Bev D said:
yes the theoretical requirement for the Poisson is not met. This is a consistant problem with very low defect rates...but we must remember that both teh Poisson and the Binomial are only models and estimates. The real proof is if they are useful for need. (to paraphrase George Box). Other factors suchas how the samples are taken and how the defects may or may not cluster will add more 'inaccuracy' to the result thant the choice of distributional model. and as you point out the differences are slight anyway.
I choose to use the Poisson in most cases (not all) because it is easy to calculate
But of course the real point here is that with small defect rates we need to stop looking for proportional sampling plans and begin assessing alternatives sucha s poke yoke and continuous data plans. you simply cannot guarantee zero defects with proportional sampling plans adn this is where so much of industry is headed - an drightly so in my opinion.
I choose to use the Poisson in most cases (not all) because it is easy to calculate
But of course the real point here is that with small defect rates we need to stop looking for proportional sampling plans and begin assessing alternatives sucha s poke yoke and continuous data plans. you simply cannot guarantee zero defects with proportional sampling plans adn this is where so much of industry is headed - an drightly so in my opinion.