I tried using the poisson approximation for these types of questions but am still a little unsure of their outcome.

The approximation basically uses: Z=Xa-lamda/SQRT(lamda), where:

lamda = mean or C bar

SQRT lambda = standard deviation of the c-chart

Xa=Cbar-.5 or Cbar+.5 as appropriate.

What are your thoughts on using the above?

Here is one of the questions: Using c charts, you inspect 40 units and find 85 imperfections, assuming the processing is in statistical control calculate:

3 sigma control limits

Prob of type I error, and prob of type 2 error should the mean shift to 5.2.

I calculate my C bar to be 2.125., UCL=6.50, LCL=0 (since <0).

For prob of type one should i use Z=((6.5+.5)-2.125)/SQRT(2.125)=3.34 or Z=((6.5-.5)-2.125)/SQRT(2.125)=2.65.

For prob of type two, should i use Z=((6.5+.5)-5.2)/SQRT(2.125)=1.23 or Z=((6.5-.5)-5.2)/SQRT(2.125)=.548.

Thank you!