Hello everyone,
I'm new in the community, sorry by advance if I post at the wrong place or if the question has been already answered. My issue concerned factors of DOE when they are not independant. In my example, it concerns the pressure step. For confidentiality reasons, I remove steps of the process and simplify the "recipes".
Context :
The DOE concerns the process in a reactor in a cocoa factory.
Process : We put cocoa in the reactor (like a pressure canner), realize the recipe and then empty the reactor for the next process.
A recipe has 3 steps : Inject Steam, Apply Pressure in the reactor, Inject Air to dry the product. The order of the steps is important and not changed during this DOE.
Aim : See the impact of the steps and optimize the recipe
Answer : pH of the end product
We have 3 recipes possible today :
Recipe 1 : No pressure step in the recipe. 0 min at 0 bar
Recipe 2 : Pressure at an intermediate level. 10 min at 1 bar
Recipe 3 : Pressure at an high level. 30 min at 2 bars
If I want to cover the 3 recipes in 1 DOE, I need to have some trials with pressure and some without pressure.
Issue :
How to manage linked factors as the pressure ? With a classic DOE I risk to have impossible designs (like 0 min at 2 bars or 30 min at 0 bar)
Parameters | Pressure 0 min | Pressure 30 min |
Pressure at 0 bar | Possible | Not possible |
Pressure at 2 bars | Not possible | Possible |
What I have already done :
To compensate this issue, I realized two DOE , one with no pressure and the other with pressure step. I put the two DOE tables in one table and then analyze the data with linear regression model.
But I have the feeling that it is not the better way because :
- My data are not well balanced, I'm afraid to have biais due to the number of trials per "recipe"
- Maybe the Factor Constraints option could be useful. When I tried Disallowed Combinations Filter , I add pressure as categorical factor (yes/no), it didn't work (maybe I miss something)
Please find attached my data.
Best regards,
Julia
Hi @JuliaL,
From what I understand, it seems your process involves multiple steps ordered and linked one after another (you can't change factors levels independantly/randomly between several steps ?).
So you seem to be in a Split-Split-Plot design situation, with "very hard" to change factor ("Time of steam injection" in step 1), "hard to change" factors (those in step 2) and "Easy to change" factors (those in step 3, applied after all the ones from step 1 and 2).
About the step 2, do you want to only test these 3 recipes or would you like to test other combinations, so that the pressure and time factors could be tested independantly ?
If you have no other options than these 3 recipe, maybe you could merge these factors into a single categorical factor "Pressure recipe" with 3 levels :
Recipe 1 : No pressure step in the recipe. 0 min at 0 bar
Recipe 2 : Pressure at an intermediate level. 10 min at 1 bar
Recipe 3 : Pressure at an high level. 30 min at 2 bars
With these possibilities, I created a Split-Split-Plot design that could match your requirements :
- Definition of response and factors :
- Model specification (Response Surface Model, but you can change it based on your needs) :
- Resulting design with 40 runs, 5 whole plots (5 conditions for Step 1), 10 subplots (10 conditions for step 2 factors) :
This specific split-plot design structure helps you to realize batch experiments for ordered process steps and helps you save more time. If you can vary more the levels of the factor in step 1, you can increase the number of whole plots (you'll have more conditions changes in the design for factor in step 1). If you can vary more the levels of factor in step 2, you can increase the number of subplots (you'll have more conditions changes in the design for factor in step 2, but the subplot should be a multiple number of the whole plot number). Finally, you can also increase the total number of runs depending on your ressources.
It's a good idea to test several design and use the platform Compare Designs to choose the most relevant and practical one.
Please find attached the corresponding datatable for the design.
Hope this answer might help you,