Stats
Calculating a P control chart (March 7, 2007).
Category: Control charts
If you are collecting data on proportions with a consistent denominator for each
proportion, then you can plot this data on a control chart. This type of chart is called a P
chart and it is very simple to calculate. Here is an example of some data that is appropriate
for a P chart. An employee was asked to take a hearing test on 24 consecutive weeks. The
hearing test consisted of listening to and trying to recognize 50 spoken words that were
recorded with some background noise. The score is the percentage of words recognized
correctly. This data set is loosely adapted from a larger data set at
Here is the data:
28 24 32 30 34 30 36 32 48 32 32 38
32 40 28 48 34 28 40 18 20 26 36 40
The formula for the upper and lower control limits is
where pbar is the average of the individual proportions and n is the denominator for each
individual proportion. If you want to compute upper and lower warning limits, the formula for
these is
The average proportion is 0.3275 and n is 50. The control limits are computed as
Here is what the control chart looks like:
Notice that all data points are inside the upper and lower control limits and that we do
not observe 2 out of 3 consecutive points outside the warning limits. Neither do we see eight
consecutive points on the same side of the center line. Thus, this process is in statistical
control. This individual's hearing may not be all that good, but there are no unusual
deviations from what you would normally expect.
On your own. Two other workers also took the same series of hearing tests (see data
below). Compute a P chart for each worker. Don't peek until you've done the work, but the
answers are available on a separate web page.
Worker #2:
60 56 78 60 74 70 70 68 82 76 72 76
68 78 76 68 74 56 74 62 60 70 60 84
Worker #3:
34 42 30 24 42 32 30 36 36 48 40 26
46 42 48 24 36 24 48 30 24 28 32 44
07/08/2008.
