Introduction – updated 2020-11-22
When a process is at steady state (SS), we can claim that a transient has ended, and use data to adjust steady state models, take data for an experimental run, use the data to analyze process performance, claim convergence in a procedure, etc. Alternately, when a process is in a transient state (TS), the data are useful for adjusting model coefficients that represent delays and time-constants. Further, recognition that a TS has begun can be used to wake-up response to change.
It would be nice to have a procedure that can be automated to identify steady-state (SSID) or a transient-state (TSID). Such a procedure needs to be robust to diverse phenomena, easy to understand, and computationally simple. I think the method of S. Cao and R. R. Rhinehart (“An Efficient Method for On-Line Identification of Steady-State,” Journal of Process Control, Vol. 5, No 6, 1995, pp. 363-374) is a good one for independent and uncorrelated random data. I’ve been especially pleased with it as a method of identifying steady state for determining convergence in regression and stochastic optimization. However, an appropriated Statistical Process Control, Shewhart X-Bar and R analysis seems best in performance, and a 4-Point approach related to it is nearly as good in performance and much simpler.
This tutorial r3eda site SS&TSID Tutorial 2019-05-08 develops, explains, and analyzes five different techniques. Use the macro-enabled Excel file (like below) that demonstrates the five techniques on simulated data. Or, you could import your own data and test the techniques on that.