Model process parameter interactions with process timeHello everyone,
I have a 3 step process with 7 factors A, B, C, D, E, F, G and a single response Y.
Step 1: A and B are some continuous machine settings and C is the time for which those settings are applied
20 <= A <= 100
300 <= B <= 700
30 <= C <= 180
Step 2: D and E are continuous factors for a treatment that is applied to the samples after step 1.
Step 3: F and G are discrete numeric factors for a post conditioning that is applied done to the samples after step 2.
I am trying to estimate main effects and 2 way interactions within the above limits as well as 3 way interactions for step 1. I am also interested in what happens if I omit step 1 altogether, which is the giving me the headache here. My naive approach was extending the limits of time C in step 1 to 0, i.e. 0 <= C < 180, but that of course creates nonphysical runs where C = 0 but A, B are at some factor level. It feels wrong to me to have such runs, but then again, that would probably result in A and B being insignificant factors , but the interactions with C might then be significant, which does not sound to far off from the physical reality of the problem.
I feel like I am missing something obvious here in how to construct an appropriate design for such a problem and I'd be grateful for any help I can get!
Many thanks!
DOERe: Model process parameter interactions with process timeWelcome to the community. I don't have enough information about your situation to suggest an appropriate strategy, but I do have some thoughts/questions:
1. If you really want to omit step 1, can you measure the current output of step 1? Can you treat the output of step 1 as a covariate? If you want to omit it, why are you doing it? What is being machined? I'm trying to guess what you are manipulating and why there might be a time effect? Is it a lapping/honing operation (surface finish)? Or a curing operation?
2. Can anything be measured after each step in the sequence?
3. Have you tried directed sampling vs. DOE? You may be able to use a nested sampling plan to provide clues.
4. Is the measurements system for the response adequate? Has it been studied?
5. You say your are interested in the factorial effects from step 1, but no mention of what effects you want from steps 2 or 3?
6. Sequential step experiments are ideal for split-plot designs.
Re: Model process parameter interactions with process timeI completely concur with @statman. Please see the JMP Help about split-plot designs. You will treat the upstream factors as hard-to-change and very hard-to-change factors because they are randomized less often that the factors in the last step. The randomization aspect of how you conduct your experiment is important in the modeling of the random effects of changing factor levels.
