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

Steve Simon

2007-03-02

Categories: Blog post Tags: Control charts

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).