EWMA CONTROL CHART

EWMA CONTROL CHART

Graphics Command

Generates a an exponentially weighted moving average (EWMA) control chart. These are also referred to as geometric moving average control charts.

An EWMA control chart is a data analysis analysis technique for determining if a measurement process has gone out of statistical control. Similar to the cusum control chart, it is better than the standard xbar control chart for detecting small shifts in the process mean.

For the EWMA control chart, we plot

\( y_{t} = p\bar{x}_t + (1 - p)y_{t-1} \)

where p is a fraction between 0 and 1 and \( \bar{x_t} \) is the subgroup average at time t. That is, we plot a weighted average of the current subgroup mean with the previous weighted average. The starting value of y is set to the overall mean. The closer the value of p is to 1, the less prior data affects the current estimate.

The control limits are computed as

\( \bar{x} \pm 3.092\hat{\sigma}\sqrt{\frac{p} {n(2 - p)}} \)

where \( \bar{X} \) is the overall mean and \( \hat{\sigma} \) is an estimate of the process standard deviation.

In some cases, there may be historical data or engineering considerations that determine the control limits. You can set your own control limits by entering the commands:

LET TARGET = <value>
LET USL = <value>
LET LSL = <value>

where TARGET is the desired target value and USL and LSL are the desired upper and lower control limits.

You can control the appearance of this chart by setting the switches for the LINE, CHARACTER, SPIKE, and BAR commands appropriately. Specifically,

Trace 1 =	the EWMA statistic
Trace 2 =	Target reference line (the overall mean)
Trace 3 =	Dataplot calculated upper control limit
Trace 4 =	Dataplot calculated lower control limit
Trace 5 =	User specified target value
Trace 6 =	User specified upper control limit
Trace 7 =	User specified lower control limit

For example, to draw the EWMA values as a solid line and an X, the reference line and the Dataplot calculated control limits as dotted lines, and no user specified control limit, enter the commands:

LINE SOLID DOTTED DOTTED DOTTED BLANK BLANK BLANK
CHARACTER X BLANK BLANK BLANK BLANK BLANK BLANK

EWMA CONTROL CHART <y> <group> <SUBSET/EXCEPT/FOR qualification>
where <y> is a response variable;
          <group> is a sub-group identifier variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax is used for the most common case where the data is divided into subgroups.

EWMA CONTROL CHART <y>             <SUBSET/EXCEPT/FOR qualification>
where <y> is a response variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax is used for the case of ungrouped data.

EWMA CONTROL CHART Y1 X
EWMA CONTROL CHART Y
EWMA CONTROL CHART Y1 X SUBSET X > 1

None

EWMA CHART is a synonym for EWMA CONTROL CHART.

WEIGHT is a synonym for the parameter P. That is, you can enter

LET WEIGHT = <value>

to specify the weighting parameter.

CONTROL CHART

= Generate various types of control charts.

Thomas Ryan (1989), "Statistical Methods For Quality Improvement," John Wiley and Sons, pp. 122-124.

Quality Control

1997/9

TITLE Silicon Wafer Thickness Analysis
LABEL CASE ASIS
TITLE CASE ASIS
Y1LABEL Wafer Thickness
X1LABEL Day
LEGEND 1 Statistical Process Control
LEGEND 2 EWMA Control Chart
.
SKIP 25
READ CCXBAR.DAT Y X
.
CHARACTERS CONTROL CHART
CHARACTER FILL ON
LINES CONTROL CHART
.
LET P = 0.5
EWMA CONTROL CHART Y X