Two Nonparametric Control Charts for Detecting Arbitrary Distribution Changes

References

• Acosta-Mejia, C. A.; Pignatiello, J. J.; and Rao, B. V. (1999). “A Comparison of Control Charting Procedures for Monitoring Process Dispersion”. IIE Transactions 31, pp. 569–579.
   Web of Science ®Google Scholar
• Albers, W. and Kallenberg, W. C. M. (2009). “CUMIN Charts”. Metrika 70, pp. 111–130.
   Web of Science ®Google Scholar
• Anderson, T. W. (1962). “On the Distribution of the Two-Sample Cramer–Von Mises Criterion”. Annals of Mathematical Statistics 33, pp. 1148–1159.
   Google Scholar
• Ansari, R. A. and Bradley, R. A. (1960). “Rank Sum Tests for Dispersions”. Annals of Mathematical Statistics 31, pp. 1174–1189.
   Google Scholar
• Basseville, M. and Nikiforov, I. V. (1993). Detection of Abrupt Change Theory and Application. Englewood Cliffs, NJ: Prentice Hall.
   Google Scholar
• Buning, H. (2002). “Robustness and Power of Modified Lepage, Kolmogorov–Smirnov and Cramer–von-Mises Two Sample Tests”. Journal of Applied Statistics 29, pp. 907–924.
   Web of Science ®Google Scholar
• Chakraborti, S. and van de Wiel, M. A. (2008). “A Nonparametric Control Chart Based on the Mann–Whitney Statistic”. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, pp. 156–172.
   Google Scholar
• Feller, W. (1948). “On the Kolmogorov–Smirnov Limit Theorems for Empirical Distributions”. Annals of Mathematical Statistics 19, pp. 77–189.
   Google Scholar
• Gibbons, J. D. (1985) Nonparametric Statistical Inference. New York, NY: McGraw-Hill.
   Google Scholar
• Greenwell, R. N. and Finch, S. J. (2004). “Randomized Rejection Procedure for the Two-Sample Kolmogorov–Smirnov Statistic”. Computational Statistics # Data Analysis 46, pp. 257–267.
   Web of Science ®Google Scholar
• Hackl, P. and Ledolter, J. (1991). “A Control Chart Based on Ranks”. Journal of Quality Technology 23, pp. 117–124.
   Web of Science ®Google Scholar
• Hawkins, D. M.; Qiu, P. H.; and Kang, C. W. (2003). “The Changepoint Model for Statistical Process Control”. Journal of Quality Technology 35, pp. 355–366.
   Web of Science ®Google Scholar
• Hawkins, D. M. and Zamba, K. D. (2005). “A Change-Point Model for a Shift in Variance”. Journal of Quality Technology 37, pp. 21–31.
   Web of Science ®Google Scholar
• Hawkins, D. M. and Deng, Q. (2010). “A Nonparametric Change-Point Control Chart”. Journal of Quality Technology 42, pp. 165–173.
   Web of Science ®Google Scholar
• Jensen, W. A.; Jones-Farmer, L. A.; Champ, C. W.; and Woodall, W. H. (2006). “Effects of Parameter Estimation on Control Chart Properties: A Literature Review”. Journal of Quality Technology 38, pp. 349–364.
   Web of Science ®Google Scholar
• Jones-Farmer, L. A. and Champ, C. W. (2010). “A Distribution-Free Phase I Control Chart for Subgroup Scale”. Journal of Quality Technology 42, pp. 373–387.
   Web of Science ®Google Scholar
• Kim, P. K. (1969). “On the Exact and Approximate Sampling Distribution of the Two Sample Kolmogorov Smirnov Criterion”. Journal of the American Statistical Association 64, pp. 1625–1637.
   Web of Science ®Google Scholar
• Mann, H. B. and Whitney, D. R. (1947). “On a Test of Whether One of Two Random Variables Is Stochastically Larger than the Other”. The Annals of Mathematical Statistics 18, pp. 50–60.
   Google Scholar
• Montgomery, D. C. (2005). Introduction to Statistical Quality Control. Hoboken, NJ: Wiley.
   Google Scholar
• Reynolds, Jr., M. R. and Stoumbos, Z. (2005). “Should Exponentially Weighted Moving Average and Cumulative Sum Charts Be Used with Shewhart Limits?” Technometrics 47, pp. 409–424.
   Web of Science ®Google Scholar
• Schmid, F. and Trede, M. (1995). “A Distribution Free Test for the Two Sample Problem for General Alternatives”. Computational Statistics and Data Analysis 20, pp. 409–419.
   Web of Science ®Google Scholar
• Yeh, A. B.; McGrath, R. N.; Sembower, M. A.; and Shen, Q. (2008). “EWMA Control Charts for Monitoring High-Yield Processes Based on Non-Transformed Observations”. International Journal of Production Research 46, pp. 5679–5699.
   Web of Science ®Google Scholar
• Zamba, K. D. and Hawkins, D. M. (2009). “Multivariate Change-Point Model for Change in Mean Vector and/or Co-variance Structure”. Journal of Quality Technology 41, pp. 285–303.
   Web of Science ®Google Scholar
• Zhang, J. (2002). “Powerful Goodness-of-Fit Tests Based on Likelihood Ratio”. Journal of the Royal Statistical Society Series B (Methodological) 64, pp. 281–294.
   Web of Science ®Google Scholar
• Zhou, C.; Zou, C.; Zhang, Y.; and Wang, Z. (2009). “Nonparametric Control Chart Based on Change-Point Model”. Statistical Papers 50, pp. 13–28.
   Web of Science ®Google Scholar
• Zou, C. and Tsung, F. (2010). “Likelihood Ratio-Based Distribution-Free EWMA Control Charts”. Journal of Quality Technology 42, pp. 174–196.
   Web of Science ®Google Scholar