control chart for controlling variability based on rank test. Economic Quality Control 23 (2):227–42.
   Google Scholar
• Das, N. 2009. A new multivariate nonparametric control chart based on the sign test. Quality Technology & Quantitative Management 6 (2):155–69. doi:10.1080/16843703.2009.11673191.
   Web of Science ®Google Scholar
• Deng, H., G. Runger, and E. Tuv. 2012. System monitoring with Real-Time contrasts. Journal of Quality Technology 44 (1):9–27. doi:10.1080/00224065.2012.11917878.
   Web of Science ®Google Scholar
• Dietz, E. J. 1982. Bivariate nonparametric tests for the one-sample location problem. Journal of the American Statistical Association 77 (377):163–9. doi:10.1080/01621459.1982.10477781.
   Web of Science ®Google Scholar
• Diko, M. D., S. Chakraborti, and M. A. Graham. 2016. Monitoring the process mean when standards are unknown: A classic problem revisited. Quality and Reliability Engineering International 32 (2):609–22. doi:10.1002/qre.1776.
   Web of Science ®Google Scholar
• Dovoedo, Y. H., and S. Chakraborti. 2017. Effects of parameter estimation on the multivariate distribution-free phase II sign EWMA chart. Quality and Reliability Engineering International 33 (2):431–49. doi:10.1002/qre.2019.
   Web of Science ®Google Scholar
• Ghute, V. B., and D. T. Shirke. 2012. A nonparametric signed-rank control chart for bivariate process location. Quality Technology & Quantitative Management 9 (4):317–28. doi:10.1080/16843703.2012.11673296.
   Web of Science ®Google Scholar
• Gibbons, J. D., and S. Chakraborti. 2010. Nonparametric statistical inference. 5th ed. Boca Raton, FL: Taylor and Francis.
   Google Scholar
• Graham, M. A., S. Chakraborti, and S. W. Human. 2011a. A nonparametric EWMA sign chart for location based on individual measurements. Quality Engineering 23 (3):227–41. doi:10.1080/08982112.2011.575745.
   Web of Science ®Google Scholar
• Graham, M. A., S. Chakraborti, and S. W. Human. 2011b. A nonparametric exponentially weighted moving average signed-rank chart for monitoring location. Computational Statistics and Data Analysis 55 (8):2490–503. doi:10.1016/j.csda.2011.02.013.
   Web of Science ®Google Scholar
• Graham, M. A., S. W. Human, and S. Chakraborti. 2010. A phase I nonparametric shewhart-type control chart based on the median. Journal of Applied Statistics 37 (11):1795–813. doi:10.1080/02664760903164913.
   Web of Science ®Google Scholar
• Graham, M. A., A. Mukherjee, and S. Chakraborti. 2012. Distribution-free exponentially weighted moving average control charts for monitoring unknown location. Computational Statistics and Data Analysis 56 (8):2539–61. doi:10.1016/j.csda.2012.02.010.
   Web of Science ®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
• Hamurkarouglu, C., M. Mert, and Y. Sayken. 2004. Nonparametric control charts based on mahalanobis depth. Hacettepe Journal of Mathematics and Statistics 33:57–67.
   Google Scholar
• Hawkins, D. M., and Q. Deng. 2010. A nonparametric change-point control chart. Journal of Quality Technology 42 (2):165–73. doi:10.1080/00224065.2010.11917814.
   Web of Science ®Google Scholar
• Hawkins, D. M., P. Qiu, and C. W. Kang. 2003. The changepoint model for statistical process control. Journal of Quality Technology 35 (4):355–66. doi:10.1080/00224065.2003.11980233.
   Web of Science ®Google Scholar
• Hayter, A. J., and K.-L. Tsui. 1994. Identification and quantification in multivariate quality control problems. Journal of Quality Technology 26(3):197–208. doi:10.1080/00224065.1994.11979526.
   Web of Science ®Google Scholar
• He, S., W. Jiang, and H. Deng. 2016. A distance-based control chart for monitoring multivariate processes using support vector machines. Annals of Operations Research 1–17.
