The funnel experiment: The Markov-based SPC approach

The classical funnel experiment was used by Deming to promote the idea of statistical process control (SPC). The popular example illustrates that the implementation of simple feedback rules to stationary processes violates the independence assumption and prevents the implementation of conventional SPC. However, Deming did not indicate how to implement SPC in the presence of such feedback rules. This pedagogical gap is addressed here by introducing a simple feedback rule to the funnel example that results in a nonlinear process to which the traditional SPC methods cannot be applied. The proposed method of Markov-based SPC, which is a simplified version of the context-based SPC method, is shown to monitor the modified process well. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  E. Mcwhinney.  Author’s Publications , 2007 .

[2]  Paul L. Stepanovich,et al.  Using System Dynamics to Illustrate Deming’s System of Profound Knowledge , 2004 .

[3]  S. Kullback,et al.  Information Theory and Statistics , 1959 .

[4]  Junghui Chen,et al.  Applying wavelet-based hidden Markov tree to enhancing performance of process monitoring , 2005 .

[5]  Wei Jiang,et al.  A New SPC Monitoring Method: The ARMA Chart , 2000, Technometrics.

[6]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[7]  Jianjun Shi,et al.  The GLRT for statistical process control of autocorrelated processes , 1999 .

[8]  Solomon Kullback,et al.  Information Theory and Statistics , 1960 .

[9]  赵仪.  Improved design of proportional integral derivative charts , 2006 .

[10]  Duane S. Boning,et al.  Run by run control of chemical-mechanical polishing , 1995, Seventeenth IEEE/CPMT International Electronics Manufacturing Technology Symposium. 'Manufacturing Technologies - Present and Future'.

[11]  J. Kalbfleisch,et al.  The Analysis of Panel Data under a Markov Assumption , 1985 .

[12]  John F. MacGregor,et al.  A different view of the funnel experiment , 1990 .

[13]  George E. P. Box,et al.  Statistical process monitoring and feedback adjustment: a discussion , 1992 .

[14]  Bengt Klefsjö,et al.  Statistical process adjustment for quality control , 2003 .

[15]  Douglas H. Timmer,et al.  The development and evaluation of CUSUM-based control charts for an AR(1) process , 1998 .

[16]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[17]  A. T. Bharucha-Reid.  Elements of the theory of Markov processes and their applications , 1961 .

[18]  D. Hinkley.  Inference about the change-point from cumulative sum tests , 1971 .

[19]  Richard A. Johnson,et al.  The Effect of Serial Correlation on the Performance of CUSUM Tests II , 1974 .

[20]  Golan Yona,et al.  Variations on probabilisti suÆx trees : statisti al modeling andpredi tion of protein , 2001 .

[21]  Marion R. Reynolds,et al.  EWMA and CUSUM control charts in the presence of correlation , 1997 .

[22]  Douglas C. Montgomery,et al.  Some Statistical Process Control Methods for Autocorrelated Data , 1991 .

[23]  G. Robin Henderson,et al.  EWMA and industrial applications to feedback adjustment and control , 2001 .

[24]  A. J. Lawrance,et al.  A new autoregressive time series model in exponential variables (NEAR(1)) , 1981, Advances in Applied Probability.

[25]  Murat Caner Testik,et al.  Model Inadequacy and Residuals Control Charts for Autocorrelated Processes , 2005 .

[26]  Anthony N. Pettitt,et al.  A simple cumulative sum type statistic for the change-point problem with zero-one observations , 1980 .

[27]  W. G. Cochran.  The $\chi^2$ Test of Goodness of Fit , 1952 .

[28]  Armin Shmilovici,et al.  Context-Based Statistical Process Control , 2003, Technometrics.

[29]  Wei Jiang,et al.  Proportional Integral Derivative Charts for Process Monitoring , 2002, Technometrics.

[30]  Douglas C. Montgomery,et al.  Integrating Statistical Process Control and Engineering Process Control , 1994 .

[31]  Marion R. Reynolds,et al.  Cusum Charts for Monitoring an Autocorrelated Process , 2001 .

[32]  Benjamin M. Adams,et al.  Monitoring autocorrelated processes with an exponentially weighted moving average forecast , 1994 .

[33]  Douglas W. Coleman.  Adapting Deming’s Funnel Experiment to a Content-Specific Area , 1999 .

[34]  P Winkel,et al.  Serial correlation of quality control data–on the use of proper control charts , 2004, Scandinavian journal of clinical and laboratory investigation.

[35]  I. Ben-Gal,et al.  SPC via Context Modeling of Finite State Processes : An Application to Production Monitoring , 2003 .

[36]  George C. Runger,et al.  Average run lengths for cusum control charts applied to residuals , 1995 .

[37]  JORMA RISSANEN,et al.  A universal data compression system , 1983, IEEE Trans. Inf. Theory.

[38]  Emmanuel Yashchin,et al.  Performance of CUSUM control schemes for serially correlated observations , 1993 .

[39]  Benjamin Friedlander,et al.  Asymptotically optimal estimation of MA and ARMA parameters of non-Gaussian processes from high-order moments , 1990 .

[40]  R. Rigby,et al.  Generalized Autoregressive Moving Average Models , 2003 .

[41]  Armin Shmilovici,et al.  CSPC: A Monitoring Procedure for State Dependent Processes , 2003 .

[42]  Jean-Philippe Vert,et al.  Adaptive context trees and text clustering , 2001, IEEE Trans. Inf. Theory.

[43]  Layth C. Alwan,et al.  Time-Series Modeling for Statistical Process Control , 1988 .

[44]  Marion R. Reynolds,et al.  EWMA CONTROL CHARTS FOR MONITORING THE MEAN OF AUTOCORRELATED PROCESSES , 1999 .

[45]  G. Barnard.  Control Charts and Stochastic Processes , 1959 .

[46]  George E. P. Box,et al.  Statistical Control: By Monitoring and Feedback Adjustment , 1997 .

[47]  Enrique Del Castillo.  A note on two process adjustment models , 1998 .

[48]  W. Edwards Deming,et al.  Out of the Crisis , 1982 .