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).  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.