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Harry Nyquist would probably have something to say about the validity of rule four. Fourteen points in a row of alternating increasing and decreasing isn't just indicative of an oscillation, but an oscillation that's close enough to your measurement frequency that you aren't actually able to measure it accurately. It could be a real oscillation, or it could be an artifact of much higher frequency behavior.

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I think Rule 4 is valid because it is intended to catch both situations you describe: oscillations at approximately the Nyquist frequency and also much higher frequency behavior (Rule 8 is intended to catch oscillations below the Nyquist frequency).

In any of these cases, the Nelson Rules state that the signal is unlikely to be a stochastic random variable around the given mean. It is instead likely to have some underlying shape that is not being described.

The thing is, something going on above the Nyquist frequency could create ANY of the Nelson rule patterns - or none of them. Expecting it to create a nice alternating up/down pattern is wishful thinking.

Yeah but the rule isn't "if this doesn't happen everything is fine", rather "if this happens, something's probably wrong".

I'm also thinking that in the case of rule 2 or 3 you could also have an oscillation that has a frequency close to or equal to the acquisition frequency.

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