We discovered that a process is resulting in a defect rate of 14% for some batches.

Each batch of product contains 2,500 units.

I want to sample each batch to determine if the problem exists in that batch or not, to a 95% confidence level. I need to calculate the sample size required that will give me a 95% chance of detecting the problem.

I have performed a calculation using probability where we sample without replacement and based on this it gives me a sample size of 20 per batch, which shows we should be 95% confident of identifying a defective unit. Data below.

I also considered solving this problem using the Binomial distribution with Minitab, but this seems to give me a different answer.

Is this a sound approach or can you suggest an alternative?

Unit No. good Total post sample Prob. Good unit Prob. next pump good

1 2150 2500 0.86

2 2149 2499 0.860 0.740

3 2148 2498 0.860 0.636

4 2147 2497 0.860 0.547

5 2146 2496 0.860 0.470

6 2145 2495 0.860 0.404

7 2144 2494 0.860 0.347

8 2143 2493 0.860 0.299

9 2142 2492 0.860 0.257

10 2141 2491 0.859 0.221

11 2140 2490 0.859 0.190

12 2139 2489 0.859 0.163

13 2138 2488 0.859 0.140

14 2137 2487 0.859 0.120

15 2136 2486 0.859 0.103

16 2135 2485 0.859 0.089

17 2134 2484 0.859 0.076

18 2133 2483 0.859 0.066

19 2132 2482 0.859 0.056

20 2131 2481 0.859 0.048

21 2130 2480 0.859 0.042

Thank you for reading,

Joe