P-charts are used to measure the proportion that is defective in a sample. The computation of the center line as well as the upper and lower control limits is similar to the computation for the other kinds of control charts. The center line is computed as the average proportion defective in the population, . This is obtained by taking a number of sample observations at random and computing the average value of p across all samples.
A control chart that monitors the proportion of defects in a sample
To construct the upper and lower control limits for a p-chart, we use the following formulas:
where z = standard normal variable
= the sample proportion defective
σp = the standard deviation of the average proportion defective
As with the other charts, z is selected to be either 2 or 3 standard deviations, depending on the amount of data we wish to capture in our control limits. Usually, however, the deviations are set at 3
The sample standard deviation is computed as follows
where n is the sample size.
EXAMPLE 6.4 Constructing a p-Chart
A production manager at a tire ...