If each sample taken has 500 units, and the average proportion nonconforming is 0.034, what is the upper and lower control limits for the p-chart?

The control limits are set at +- 3 standard errors. For this sort of yes/no process the standard errors are given by sqrt(p(1-p)/n) where p is the probability of nonconforming and n is the sample size.

Thus, this is the upper control limit:

UCL = p + 3 * sqrt(p(1-p)/n)

This is the lower control limit:

LCL = p - 3 * sqrt(p(1-p)/n)

Since p = 0.034 and n = 500, sqrt(p(1-p)/n) = 0.0081

Therefore these are the upper and lower control limits:

UCL = 0.034 + 3*(0.0081) = 0.0583

LCL = 0.034 - 3*(0.0081) = 0.0097

We will estimate that the process is under control as long as the observed nonconforming rate is between 0.97% and 5.83%.