StATS: XBAR-S control chart, answers to on your own exercise (March 2, 2007).

On the web page

you were asked to calculate an XBAR-S control chart. Here is the data for that problem.

Week01 1.097 1.204
Week03 1.030 1.362
Week05 0.682 0.978
Week07 0.820 1.080
Week09 1.042 0.858
Week11 1.398 1.146
Week13 1.301 1.204

Here are the summary statistics.

       Mean  Stdev
Week01 1.151 0.076
Week03 1.196 0.235
Week05 0.830 0.209
Week07 0.950 0.184
Week09 0.950 0.130
Week11 1.272 0.178
Week13 1.252 0.069

The mean of the seven means is 1.09 and the mean of the seven standard deviations is 0.15. For subgroups of size 2, the constants are

A3=2.659,
B3=0,
B4=3.267.

The upper and lower control limits for the XBAR chart are

1.09+2.659*0.15=1.49 and
1.09-2.659*0.15=0.69.

The warning limits are

1.09+2.659*0.15*2/3=1.36 and
1.09-2.659*0.15*2/3=0.82.

Here is the control chart for the means (note that the numbers are slightly different because of rounding).

The upper control limit for the S chart is

3.267*0.15=0.49.

The distance from the center line to the upper control limit is

0.49-0.15=0.34.

The warning limit is placed at 2/3 of the distance from the center line or

0.15+0.34*2/3=0.38.

Here is the S chart (note again some slight discrepancies due to rounding).

Creative Commons License This work is licensed under a Creative Commons Attribution 3.0 United States License. It was written by Steve Simon.

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Control charts.