J
Here is an interesting point. You can plug in all sorts of data into all sorts of equations, but there are some empirical statistical concepts that you need to consider. First what is the point of the question? Is the point to determine what your ongoing sample size should be if you know your Cpk (and...assuming your Cpk is even valid, which should always be called into question)?
If so, then the next empirical statistical point is that the lower the probability of defect (higher Cpk) the larger your sample size has to be. It reaches 100% very quickly. Why?The fewer rejects, the harder they will be to find - pure and simple. Think needle in a haystack. Would you assume the fewer needles you have, the less hay you would need to dig through to find them? Well, the same issue applies to sampling. So, seeking out any statistical method that would support lesser size sample when your capability is greater does not end up making any sense if you think of the point of the exercise.
If so, then the next empirical statistical point is that the lower the probability of defect (higher Cpk) the larger your sample size has to be. It reaches 100% very quickly. Why?The fewer rejects, the harder they will be to find - pure and simple. Think needle in a haystack. Would you assume the fewer needles you have, the less hay you would need to dig through to find them? Well, the same issue applies to sampling. So, seeking out any statistical method that would support lesser size sample when your capability is greater does not end up making any sense if you think of the point of the exercise.
What if the purpose of sample is not to detect but to demonstrate ongoing capability?
