XBAR-S control chart, answers to on your own exercise

Steve Simon


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

The warning limits are

1.09+2.659*0.15*2/3=1.36 and

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


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


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


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

You can find an earlier version of this page on my old website.