Monitoring processes that wander using integrated moving average models

Often the least appropriate assumption in traditional control-charting technology is that process data constitute a random sample. In reality most process data are correlated—either temporally, spatially, or due to nested sources of variation. One approach to monitoring temporally correlated data uses a control chart on the forecast errors from a time series model of the process with, possibly, a transfer-function term to model compensatory adjustments. If the time series term is an integrated moving average, then a sudden level shift in the process results in a patterned shift in the mean of forecast errors. Initially the mean shifts by the same amount as the process level, but then it decays geometrically back to 0 corresponding to the ability of the forecast to “recover” from the upset. We study four monitoring schemes—umulative sums (CUSUM's), exponentially weighted moving averages, Shewhart individuals charts, and a likelihood ratio scheme. Comparisons of signaling probabilities and average run lengt...

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

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

[3]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[4]  Benjamin M. Adams,et al.  An evaluation of forecast-based quality control schemes , 1994 .

[5]  Box Ge,et al.  Time series analysis: forecasting and control rev. ed. , 1976 .

[6]  R. Brown,et al.  Smoothing, Forecasting, and Prediction of Discrete Time Series , 1965 .

[7]  W. Woodall.  On the Markov Chain Approach to the Two-Sided CUSUM Procedure , 1984 .

[8]  Fah Fatt Gan,et al.  An optimal design of CUSUM quality control charts , 1991 .

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

[10]  Robert Goodell Brown,et al.  Smoothing, forecasting and prediction of discrete time series , 1964 .

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

[12]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[13]  T. Harris,et al.  Statistical process control procedures for correlated observations , 1991 .

[14]  S. Crowder.  Average Run Lengths of Exponentially Weighted Moving Average Control Charts , 1987 .

[15]  D. W. Trigg.  Monitoring a Forecasting System , 1964 .

[16]  S. Goldberg,et al.  Introduction to Difference Equations , 1958 .

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

[18]  Herbert Moskowitz,et al.  Control Charts in the Presence of Data Correlation , 1992 .

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

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

[21]  A. Goel,et al.  Determination of A.R.L. and a Contour Nomogram for Cusum Charts to Control Normal Mean , 1971 .

[22]  Herbert Moskowitz,et al.  Run-Length Distributions of Special-Cause Control Charts for Correlated Processes , 1994 .

[23]  A. Vasilopoulos,et al.  Modification of Control Chart Limits in the Presence of Data Correlation , 1978 .

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

[25]  G. Box,et al.  Cumulative score charts , 1992 .

[26]  John F. MacGregor,et al.  On-line statistical process control , 1988 .

[27]  Allan R. Wilks,et al.  The new S language: a programming environment for data analysis and graphics , 1988 .

[28]  P. Goldsmith,et al.  Average Run Lengths in Cumulative Chart Quality Control Schemes , 1961 .

[29]  Charles W. Champ,et al.  A a comparison of the markov chain and the integral equation approaches for evaluating the run length distribution of quality control charts , 1991 .

[30]  W. T. Tucker,et al.  Algorithmic statistical process control: concepts and an application , 1992 .

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

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

[33]  E. R. Golder,et al.  Monitoring Schemes in Short-term Forecasting , 1976 .

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

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

[36]  Gordon Latta,et al.  Introduction to Difference Equations , 1958 .