Since I was preempted for the comment "this is typical quality-control ad-hockery BS", I'll play devil's advocate and argue that the point of quality control is

Since I was preempted for the comment "this is typical quality-control ad-hockery BS", I'll play devil's advocate and argue that the point of quality control is to identify two components of a mixture distribution[0]: a bounded distribution of uncertainty, which can be modeled as a beta ("PERT", in some patois), and an unbounded, "error" term that functions more like a Poisson or even a Pareto. This is already an adhockish simplification of something like Mandelbrot's seven regimes of randomness [1], which is itself, well, an oversimplification of his own work. But it formalizes the insight that quality-control is trying to impart -- the identification of inconsistencies among consistent variation. So let's run some simulations in Matlab. We'll generate M numbers distributed like Beta and N like a Pareto (a "long tail", "black swan" distribution) with identical mean and standard deviation, and shuffle them before we interpret them as a time-series. Then we'll check Nelson's rules. Since we know how many ordinaries there are, we have a target. In 10^4 repeated simulations each with samples of 180 ordinary betas and 20 Paretos, we expect to identify 10% of abnormals. Now, my samples are shuffled, and Nelson rules rely on time-structure (but this is precisely their weak spot); my code [2] also has visible bugs I didn't bother to fix because they'd involve thinking too hard and didn't seem so serious in large samples. Still, here are identification rates: - Rule 1: 0.5%. This will be counter-intuitive to students of the normal distribution, but recall that the ordinary observations have a bounded distribution and we're really catching only the abnormals. Now, we've missed a lot of the 10% by this rule. - Rule 2: 6.32535% - Rule 3: 3.4421% - Rule 4: 4.484% - Rule 5: 27.83735%. This is the "medium tendency for samples to be mediumly out of control". - Rule 6: 8.49465% - Rule 7: 4.38775% - Rule 8: 2.1294% (Edited after some bug fixes that, comfortingly, didn't change the results by much!) [0] https://en.wikipedia.org/wiki/Mixture_distribution https://en.wikipedia.org/wiki/Mixture_distribution [1] https://en.wikipedia.org/wiki/Seven_states_of_randomness https://en.wikipedia.org/wiki/Seven_states_of_randomness [2] http://lpaste.net/137664 http://lpaste.net/137664