2
$\begingroup$

I'm trying to figure out what statistical test to use to determine when a chemical process has reached steady state for temperature and the process for a process tool. For example I have a process where I'm ramping the temperature up to 100 °C and monitoring the output in ppm. I can visually see when the temp and process has hit steady state but I would like to use a statistical test to show this.

Here is an example of the data set (The actual data set is measure in seconds over the course of 4 days) I'm working with :

Time               Temperature    ppm
2018-01-30 11:30   25             90
2018-01-30 11:31   50             120
2018-01-30 11:32   75             150
2018-01-30 11:34   100            175
2018-01-30 11:35   101            205
2018-01-30 11:36   102            195
2018-01-30 11:37   99             200
2018-01-30 11:38   102            205
2018-01-30 11:39   101            195
2018-01-30 11:40   100            200

Visually I can see the temperature has reached steady state around 11:34 and the output has reached a steady state around 11:35 (±5 ppm). My thought is to take a moving average and then take the derivative to show the rate of change has reached zero. Is there a better way to show this statistically?

Improve this question
$\endgroup$
3
  • $\begingroup$ Try to take a window sample of Temperature values, and conduct a stationarity test on these values. I will think later on what best test suits the goal. $\endgroup$
    – alexeymosco
    Commented Apr 25, 2018 at 16:21
  • $\begingroup$ I think it could be done by R base functions as follows: first, fit a linear model of the form Temperature ~ Time. Test a hypothesis that the Time coefficient is not different from zero. Next, take the model's residuals and test whether their variance is constant. As a simple way to do (maybe not the rightest one) is to divide the residuals into two equal parts (time_1, and time_2) and run ANOVA where you test whether the variance of residuals is different between parts. If at least one of the 2 p-values you will get are greater than alpha, you cannot reject hypothesis of non-stationarity. $\endgroup$
    – alexeymosco
    Commented Apr 25, 2018 at 16:39
  • $\begingroup$ Classic control systems use a Shewhart chart and previous work to figure it out. itl.nist.gov/div898/handbook/mpc/section2/mpc22.htm $\endgroup$
    – EngrStudent
    Commented Feb 16 at 20:29

1 Answer 1

Reset to default
1
$\begingroup$

The temperature ramp looks like it is a controlled process, probably with a PID control algorithm. In that case there seems to me that there is no need to do statistical analysis: you know more about the system than statistics do (does?). Statistical approaches are not always best...

Test it a few times to see if there is any overshoot (there is none in the data you supplied) and then you know how long to wait for it to be steady after it reaches the set point. If there is no overshoot then as soon as it reaches the set point then it is steady!

Then your task would be to determine how long it takes for the ppm to reach a steady state after the temperature is steady.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.