   Web of Science ®Google Scholar
• Holland, M. D., and D. M. Hawkins. 2014. A control chart based on a nonparametric multivariate change-point model. Journal of Quality Technology 46 (1):63–77. doi:10.1080/00224065.2014.11917954.
   Web of Science ®Google Scholar
• Jensen, W. A., J. B. Birch, and W. H. Woodall. 2007. High breakdown estimation methods for phase I multivariate control charts. Quality and Reliability Engineering International 23 (5):615–29. doi:10.1002/qre.837.
   Web of Science ®Google Scholar
• Jang, S., S. H. Park, and J. G. Baek. 2017. Real-time contrasts control chart using random forests with weighted voting. Expert Systems with Applications 71:358–69. doi:10.1016/j.eswa.2016.12.002.
   Web of Science ®Google Scholar
• Jones-Farmer, L. A., V. Jordan, and C. W. Champ. 2009. Distribution-free phase I control charts for subgroup location. Journal of Quality Technology 41 (3):304–16. doi:10.1080/00224065.2009.11917784.
   Web of Science ®Google Scholar
• Jones-Farmer, L. A., and C. W. Champ. 2010. A distribution-free phase I control chart for subgroup scale. Journal of Quality Technology 42 (4):373–87. doi:10.1080/00224065.2010.11917834.
   Web of Science ®Google Scholar
• Jones-Farmer, L. A., W. H. Woodall, S. 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
• Kang, J. H., and S. B. Kim. 2013. A clustering algorithm-based control chart for inhomogeneously distributed TFT-LCD processes. International Journal of Production Research 51 (18):5644–5657. doi:10.1080/00207543.2013.793427.
   Google Scholar
• Kapatou, A., and M. R. Reynolds. Jr. 1994. Multivariate nonparametric control charts using small sample sizes. Proceedings of the Section on Quality and Productivity, American Statistical Association 241–6.
   Google Scholar
• Kapatou, A., and M. R. Reynolds. Jr. 1998. Multivariate nonparametric control charts for the case of known Σ. Proceedings of the Section on Quality and Productivity, American Statistical Association 77:82.
   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. 2012. Nonparametric synthetic control charts for process variation. Quality and Reliability Engineering International 28 (2):193–202. doi:10.1002/qre.1233.
   Web of Science ®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
• Lepage, Y. 1971. A combination of wilcoxon’s and Ansari-Bradley’s statistics. Biometrika 58 (1):213–7. doi:10.1093/biomet/58.1.213.
   Web of Science ®Google Scholar
• Li, J. 2015. Nonparametric multivariate statistical process control charts: a hypothesis testing-based approach. Journal of Nonparametric Statistics 27 (3):384–400. doi:10.1080/10485252.2015.1062889.
   Web of Science ®Google Scholar
• Li, Z., Y. Dai, and Z. Wang. 2014. Multivariate change point control chart based on data depth for phase I analysis. Communications in Statistics – Simulation and Computation 43 (6):1490–507. doi:10.1080/03610918.2012.735319.
   Web of Science ®Google Scholar
• Li, Z., C. Zou, Z. Wang, and L. Huwang. 2013. A multivariate sign chart for monitoring process shape parameters. Journal of Quality Technology 45 (2):149–65. doi:10.1080/00224065.2013.11917923.
   Web of Science ®Google Scholar
• Liang, W., D. Xiang, and X. Pu. 2016. A robust multivariate EWMA control chart for detecting sparse mean shifts. Journal of Quality Technology 48 (3):265–83. doi:10.1080/00224065.2016.11918166.
   Web of Science ®Google Scholar
• Liu, L.,. X. Zi, J. Zhang, and Z. Wang. 2013. A sequential rank-based nonparametric adaptive EWMA control chart. Communications in Statistics – Simulation and Computation 42 (4):841–59. doi:10.1080/03610918.2012.655829.
   Web of Science ®Google Scholar
• Liu, L.,. B. Chen, J. Zhang, and X. Zi. 2015. Adaptive phase II nonparametric EWMA control chart with variable sampling interval. Quality and Reliability Engineering International 31 (1):15–26. doi:10.1002/qre.1742.
