Chapter 4
EWMA-type control charts
for the mean
In the previous chapter, we discussed Shewhart-type control charts. These
control charts only use the current observation or sample to monitor the
process. In the next two chapters we consider control charts that also uti-
lize previous observations. In Chapter 5, the CUmulative SUM (CUSUM)
chart is discussed. In its basic form, an unweighted cumulative sum of the
(standardized) observations is plotted against time in the CUSUM chart.
This chart has a long ‘memory’.
In the present chapter, we consider the Exponentially Weighted Moving
Average (EWMA) control chart. Like the CUSUM, the EWMA utilizes
all previous observations, but the weight attached to data is exponentially
declining as the observations get older and older. By varying the param-
eter of the EWMA statistic the ‘memory’ of the EWMA control chart
can be influenced. A control chart based on the EWMA was introduced
by Roberts (1959). More recent references include Hunter (1986), Crow-
der (1987), and Lucas and Saccucci (1990).
In the previous chapter, the EWMA statistic was used as a local es-
timator for the level of the data. The EWMA ‘smoothes out’ the effect
of single disturbances, and shows the behavior of the level of the data.
This suggests using the EWMA as a statistic to monitor the mean of a
process. Originally, the EWMA was developed by time series analysts to
distinguish short term variation from long term variation such as trends
and cyclic behavior.
Another application of the EWMA was mentioned in Section 3.7 of
the previous chapter. The EWMA of previous observations provides an
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CHAPTER 4. EWMA-TYPE CONTROL CHARTS
approximate one-step-ahead predictor. It is easily shown that the EWMA
is an optimal (in the sense of minimal Mean Squared Error (MSE)) one-
step-ahead predictor if the underlying time series model is IMA(1,1). This
property will be illustrated in Chapter 8.
The setup of this chapter is similar to that of the previous chapter.
In Section 4.1, we discuss the EWMA control chart