Introduction – updated 2024-04-19
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.
SSID and TSID is also covered in my book on Applied Engineering Statistics.