Dataplot Vol 1 Vol 2

# MOVING STATISTIC CONTROL CHART

Name:
MOVING <STATISTIC> CONTROL CHART
Type:
Graphics Command
Purpose:
Generates a moving average, a moving range, or a moving standard deviation control chart.
Description:
The xbar, range, and standard deviation control charts are applied for grouped data. The moving average, moving range, and moving standard deviation control charts are an alternative that can be applied to ungrouped data. Although these charts can also be applied to grouped data, they have less desirable statistical properties than the xbar, range, and standard deviation control charts for grouped data.

For ungrouped data, the moving average control chart is formed by plotting the moving average. The moving average depends on a filter width. For example, if this width is 3, then the first point plotted is the average of points one through three, the second poing plotted is the average of points two through five, and so on. The x coordinate is in the middle of the points (i.e., the x coordinate of the first point plotted is 2). In Dataplot, you specify the filter width by entering the following command before generating the control chart:

LET K = <value>

Filter widths are typically small (e.g., k = 3). The control limits are computed as

$$\bar{x} \pm 3.09\frac{\bar{RM}} {E_2(k)\sqrt{k}}$$

where $$\bar{X}$$ is the overall mean, K is the filter width, and $$\bar{RM}$$ is an estimate of $$\hat{\sigma}$$ based on a moving range. Specifically, we compute a moving range comparable to the moving average described above and then we take the average of these moving ranges. Dataplot uses the same filter width for this moving range as it does for computing the moving average. E2 is a tabulated value.

The technique for constucting moving range and moving standard deviation charts is similar. However, the control limits are:

$$\mbox{FACT*} \bar{RM}$$

where FACT is a tabulated value (it is different for the moving range and moving standard deviation control charts).

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 moving average/range/standard deviation 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
Syntax 1:
MOVING <stat> CONTROL CHART <y> <group>
<SUBSET/EXCEPT/FOR qualification>
where <stat> is AVERAGE, RANGE, or SD;
<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 grouped data.

Syntax 2:
MOVING <stat> CONTROL CHART <y>
<SUBSET/EXCEPT/FOR qualification>
where <stat> is AVERAGE, RANGE, or SD;
<y> is a response variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax is used for ungrouped data.

Examples:
MOVING AVERAGE CONTROL CHART Y
MOVING RANGE CONTROL CHART Y
MOVING SD CONTROL CHART Y
MOVING AVERAGE CONTROL CHART Y X
MOVING AVERAGE CONTROL CHART Y X SUBSET X > 1
Note:
The data should be checked for normality before applying these charts. This can be done with a normal probability plot or a Wilks-Shapiro test.
Note:
The Dataplot control limits should not be applied if the data contain a know trend. See chapter 6 of Ryan for determining acceptable control limits for this case.
Default:
None
Synonyms:
MOVING AVERAGE CHART is a synonym for MOVING AVERAGE CONTROL CHART.
MOVING RANGE CHART is a synonym for MOVING RANGE CONTROL CHART.
MOVING SD CHART is a synonym for MOVING SD CONTROL CHART.
Related Commands:
 CONTROL CHART = Generates various types of control charts. NORMAL PROBABILITY PLOT = Generate a normal probability plot. WILKS-SHAPIRO TEST = Compute the Wilks-Shapiro test for normality.
Reference:
Thomas Ryan (1989), "Statistical Methods For Quality Improvement", John Wiley and Sons, chapter 6.
Applications:
Quality Control
Implementation Date:
1997/9
Program:
LABEL CASE ASIS
CASE ASIS
Y1LABEL Distance (Micrometers)
LINE SOLID DOTT DOTT DOTT
XLIMITS 0 100
XTIC OFFSET 2 10
X3LABEL AUTOMATIC
.
SKIP 25
READ CROARK3.DAT Y
.
MULTIPLOT CORNER COORDINATES 5 5 95 95
MULTIPLOT 2 2
MOVING AVERAGE CONTROL CHART Y
MOVING RANGE CONTROL CHART Y
MOVING SD CONTROL CHART Y
END OF MULTIPLOT
MOVE 50 95
JUSTIFICATION CENTER
TEXT Magnification Standard for SEMs

NIST is an agency of the U.S. Commerce Department.

Date created: 6/5/2001
Last updated: 10/19/2015

Please email comments on this WWW page to alan.heckert@nist.gov.