Fractal geometry statistical process control for non-linear pattern-based processes

References

• Alwan , L. C. , Ebrahimi , N. and Soofi , E. S. 1998 . Information theoretic framework for process control . European Journal of Operations Research , 111 : 526 – 542 .
   Web of Science ®Google Scholar
• Alwan , L. C. and Roberts , H. V. 1988 . Time-series modeling for statistical process control . Journal of Business & Economics Statistics , 6 ( 1 ) : 87 – 95 .
   Web of Science ®Google Scholar
• Apley , D. W. and Shi , J. 1999 . The GLRT for statistical process control of autocorrelated processes . IIE Transactions , 31 : 1123 – 1134 .
   Web of Science ®Google Scholar
• Barnsley , M. 1988 . Fractals Everywhere , Boston , MA : Academic Press .
   Google Scholar
• Barnsley , M. and Hurd , L. P. 1993 . Fractal Image Compression Edited by: Peters , A. K. Boston , MA
   Google Scholar
• Basarin , G. R. 1959 . On a statistical estimate for the entropy of a sequence of independent random variables . Teor Verojanost. i Primenen. , 4 : 361 – 364 .
   Google Scholar
• Ben-Gal , I. , Morag , G. and Shmilovici , A. 2003 . CSPC: A monitoring procedure for state dependent processes . Technometrics , 45 ( 4 ) : 293 – 311 .
   Web of Science ®Google Scholar
• Ben-Gal , I. and Singer , G. 2004 . Statistical process control via context modeling of finite state processes: an application to production monitoring . IIE Transactions on Quality and Reliability , 36 ( 5 ) : 401 – 415 .
   Web of Science ®Google Scholar
• Boardman , T. J. and Boardman , E. C. 1990 . Don't touch that funnel . Quality Progress , 23 : 56 – 69 .
   Google Scholar
• Box , G. E.P. and Jenkins , G. M. 1976 . Times Series Analysis, Forecasting and Control , Oakland , CA : Holden-Day .
   Google Scholar
• Castagliola , P. and Tsung , F. 2005 . Autocorrelated SPC for non-normal situations . Quality and Reliability Engineering International , 21 : 131 – 161 .
   Web of Science ®Google Scholar
• Chen , C. C. and Chen , C. C. 2003 . Texture synthesis, a review and experiments . Journal of Information Science and Engineering , 19 : 371 – 380 .
   Web of Science ®Google Scholar
• Cheng , S. and Thaga , K. 2005 . Max-CUSUM chart for autocorrelated processes . Statistical Sinica , 15 ( 2 ) : 527 – 546 .
   Web of Science ®Google Scholar
• Cochran , W. G. 1952 . The chi-square test of goodness of fit . The Annals of Mathematical Statistics , 23 : 315 – 345 .
   Google Scholar
• Cover , T.M. and Thomas , J.A. 1995 . Elements of Information Theory 2nd ed., John Wiley & Sons Inc., Hoboken, NJ.
   Google Scholar
• English , J. R. , Martin , T. , Yaz , E. and Elsayed , E. 2001 . Change point detection and control using statistical process control and automatic process control . Presented at the IIE Annual Conference , Dallas, TX
   Google Scholar
• Grassberger , P. 1983 . Characterization of strange attractors . Physical Review Letters , 50 : 346 – 349 .
   Web of Science ®Google Scholar
• Grassberger , P. and Procacciaa , I. 1983 . Measuring the strangeness of strange attractors . Physica D: Nonlinear Phenomena , 9 ( 1-2 ) : 189 – 208 .
   Web of Science ®Google Scholar
• Harris , B. 1975 . “ The statistical estimation of entropy in the non-parametric case ” . Madison : Mathematics Research Center, University of Wisconsin–Madison . Technical Summary Report no. 1605
   Google Scholar
• Harris , T. J. and Ross , W. H. 1991 . Statistical process control procedures for correlated observations . Canadian Journal of Chemical Engineering , 69 ( 1 ) : 48 – 57 .
   Web of Science ®Google Scholar
• Jolayemi , J. K. 1992 . Convolution of independent binomial variables: an approximation method and a comparative study . Computation Statistics and Data Analysis , 18 : 403 – 417 .
   Web of Science ®Google Scholar
• Jolayemi , J. K. 1999 . A statistical model for the design of multiattribute control chart . The Indian Journal of Statistics , 61 ( 2 ) : 351 – 365 .
   Google Scholar
• Kaminski , F. C. , Benneyan , J. C. , Davis , R. D. and Burke , R. J. 1992 . Statistical control charts based on a geometric distribution . Journal of Quality Technology , 24 : 63 – 69 .
   Web of Science ®Google Scholar
• Keim , D. A. 2002 . Information visualization and visual data mining . IEEE Transactions of Visualization and Computer Graphics , 7 ( 1 ) : 100 – 107 .
   Google Scholar
• Kim , S. H. , Alexopoulos , C. , Tsui , K. L. and Wilson , J. R. 2007 . A distribution free tabular CUSUM chart for autocorrelated data . IIE Transactions , 39 : 317 – 330 .
   Web of Science ®Google Scholar
• Lu , C. W. and Reynolds , M. R. 1999a . Control charts for monitoring the mean and variance of autocorrelated processes . Journal of Quality Technology , 31 ( 3 ) : 259 – 274 .
   Web of Science ®Google Scholar
• Lu , C. W. and Reynolds , M. R. 1999b . EWMA control charts to monitor the mean of autocorrelated processes . Journal of Quality Technology , 31 ( 2 ) : 166 – 188 .
   Web of Science ®Google Scholar
• Luce , R. D. 1955 . “ The theory of selective information and some of its behavioral applications ” . In Developments in Mathematical Psychology , Edited by: Luce , R. D. 45 – 46 . Glencoe , IL : The Free Press .
