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Simultaneous Monitoring of the

Mean, Variance and

Autocorrelation Structure of

Serially Correlated Processes

O. O. Atienza and L. C. Tang

Statistical process control techniques for monitoring serially correlated or autocor-
related processes have received significant attention in the statistical quality engi-
neering literature. The focus of most studies, however, is on the detection of the
mean shift of the process. The detection of changes in the variance and autocorre-
lation structure of the series due to some special causes of variation affecting the
system is often overlooked. Ideally, one needs to maintain three control charts in
order to effectively detect changes in the process: one each for detecting change in
the mean, variance and autocorrelation structure (MVAS) of a series. Such an ap-
proach can be quite cumbersome to implement. One alternative is to develop a mon-
itoring scheme that has good sensitivity in simultaneously detecting changes in the
MVAS of a series. An example of such an approach is the sample autocorrelation
1
chart (SACC) proposed by Montgomery and Friedman . Unfortunately, it has been
found that the SACC has poor sensitivity in detecting shifts in the mean and vari-
ance. As an alternative, we propose a new monitoring scheme based on the charac-
teristics of a Gaussian stationary time series. Compared to the SACC, the proposed
scheme is simpler to implement and is more sensitive to changes in the MVAS of a
series.

Six Sigma: Advanced Tools for Black Belts and Master Black Belts L. C. Tang, T. N. Goh, H. S. Yam and T. Yoap
C 2006 John Wiley & Sons, Ltd
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