Phase II monitoring of covariance stationary autocorrelated processes

Statistical process control charts are intended to assist operators in detecting process changes. If a process change does occur, the control chart should detect the change quickly. Owing to the recent advancements in data retrieval and storage technologies, today's industrial processes are becoming increasingly autocorrelated. As a result, in this paper we investigate a process-monitoring tool for autocorrelated processes that quickly responds to process mean shifts regardless of the magnitude of the change, while supplying useful diagnostic information upon signaling. A likelihood ratio approach was used to develop a phase II control chart for a permanent step change in the mean of an ARMA (p, q) (autoregressive-moving average) process. Monte Carlo simulation was used to evaluate the average run length (ARL) performance of this chart relative to that of the more recently proposed ARMA chart. Results indicate that the proposed chart responds more quickly to process mean shifts, relative to the ARMA chart, while supplying useful diagnostic information, including the maximum likelihood estimates of the time and the magnitude of the process shift. These crucial change point diagnostics can greatly enhance the special cause investigation. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  Nien Fan Zhang,et al.  A statistical control chart for stationary process data , 1998 .

[2]  James R. Wilson,et al.  A distribution-free tabular CUSUM chart for autocorrelated data , 2007 .

[3]  D. Siegmund,et al.  Using the Generalized Likelihood Ratio Statistic for Sequential Detection of a Change-Point , 1995 .

[4]  Joseph J. Pignatiello,et al.  A magnitude‐robust control chart for monitoring and estimating step changes for normal process means , 2002 .

[5]  Johannes Ledolter,et al.  Statistical methods for forecasting , 1983 .

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

[7]  Wei Jiang,et al.  Some properties of the ARMA control chart , 2001 .

[8]  Fugee Tsung,et al.  A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison , 2006 .

[9]  Marion R. Reynolds,et al.  Control Charts for Monitoring the Mean and Variance of Autocorrelated Processes , 1999 .

[10]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

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

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

[13]  Gülser Köksal,et al.  The effect of Phase I sample size on the run length performance of control charts for autocorrelated data , 2008 .

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

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

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

[17]  George C. Runger,et al.  Model-Based and Model-Free Control of Autocorrelated Processes , 1995 .

[18]  Chao-Yu Chou,et al.  A real-time inventory decision system using Western Electric run rules and ARMA control chart , 2008, Expert Syst. Appl..

[19]  Steven E. Rigdon.  Properties of the Duane plot for repairable systems , 2002 .

[20]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[21]  Douglas C. Montgomery,et al.  SPC with correlated observations for the chemical and process industries , 1995 .

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

[23]  Fugee Tsung,et al.  A generalized EWMA control chart and its comparison with the optimal EWMA, CUSUM and GLR schemes , 2003 .