p- and c-Charts

In order to monitor proportions of a process, such as the proportion of defect products in a production line, we can use either p-charts or c-charts.

p-charts display the fraction of outcomes of a process which do not, or do obey some rules. The lower and upper control limits are again set in a way that the probability of a fraction falling outside these limits is quite low (i.e. <1 %). The lower control limit may often fall below zero, which does not make any sense in connection with fractions; in this case the lower control limit is set to zero.

The control limits are usually set by the following equations:

with  being the mean of n proportions considered. Note that the band of tolerance is given by +/- 3 standard deviations of the distribution of proportions (binomial distribution).

A c-chart is quite similar to the p-chart, except that in this case the special outcomes (like defects) of a process are counted. The control limits are given by

again forming a band of +/- 3 standard deviations of an assumed Poisson distribution.