A Markov Chain Model for the Adaptive CUSUM Control Chart

In practice, when the magnitude of a future mean shift is unknown, it is always desired to design a control chart to perform reasonably well over a range of shifts rather than to optimize the performance at detecting a particular level of shifts. Compared with the conventional cumulative sum (CUSUM) control chart designed based on a prespecified mean shift, the adaptive CUSUM (ACUSUM) chart proposed by Sparks (2000) can detect a broader range of mean shifts. This paper develops a two-dimensional Markov chain model to analyze the performance of ACUSUM charts. Moreover, a more general operating model is suggested for the current ACUSUM chart to simplify its implementation.

[1]  M. Pollak.  Optimal Detection of a Change in Distribution , 1985 .

[2]  G. Lorden.  PROCEDURES FOR REACTING TO A CHANGE IN DISTRIBUTION , 1971 .

[3]  G. Moustakides.  Optimal stopping times for detecting changes in distributions , 1986 .

[4]  E. S. Page.  CONTROL CHARTS WITH WARNING LINES , 1955 .

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

[6]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[7]  D. Siegmund.  Sequential Analysis: Tests and Confidence Intervals , 1985 .

[8]  Ronald B. Crosier,et al.  A new two-sided cumulative sum quality control scheme , 1986 .

[9]  Igor V. Nikiforov.  A simple change detection scheme , 2001, Signal Process..

[10]  Ross Sparks,et al.  CUSUM Charts for Signalling Varying Location Shifts , 2000 .

[11]  G. Box,et al.  Cumulative Sum Tests: Theory and Practice , 1968 .

[12]  D. A. Evans,et al.  An approach to the probability distribution of cusum run length , 1972 .

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

[14]  Douglas M. Hawkins,et al.  The Changepoint Model for Statistical Process Control , 2003 .

[15]  W. Jiang,et al.  AVERAGE RUN LENGTH COMPUTATION OF ARMA CHARTS FOR STATIONARY PROCESSES , 2001 .

[16]  William H. Woodall,et al.  THE STATISTICAL DESIGN OF CUSUM CHARTS , 1993 .

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

[18]  Lonnie C. Vance.  Computer Programs: Average Run Lengths of Cumulative Sum Control Charts for Controlling Normal Means , 1986 .

[19]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[20]  S. W. Roberts,et al.  Control Chart Tests Based on Geometric Moving Averages , 2000, Technometrics.

[21]  Roger M. Sauter,et al.  Introduction to Statistical Quality Control (2nd ed.) , 1992 .

[22]  James M. Lucas,et al.  Combined Shewhart-CUSUM Quality Control Schemes , 1982 .

[23]  T. Lai.  SEQUENTIAL ANALYSIS: SOME CLASSICAL PROBLEMS AND NEW CHALLENGES , 2001 .

[24]  Douglas M. Hawkins.  A fast accurate approximation for average run lengths of CUSUM control charts , 1992 .

[25]  James M. Lucas,et al.  Exponentially weighted moving average control schemes: Properties and enhancements , 1990 .

[26]  James M. Lucas,et al.  Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start , 2000, Technometrics.

[27]  George C. Runger,et al.  A Markov Chain Model for the Multivariate Exponentially Weighted Moving Averages Control Chart , 1996 .

[28]  Giovanna Capizzi,et al.  An Adaptive Exponentially Weighted Moving Average Control Chart , 2003, Technometrics.

[29]  P. L. Goldsmith,et al.  Cumulative Sum Tests: Theory and Practice , 1969 .