In a production line, random samples are drawn to be tested for properties A and B. A has to be tested at a higher cadence than B and the assumption is that A and B have zero correlation.
Since the testing destroys the product, it is desirable to test a sample for both A and B, so my questions is, would it be statistically correct to extract the samples needed to test for A, and then from this subset extract the samples needed to test for B, so that for each sample that is tested for A there is a certain chance that it will also be tested for B? Would the samples that are tested for B truly be a random subsample of the production or would I introduce a bias?
The testing is a continuous and ongoing process, where every product has a certain (small) chance of being selected for testing, such that, on average, 0.1% is tested for A and 0.02% is tested for B.