I have a question related to the use of p-chart in a process where there are defect rates measured.

The control limits for this type of chart is calculated with +/- 3 sigmas around the mean (with

*mean = np*and

*sd = sqrt(n*(1-p)*p*))

As it is using i +/- 3 sigmas it assumes that we can approximate the binomial distribution by a normal distribution, am I right?

NB: for a normal process, control limits computed with mean +/- 3 sd gives 0.27% probability of being out of control limits

From approximating the binomial with a normal distribution, it is commonly said that the binomial distribution must meet this criteria:

np >= 5 and n*(1-p) >= 5

**Why this condition is never mentioned (as I know) in most statistical books dealing with SPC?**(Such as Statistical Quality Control - Douglas C. Montgomery)

In practice, when having a binomial distribution with very small p and using control limits proposed (np +/- 3 *

*sqrt(n*(1-p)*p*)), the control limits when following the control limits formula is not appropriate.

**Has anyone dealt with a control chart monitoring defect rates with small values of p?**For your information, n = 72000 and p = 0.000009

Thank you.