Constraint set-up in an optimal design

[#1]

Hello,

I am a new user of JMP and i have some issues with my first optimal design.

The aim is to add 1 additive to a polymer to make the process easier => find the additive the most efficient and the lowest level. So, I have 2 type of mould (categorical), 2 grades of polymer (continuous) and 6 type additives (categorical).

I have defined as values for the polymer the lowest and highest pourcentage of additive (0.2 - 1.4%).

Now, I have to define linear constraints but I don't know how to define them.

I have already read the dedicated part in the DOE guide but it's not clear.

Thank you in advance for your help

Olivier

[#2]

What are the linear constraints you wish to define?

[#3]

In fact, each additive has specific rates (low and high) and they are different for each product.

Limits of continuous factor (polymer) correspond to the lowest and highest level  for all additives.

So, with the linear constraints, I would like to restrain more the level for each additive.

I hope my answer is clear.

[#4 · Accepted solution]

Thanks for the details of your experiment. I think you said that you already defined the additive level this way but make sure that the definition spans the full range of additive level. You won't be able to use the linear constraint in this case because of the categorical factors. I recommend using Disallowed Combinations Filter where you can specify the conditions to be excluded with the same user interface as a Data Filter.

Follow these steps:

1. Open the Define Factor Constraints outline.
2. Select Use Disallowed Combinations Filter.
3. Select Polymer Grade and Additive.
4. Click Add.
5. Select the first level of Additive.
6. Set the disallowed range of Polymer Grade.
7. Click OR and repeat steps 3-7 for all disallowed combinations.

Here I mocked up your experiment where the Polymer Grade should be restrained to 0.2 to 1.2 for Additive 1 (so disallow 1.2-1.4) and 0.4 to 1.4 for Additive 2 (so disallow 0.2-0.4):

Also, be careful that you do not restrict the range unnecessarily. Of course I do not know your reasoning for these restrictions but it is tempting to guess at the region where the performance is the best and restrict the range accordingly. This approach has several disadvantages. You might guess wrong. Your restricted range will produce a smaller effect in the response. The parameter estimate will have higher variance. The power to find a significant effect will be lower. You might even cause a singularity where the set of all disallowed regions does not permit estimation of all the parameters in your model. So always keep the ranges as wide as possible because, unlike a test, the purpose of an experiment is to provide the best, most powerful data to support the estimation of the model.

[#5]

Here is the JMP script that you can run to reproduce the mock up I made so you can see how it is done and adjust it to suit your purpose.

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ),
	Add Factor( Categorical, {"M1", "M2"}, "Mould", 0 ),
	Add Factor( Continuous, 0.2, 1.4, "Polymer Grade", 0 ),
	Add Factor( Categorical, {"A1", "A2", "A3", "A4", "A5", "A6"}, "Additive", 0 ),
	Set Random Seed( 66045 ), Number of Starts( 3834 ), Add Term( {1, 0} ),
	Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ),
	Add Term( {1, 1}, {2, 1} ), Add Term( {1, 1}, {3, 1} ),
	Add Term( {2, 1}, {3, 1} ), Set Sample Size( 24 ),
	Disallowed Combinations(
		Polymer Grade >= 1.2 & Polymer Grade <= 1.4 & Additive == 1 | Polymer Grade
		 >= 0.2 & Polymer Grade <= 0.4 & Additive == 2 | Polymer Grade >= 0.2 &
		Polymer Grade <= 0.5 & Additive == 3 | Polymer Grade >= 1 & Polymer Grade
		 <= 1.4 & Additive == 4 | Polymer Grade >= 1.2 & Polymer Grade <= 1.4 &
		Additive == 5
	), Simulate Responses( 0 ), Save X Matrix( 0 )}
);

[#6]

I should say the the filter user interface is only available when you define the constraints. It is replaced with the actual Boolean expressions written in the JMP scripting language. I think that the picture and explanation above should make the expressions clear. You should be able to modify them to suite your situation.

[#7]

Many thanks Mark for your help.

Yes, all additives have an optimal range of dosage. In an other side, we have also some economical restriction as the use of the additive should not be higher than a specific cost.

I will implement your process.

One more time, many thanks !!!