   Google Scholar
• Mason , R. L. , Tracy , N. D. and Young , J. C. 1995 . Decomposition of T 2 for multivariate control chart interpretation . Journal of Quality Technology , 27 : 99 – 108 .
   Web of Science ®Google Scholar
• Miller , G. A. and Madow , W. G. 1954 . “ On the maximum likelihood estimate of the Shannon-Weaver measure of information ” . Technical Report, Air Force Cambridge Research Center .
   Google Scholar
• Montgomery , D. C. and Mastrangelo , C. M. 1991 . Some statistical process control methods for autocorrelated data . Journal of Quality Technology , 23 ( 3 ) : 179 – 204 .
   Web of Science ®Google Scholar
• Perry , M. B. and Pignatiello , J. J. 2006 . Estimation of the change point of a normal process mean with a linear step disturbance in SPC . Quality Technology and Quantitive Management , 3 ( 3 ) : 325 – 334 .
   Google Scholar
• Quesenberry , C. P. 1991a . SPC Q charts for a binomial parameter: short or long runs . Journal of Quality Technology , 23 : 239 – 246 .
   Web of Science ®Google Scholar
• Quesenberry , C. P. 1991b . SPC Q charts for a Poisson parameter k: short or long runs . Journal of Quality Technology , 23 : 296 – 303 .
   Web of Science ®Google Scholar
• Ren , Y. , Ding , Y. and Zhou , S. 2006 . A data-mining approach to study the significance of nonlinearity in multi-station assembly processes . IIE Transactions , 38 ( 12 ) : 10691083
   Web of Science ®Google Scholar
• Rokach , L. , Romano , R. and Maimon , O. 2008 . Mining manufacturing databases to discover the effect of operation sequence on the product quality . Journal of Intelligent Manufacturing , 19 ( 3 ) : 313 – 325 .
   Web of Science ®Google Scholar
• Runger , G. C. , Alt , F. B. and Montgomery , D. C. 1996 . Contributors to a multivariate SPC chart signal . Communications in Statistics, Theory and Methods , 25 : 2203 – 2213 .
   Web of Science ®Google Scholar
• Runger , G. C. and Willemain , T. 1995 . Model-based and model-free control of autocorrelated processes . Journal of Quality Technology , 27 : 283 – 292 .
   Web of Science ®Google Scholar
• Runger , G. C. , Willemain , T. and Prabhu , S. 1995 . Average-run-lengths for CUSUM control charts applied to residuals . Communications in Statistics, Part A—Theory and Methods , 24 : 273 – 282 .
   Web of Science ®Google Scholar
• Ruschin-Rimini , N. , Ben-Gal , I. and Maimon , O. 2011a . “ Technical paper: fractal dimension types in the context of SPC: analytical study ” . available at http://www.eng.tau.ac.il/~bengal/fractal2.pdf
   Google Scholar
• Ruschin-Rimini , N. , Ben-Gal , I. and Maimon , O. 2011b . “ Web appendix: data generated in experiments ” . available at http://www.eng.tau.ac.il/~bengal/fractalData.xlsx
   Google Scholar
• Ruschin-Rimini , N. and Maimon , O. 2010 . “ Visual analysis of sequences using fractal geometry ” . In Data Mining and Knowledge Discovery Handbook , Springer . New York, pp. 591–601, second edition
   Google Scholar
• Ruschin-Rimini , N. , Maimon , O. and Romano , R. 2012 . Visual analysis of quality-related manufacturing data using fractal geometry . Journal of Intelligent Manufacturing , 23 ( 3 ) : 481–495
   Web of Science ®Google Scholar
• Shore , H. 1992 . Total Quality, Quality Control and Quality by Design (in Hebrew), 2nd ed., 1995. Self-published.
   Google Scholar
• Shore , H. 1998 . A new approach to analyzing non-normal data with application to process capability analysis . International Journal of Production Research , 36 ( 7 ) : 1917 – 1933 .
   Web of Science ®Google Scholar
• Shore , H. 2000 . General control charts for attributes . IIE Transactions , 32 : 1149 – 1160 .
   Web of Science ®Google Scholar
• Singer , G. and Ben-Gal , I. 2007 . The funnel experiment: the Markov-based SPC approach . Quality and Reliability Engineering International , 23 : 899 – 913 .
   Web of Science ®Google Scholar
• Wasserkrug , S. , Gal , A. , Etzion , O. and Turchin , Y. 2008 . “ Complex event processing over uncertain data ” . In Presented at the IEEE Second International Conference on Distributed Event-Based Systems Rome, Italy
   Google Scholar
• Weiss , C. H. 2008 . Visual analysis of categorical time series . Statistical Methodology , 5 : 56 – 71 .
   Google Scholar
• Weiss , C. H. and Goeb , B. 2008 . Discover patterns in categorical time series . Computational Statistics & Data Analysis , 52 ( 9 ) : 4369 – 4379 .
   Web of Science ®Google Scholar
• Woodall , W. H. 1997 . Control charts based on attribute data: bibliography and review . Journal of Quality Technology , 29 ( 2 ) : 172 – 183 .
   Web of Science ®Google Scholar
• Ye , N. , Li , X. , Chen , Q. , Emran , S. M. and Xu , M. 2001 . Probabilistic techniques for intrusion detection based on computer audit data . IEEE Transactions on System, Man, and Cybernetics-Part A: Systems and Humans , 3 ( 1 ) : 266 – 274 .
   Google Scholar
• Ye , N. , Vilbert , S. and Chen , Q. 2003 . Computer intrusion detection through EWMA for autocorrelated and uncorrelated data . IEEE Transactions on Reliability , 52 : 75 – 82 .
   Web of Science ®Google Scholar