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23

Statistical Process Control for

Autocorrelated Processes:

A Survey and An

Innovative Approach

L. C. Tang and O. O. Atienza

In this chapter, we first give a quick survey of the work on statistical process control for
autocorrelated processes, which is still under very intensive research. We then present
an approach involving monitoring some statistics originating from time series models.
The performance of the proposed monitoring scheme is evaluated and compared with
the conventional method based on monitoring the residuals of a time series model.

23.1 INTRODUCTION

Traditional statistical process control (SPC) schemes, such as Shewhart and cumula-
tive sum (CUSUM) control charts, assume that data collected from the process are
independent. However, this assumption has been challenged as it has been found
that, in many practical situations, data are serially correlated. The performance of
traditional control charts deteriorates significantly under autocorrelation. This moti-
1
vated the pioneering work by Alwan and Roberts, who proposed the monitoring of
forecasted errors after an appropriate time-series model has been fitted to the process.
This method is intuitive as autocorrelation can be accounted for by the underlying
time series model while the residual terms capture the independent random errors
of the process. Traditional SPC schemes can be applied to monitoring the residuals.
Subsequent work on this problem can be broadly classified into two themes; those

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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