How do I draw an OC curve for a double sampling plan.... WITHOUT using COMPUTER :confused: .... just using scientific calculator and maybe using standard tables...

Lot Size = 1200

First Sample
Sample size=50
Acceptance number=1
Rejection number=4

Second Sample
Sample size=110
Acceptance number=5
Rejection number=6


I know how to draw for OC curve for single sampling plan i.e. Pa vs Fraction defective.... using the poisson table approximation...

Calculating OC curves certainly could be done without a computer, but it would get very tedious.

An OC curve predicts the probabilty of accepting a lot given the "true" percent defective produced by the process. To do this for a single sampling plan is relatively straightforward - just use the binomial distribution (or Poission distribution if multiple defects per itme are possible) and calculate the odds of accepting a lot. You will need to repeat the calculation for many defect rates and then "connect the dots" to get the curve. It sounds like you know about this part of the calculations.

For multiple sampling, you would have to worry about conditional probablities when the 1st sample is inconclusive. For example, with your numbers (and using Excel and the binomial distribution), if the true defect rate would be 5%, then the probabilty of finding no more than "n" defects would be

# found Probabilty
0 0.076945
1 0.279432
2 0.540533
3 0.760408
4 0.896383
5 0.962224
6 0.988214
7 0.996812
8 0.999244
9 0.999841
10 0.99997


Since you accept 1 defect, you would accept 27.9% on the first test.
Since you reject 4 defect, you would reject (1-0.760) = 24.0% on the first test.

That leaves 100% - 27.9% - 24.0% = 48.1% that needs re-testing.

Then you calculate the probabilities of accepting or rejecting the lot the second time. In your case and still using 5% defctive, I get
52.7% will be accepted on retesting, which is 48.1% * 52.7% = 25.3% of the total lots.
100%-52.7% = 47.3% will be rejected on retesting, which is 48.1%*47.2% = 22.7% of the total lots.

So assuming I haven't made any mistakes,
* 27.9% + 25.3% = 53.2% get accepted
* 24.0% + 22.7% = 46.7% get rejected.

That's just the first point on the OC curve. :bonk: Now repeat for several other % defective and plot all the points.

Tim F