What is the best way to put a specification on the single-side auto-power spectral density (PSD)?
We have a product for which we have a time signal. For this signal we calculate the PSD (or respectively the cumulative PSD or 3 sigma cumulative PSD) to determine the frequency behavior. However, each product shows slightly different behavior. Currently analysis to determine if behavior is OK is done on visual inspection of the PSD.
Now we would like to put a specification on this for the frequency range. Such that we can more easily determine if something is OK or NOK.
Does someone know how specifications are set on a PSD? How is this is done in industry for frequency data?
For continuous time domain signal you can simply set a lower and upper spec limit. Furthermore you can apply statistical process control for discrete data.
What I currently thought of; get a population of good products. Use the PSD results to calculate an mean PSD and the variance of the PSD (for each frequency point). Then all frequency data can be normalized by the standard score $(X - \mu)/\sigma$. As such giving flat lines for data which is OK, and for data which is NOK you would see deviations.
Then the spec, as an example, could be mean plus four times the standard deviation, for which we could get triggered.