Invited Session: Statistical Monitoring of Autocorrelated Processes
Statistical Monitoring of Continuous Processes
Most continuous processes are operated under feedback control which causes highly positively autocorrelated measurements. A popular practice for statistical process monitoring (SPM) of continuous processes is to build autoregressive (AR) models and develop SPM methods on their one-step-ahead residuals. It is expected that the residuals areit iidand permit the use of Shewhart ortt CUSUMcharts on residuals. However, for AR models of highly positively autocorrelated observations, residuals are insensitive to level changes, and residuals based SPM methods become inefficient.
New SPM methods are presented for continuous processes operated under feedback control. The parameter change detection (PCD) method monitors the parameters of recursive AR process models, and performs better than residuals based SPM tools in monitoring univariate measurements that are highly positively autocorrelated. The canonical variate (CV) method is used for monitoring multivariable processes with collinear, crosscorrelated and autocorrelated data. The CV realization yields VARMA models with serially independent residuals. Then, SPM charts are developed on residuals.
[Antoine Negiz, UOP, 25 East Algonquin Road, P.O. Box 5017, Des Plaines, IL 60017-5017 USA; firstname.lastname@example.org ]
Residual-Based Monitoring of Autocorrelated Processes
Scott A. Vander Wiel
Control charting technology traditionally assumes that process data constitutes a simple random sample. In reality most process data are correlated---either temporally, spatially, or because of nested sources of variation.
One approach to monitoring temporally correlated data is to use a control chart on the forecast residuals from a time series model of the process. A sudden shift in the level of a standard ARIMA process results in a patterned shift in the mean of the uncorrelated forecast errors. For a first-order IMA the pattern is a geometric decay to zero corresponding to the ability of forecasts to ``recover'' from level shifts. I will review several recent studies of control chart run-length comparisons for these situations. My study for IMA processes shows that CUSUMs can be designed to perform at least on par, and often better than several competing schemes.
I will conclude with several examples of real-life process monitoring problems that do not fit into the traditional scenarios contemplated in control charting literature.
[Scott Vander Wiel, 2C-277; 600 Mountain Avenue; Murray Hill, NJ 07023 USA; email@example.com ]
Date created: 6/5/2001