   Web of Science ®Google Scholar
• Liu, L.,. J. Zhang, and X. Zi. 2015. Dual nonparametric CUSUM control chart based on ranks. Communications in Statistics - Simulation and Computation 44 (3):756–72. doi:10.1080/03610918.2013.784985.
   Web of Science ®Google Scholar
• Liu, R. 1995. Control charts for multivariate processes. Journal of the American Statistical Association 90 (432):1380–7. doi:10.1080/01621459.1995.10476643.
   Web of Science ®Google Scholar
• Lu, S.-L. 2015. An extended nonparametric exponentially weighted moving average sign control chart. Quality and Reliability Engineering International 31 (1):3–13. doi:10.1002/qre.1673.
   Web of Science ®Google Scholar
• Lucas, J. M., and M. S. Saccucci. 1990. Exponentially weighted moving average control schemes: Properties and enhancements. Technometrics 32 (1):1–12. doi:10.1080/00401706.1990.10484583.
   Web of Science ®Google Scholar
• Malela-Majika, J. C., S. Chakraborti, and M. A. Graham. 2016. 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
• McCracken, A. K., and S. Chakraborti. 2013. Control charts for joint monitoring of mean and variance: an overview. Quality Technology & Quantitative Management 10 (1):17–36. doi:10.1080/16843703.2013.11673306.
   Web of Science ®Google Scholar
• Mood, A. M. 1954. On the asymptotic efficiency of certain non-parametric two sample test. The Annals of Mathematical Statistics 25 (3):514–22. doi:10.1214/aoms/1177728719.
   Google Scholar
• Mukherjee, A., and S. Chakraborti. 2012. A distribution-free control chart for the joint monitoring of location and scale. Quality and Reliability Engineering International 28 (3):335–52. doi:10.1002/qre.1249.
   Web of Science ®Google Scholar
• Mukherjee, A., M. A. Graham, and S. Chakraborti. 2013. Distribution-free exceedance CUSUM control charts for location. Communications in Statistics – Simulation and Computation 42 (5):1153–87. doi:10.1080/03610918.2012.661638.
   Web of Science ®Google Scholar
• Park, J., and C. H. Jun. 2015. A new multivariate EWMA control chart via multiple testing. Journal of Process Control 26:51–5. doi:10.1016/j.jprocont.2015.01.007.
   Web of Science ®Google Scholar
• Pawar, V. Y., and D. T. Shirke. 2010. A nonparametric shewhart-type synthetic control chart. Communications in Statistics: Simulation and Computation 39 (8):1493–505. doi:10.1080/03610918.2010.503014.
   Web of Science ®Google Scholar
• Phaladiganon, P., S. B. Kim, V. C. Chen, J. G. Baek, and S. K. Park. 2011. Bootstrap-based T2 multivariate control charts. Communications in Statistics – Simulation and Computation 40 (5):645–62. doi:10.1080/03610918.2010.549989.
   Web of Science ®Google Scholar
• Psarakis, S. 2015. Adaptive control charts: Recent developments and extensions. Quality and Reliability Engineering International 31 (7):1265–80. doi:10.1002/qre.1850.
   Web of Science ®Google Scholar
• Puri, M. L., and P. K. Sen. 1976. Nonparametric methods in multivariate analysis. New York, NY: John Wiley & Sons Inc.
   Google Scholar
• Qiu, P. 2014. Introduction to statistical process control. Chapman and Hall.
   Google Scholar
• Qiu, P., and D. M. Hawkins. 2003. A nonparametric multivariate cumulative sum procedure for detecting shifts in all directions. Journal of the Royal Statistical Society: Series D (the Statistician) 52 (2):151–64. doi:10.1111/1467-9884.00348.
   Google Scholar
• Qiu, P. 2008. Distribution-free multivariate process control based on log-linear modeling. IIE Transactions 40 (7):664–77. doi:10.1080/07408170701744843.
   Web of Science ®Google Scholar
• Randles, R. H. 2000. A simpler, affine-invariant, multivariate, distribution-free test. Journal of the American Statistical Association 95 (452):1263–8. doi:10.2307/2669766.
