At work one of our projects has been to monitor a certain type of mechanical system and identify anomalous behavior. Luckily for us we have access to 5+ years of system performance across many different operational settings and different units (same type of system but different physical unit).
Our initial approach has been fairly successful. We ended up using SPC with standard WECO rules assuming that the parameters we monitor have a constant variation or standard deviation regardless of operating conditions but that the mean will vary with said conditions.
In practice the variation isn't truly constant, and the upper and lower control limits aren't typically symmetric about the mean performance measures. Given that we essentially have a populations worth of data (or close to it) what is the statistically correct way to remove these assumptions?
Additionally we have been contemplating going away from the standard WECO rule set and developing our own based on probability and our observations with identified failure modes. I'd be curious to know if there are some best practices there again assuming that we have essentially a populations worth of data.
