Hi @Bertelsen92,
Which effects would you like to see in the models ?
For the screening of main effects, I'm able to create a 32-runs in 4 whole plots (so 8 runs per day like you mentioned), where you only have one process per day.
Here is the script :
DOE(
Custom Design,
{Add Response( Maximize, "Y", ., ., . ),
Add Factor( Continuous, -1, 1, "X1", 0 ),
Add Factor( Continuous, -1, 1, "X2", 0 ),
Add Factor( Continuous, -1, 1, "X3", 0 ),
Add Factor( Continuous, -1, 1, "X4", 0 ),
Add Factor( Continuous, -1, 1, "X5", 0 ),
Add Factor( Continuous, -1, 1, "X6", 0 ),
Add Factor( Continuous, -1, 1, "X7", 0 ),
Add Factor( Continuous, -1, 1, "X8", 0 ),
Add Factor( Categorical, {"L1", "L2"}, "Process", 1 ),
Set Random Seed( 235758137 ), Number of Starts( 1574 ), Add Term( {1, 0} ),
Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ),
Add Term( {5, 1} ), Add Term( {6, 1} ), Add Term( {7, 1} ), Add Term( {8, 1} ),
Add Term( {9, 1} ), Add Alias Term( {1, 1}, {2, 1} ),
Add Alias Term( {1, 1}, {3, 1} ), Add Alias Term( {1, 1}, {4, 1} ),
Add Alias Term( {1, 1}, {5, 1} ), Add Alias Term( {1, 1}, {6, 1} ),
Add Alias Term( {1, 1}, {7, 1} ), Add Alias Term( {1, 1}, {8, 1} ),
Add Alias Term( {1, 1}, {9, 1} ), Add Alias Term( {2, 1}, {3, 1} ),
Add Alias Term( {2, 1}, {4, 1} ), Add Alias Term( {2, 1}, {5, 1} ),
Add Alias Term( {2, 1}, {6, 1} ), Add Alias Term( {2, 1}, {7, 1} ),
Add Alias Term( {2, 1}, {8, 1} ), Add Alias Term( {2, 1}, {9, 1} ),
Add Alias Term( {3, 1}, {4, 1} ), Add Alias Term( {3, 1}, {5, 1} ),
Add Alias Term( {3, 1}, {6, 1} ), Add Alias Term( {3, 1}, {7, 1} ),
Add Alias Term( {3, 1}, {8, 1} ), Add Alias Term( {3, 1}, {9, 1} ),
Add Alias Term( {4, 1}, {5, 1} ), Add Alias Term( {4, 1}, {6, 1} ),
Add Alias Term( {4, 1}, {7, 1} ), Add Alias Term( {4, 1}, {8, 1} ),
Add Alias Term( {4, 1}, {9, 1} ), Add Alias Term( {5, 1}, {6, 1} ),
Add Alias Term( {5, 1}, {7, 1} ), Add Alias Term( {5, 1}, {8, 1} ),
Add Alias Term( {5, 1}, {9, 1} ), Add Alias Term( {6, 1}, {7, 1} ),
Add Alias Term( {6, 1}, {8, 1} ), Add Alias Term( {6, 1}, {9, 1} ),
Add Alias Term( {7, 1}, {8, 1} ), Add Alias Term( {7, 1}, {9, 1} ),
Add Alias Term( {8, 1}, {9, 1} ), Set N Whole Plots( 4 ), Set Sample Size( 32 ),
Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
);
And attached you can find the datatable.
The trick is to specify your 2-level categorical factor "Process" as a hard-to-change factor, and specify 4 as the number of whole plot (4 days) and 32 as the number of runs (8 runs per day). Note that for screening main effects, you could reduce the number of runs if needed (but it should be a multiple of the number of experimentation day, so if you keep 4 days, you can reduce to 28 or 24 runs for example) :
If I misunderstand your objective and/or design specifications, don't hesitate to add more details and explanations, so we can find a better solution.
I hope this will help you,
Edit: This design doesn't seem to respect your constraint of having only 4 different mixtures/day, so increasing the number of whole plots to 8 (and doing 2 whole plots of 4 experiments each per day) with the same number of runs could be an alternative, I have to check later if it works.
Sorry for the misunderstanding,
Sorry, I was naively thinking that the problem was to avoid having more than 4 stabilizers per day, but I didn't think about the complete formulation and the relation stabilizer - dosage.
I think removing the blocking factor "day" and switching both "Stabilizer" and "Dosage" as "Hard to change" factors should respect the constraints of the 4 formulations per day :
And give you slightly higher power for "stabilizer" main effects (at the expense of lower power for "dosage" main effect) :
The low power score for stabilizer main effect may be explained by the number of levels of this main effect (if you had no constraints, the highest achievable power for each level of stabilizer for 32 runs with the same model would be 0,454...) and the constraints on randomization.
I can try other options and come back to you if I'm able to find something interesting.
Hi Kristian,
It really depends what is the objective of your study, there is no definitive answer.
If you want to screen and select the best stabilizers in general, perhaps the information about the dosage is indeed not so important. But it could also have several implications/questions :
- Could the quantity of stabilizer have an influence on the rest of the ingredients of the formulation (synergistic or antagonistic effects) ?
- Could it be that behaviour of stabilizer is not linear, and fixing an "arbitrary" value of dosage would make you miss a potential important/powerful stabilizer (see graph below) as there could be different "activation"/performance concentrations depending on the chemistry of the stabilizer ? :
.PNG){kind=link}
.PNG){kind=link}
If the study concentration is fixed and below the threshold of this graph, then stabilizer A would not be retained/kept for optimization, as it can be seen as having no influence on the response. But on the opposite, if you study its effects on a range, you would have a better appreciation of its behaviour and performances, and not only a single point estimation of its performance.
Another option could be to focus first on main effects only in your model (or at least mainly on main effects Stabilizer type, dosage, process, and reduce the interaction terms in the model to have more power for the terms in the model), and then augment your initial design based on identified significant effects ? You would have more power for stabilizers main effect, so the differenciation/discrimination between different stabilizer could be easier, and you could augment the initial design only on stabilizers that show some performances.
Or perhaps you already have some data, and you could augmenting your intial dataset with new experiments through the platform "Augment Design" (and use the option "Group new runs into separate block") ?
You can have more informations on significance level and anticipated RMSE here : Power Analysis (jmp.com)
- Power is the probability to detect an effect, if it is significant. Power equal to 1 means that you can detect this effect (if significant) 100% of the time, for a certain value of significance level and Anticipated RMSE. I highly recommend the video from the Youtube channel Statquest, it helps me a lot understand statistical concepts. There is one excellent video on Power analysis : Power Analysis, Clearly Explained!!! - YouTube
- Significance level shown in this platform is also known as the alpha risk : you commonly see the alpha risk in statistical test like Student T-test for example (to evaluate if there is a difference in a response between two groups). The significance level is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis. More infos here : Significance level - Statistics By Jim
- Anticipated RMSE is the "level of noise" in your response (square root of the error variation). The higher the value, the higher the noise/variance in your response, the harder it is to determine a significant effect, so the lower your power for your effects will be. You could see it as the ratio Noise/Signal : if you have a lot of noise, Anticipated RMSE will be higher, and your power calculations for the effects will be lower. By default the calculations are done with a value of 1 (which is helpful to compare different designs on the same basis), but if you already have an idea about your measurement variance, you could enter a different value reflecting this knowledge to have more relevant Power calculations. More infos here : Example of Evaluating Power Relative to a Specified Model (jmp.com)
I hope these options will help you in your reflexion,