CUSCORE Charts for Detecting Sine Wave Signals in an
Autocorrelated Process
ABSTRACT:
CUSUM control charts are widely used in many industries to monitor
processes with the objective of improving process quality and
productivity. However CUSUM charts are only efficient for
detecting step changes in a process parameter such as the mean.
When periodic special causes are present, such as when harmonic
cycling about the target occurs, CUSCORE charts outperform the
CUSUMs for detecting this kind of signals. Actually CUSUMs are
special cases of CUSCOREs. In practical use, to judge when to
declare an out-of-control state, the decision interval CUSUM
(DI CUSUM) is widely used. We developed a decision interval
CUSCORE (DI CUSCORE) as an extension of the DI CUSUM and apply
it to both independent and autocorrelated processes. Our
simulations are related to the frequency and phase angle of the
sine wave signal as well as the autocorrelation parameters. We
use Fourier analysis and maximum likelihood methods to estimate
these values. This work is motivated by data from the lumber
industry, related to thicknesses of logs in a sawing process.
These data sets have the feature that they are highly
autocorrelated and show some periodic special causes that can
be modelled by sine wave signals. The problem seems well suited
for the development and application of CUSCORE charts.
The talk is based on joint work with Roman Viveros.
About the Speaker
Yongmin Yu is presently a PhD student, Department of Mathematics
and Statistics, McMaster University. He holds a Bachelor degree
in Physics from Fudan University (China), and Master and PhD
degrees in Physics from University of Rhode Island (USA). He
also holds a Master degree in Statistics from McMaster University.
Yongmin Yu is interested in statistical process control and its
applications, and in environmental statistics.
References
Box, G. and Luceno A. (1997). Statistical Control by Monitoring
and Feedback Adjustment. John Wiley Sons, Inc.
Hawkins D. M. and Olwell D. H. (1997). Cumulative Sum Charts and
Charting for Quality Improvement. Springer-Verlag New York, Inc.
Lu, C. W. and Reynolds M. R. JR. (2001). Cusum Charts for
Monitoring an Autocorrelated Process. Journal of Quality
Technology, 33, No. 3, 316-334.