   Web of Science ®Google Scholar
• Reynolds, M. R., Jr., R. W. Amin, J. C. Arnold, and J. A. Nachlas. 1988. Charts with variable sampling intervals. Technometrics 30 (2):181–92. doi:10.1080/00401706.1988.10488366.
   Web of Science ®Google Scholar
• Ross, G. J., and N. M. Adams. 2012. Two nonparametric control charts for detecting arbitrary distribution changes. Journal of Quality Technology 44 (2):102–16. doi:10.1080/00224065.2012.11917887.
   Web of Science ®Google Scholar
• Ross, G. J., D. K. Tasoulis, and N. M. Adams. 2011. Nonparametric monitoring of data streams for changes in location and scale. Technometrics 53 (4):379–89. doi:10.1198/TECH.2011.10069.
   Web of Science ®Google Scholar
• Siegel, S., and J. W. Tukey. 1960. Nonparametric sum of ranks procedure for relative spread in unpaired samples. Journal of the American Statistical Association 55 (291):429–45. doi:10.2307/2281906.
   Web of Science ®Google Scholar
• Sheu, S.-H., and T.-C. Lin. 2003. The generally weighted moving average control chart for detecting small shifts in the process mean. Quality Engineering 16 (2):209–31. doi:10.1081/QEN-120024009.
   Google Scholar
• Sullivan, J. H., and W. H. Woodall. 1996. A comparison of multivariate control charts for individual observations. Journal of Quality Technology 28 (4):398–408. doi:10.1080/00224065.1996.11979698.
   Web of Science ®Google Scholar
• Sullivan, J. H., and W. H. Woodall. 2000. Change-point detection of mean vector or covariance matrix shifts using multivariate individual observations. IIE Transactions – Quality and Reliability Engineering 32 (6):537–49. doi:10.1080/07408170008963929.
   Web of Science ®Google Scholar
• Wei, Q., W. Huang, W. Jiang, and W. Zhao. 2016. Real-time process monitoring using kernel distances. International Journal of Production Research 54 (21):6563–78. doi:10.1080/00207543.2016.1173257.
   Web of Science ®Google Scholar
• Western Electronic Company 1956. Statistical quality control handbook. Indianapolis, IN: Western Electric Corporation.
   Google Scholar
• Woodall, W. H., and D. C. Montgomery. 2014. Some current directions in the theory and application of statistical process monitoring. Journal of Quality Technology 46 (1):78–94. doi:10.1080/00224065.2014.11917955.
   Web of Science ®Google Scholar
• Wu, Z., and T. A. Spedding. 2000. A synthetic control chart for detecting small shifts in the process mean. Journal of Quality Technology 32 (1):32–8. doi:10.1080/00224065.2000.11979969.
   Web of Science ®Google Scholar
• Zhang, C., F. Tsung, and C. Zou. 2015. A general framework for monitoring complex processes with both in-control and out-of-control information. Computers & Industrial Engineering 85:157–68. doi:10.1016/j.cie.2015.03.007.
   Web of Science ®Google Scholar
• Zi, X., C. Zou, Q. Zhou, and J. Wang. 2013. A directional multivariate sign EWMA control chart. Quality Technology & Quantitative Management 10 (1):115–32. doi:10.1080/16843703.2013.11673311.
   Web of Science ®Google Scholar
• Zou, C., and P. Qiu. 2009. Multivariate statistical process control using LASSO. Journal of the American Statistical Association 104(488):1586–96. doi:10.1198/jasa.2009.tm08128.
   Web of Science ®Google Scholar
• Zou, C., and F. Tsung. 2010. Likelihood ratio-based distribution-free EWMA control charts. Journal of Quality Technology 42 (2):174–96. doi:10.1080/00224065.2010.11917815.
   Web of Science ®Google Scholar
• Zou, C., and F. Tsung. 2011. A multivariate sign EWMA control chart. Technometrics 53 (1):84–97. doi:10.1198/TECH.2010.09095.
   Web of Science ®Google Scholar