Problem with adding midpoints to my design (they are not randomly distributed)

[#1]

Dear Community,

I have created a design with 12 factors, 11 of them are continuous and the last one is discrete numeric with three levels. I decided to add 30 midpoints (see attached screenshot of the experimental design). Why are the factors of the midpoints not randomly distributed?
I tried the model with fewer factors, and the midpoints were randomly distributed as desired.
I also tried increasing the search time and starting points of the model design, but that didn't help.
What is the problem?
If you want more details, please ask me.
Thanks a lot

Christopher Weiß

[#2]

Hi @ChristopherWeiß,

Welcome in the Community !

When generating your design, did you select "Randomize" in the data table options ? : 

I tried to reproduce your settings, with 11 continuous factor and 1 discrete numéric factor with 3 levels, for a model with main effects and 2 factors interactions.

• When I generate a design with the "Randomize" run order, I have centre points randomized in all the datatable (see "Custom Design_Randomize" datatable). The script to get this design is :

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( Continuous, -1, 1, "X9", 0 ),
	Add Factor( Continuous, -1, 1, "X10", 0 ),
	Add Factor( Continuous, -1, 1, "X11", 0 ),
	Add Factor( Discrete Numeric, {1, 2, 3}, "X12", 0 ), Set Random Seed( 5178006 ),
	Number of Starts( 597 ), 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 Term( {10, 1} ), Add Term( {11, 1} ), Add Term( {12, 1} ),
	Add Potential Term( {12, 2} ), Add Term( {1, 1}, {2, 1} ),
	Add Term( {1, 1}, {3, 1} ), Add Term( {1, 1}, {4, 1} ),
	Add Term( {1, 1}, {5, 1} ), Add Term( {1, 1}, {6, 1} ),
	Add Term( {1, 1}, {7, 1} ), Add Term( {1, 1}, {8, 1} ),
	Add Term( {1, 1}, {9, 1} ), Add Term( {1, 1}, {10, 1} ),
	Add Term( {1, 1}, {11, 1} ), Add Term( {1, 1}, {12, 1} ),
	Add Term( {2, 1}, {3, 1} ), Add Term( {2, 1}, {4, 1} ),
	Add Term( {2, 1}, {5, 1} ), Add Term( {2, 1}, {6, 1} ),
	Add Term( {2, 1}, {7, 1} ), Add Term( {2, 1}, {8, 1} ),
	Add Term( {2, 1}, {9, 1} ), Add Term( {2, 1}, {10, 1} ),
	Add Term( {2, 1}, {11, 1} ), Add Term( {2, 1}, {12, 1} ),
	Add Term( {3, 1}, {4, 1} ), Add Term( {3, 1}, {5, 1} ),
	Add Term( {3, 1}, {6, 1} ), Add Term( {3, 1}, {7, 1} ),
	Add Term( {3, 1}, {8, 1} ), Add Term( {3, 1}, {9, 1} ),
	Add Term( {3, 1}, {10, 1} ), Add Term( {3, 1}, {11, 1} ),
	Add Term( {3, 1}, {12, 1} ), Add Term( {4, 1}, {5, 1} ),
	Add Term( {4, 1}, {6, 1} ), Add Term( {4, 1}, {7, 1} ),
	Add Term( {4, 1}, {8, 1} ), Add Term( {4, 1}, {9, 1} ),
	Add Term( {4, 1}, {10, 1} ), Add Term( {4, 1}, {11, 1} ),
	Add Term( {4, 1}, {12, 1} ), Add Term( {5, 1}, {6, 1} ),
	Add Term( {5, 1}, {7, 1} ), Add Term( {5, 1}, {8, 1} ),
	Add Term( {5, 1}, {9, 1} ), Add Term( {5, 1}, {10, 1} ),
	Add Term( {5, 1}, {11, 1} ), Add Term( {5, 1}, {12, 1} ),
	Add Term( {6, 1}, {7, 1} ), Add Term( {6, 1}, {8, 1} ),
	Add Term( {6, 1}, {9, 1} ), Add Term( {6, 1}, {10, 1} ),
	Add Term( {6, 1}, {11, 1} ), Add Term( {6, 1}, {12, 1} ),
	Add Term( {7, 1}, {8, 1} ), Add Term( {7, 1}, {9, 1} ),
	Add Term( {7, 1}, {10, 1} ), Add Term( {7, 1}, {11, 1} ),
	Add Term( {7, 1}, {12, 1} ), Add Term( {8, 1}, {9, 1} ),
	Add Term( {8, 1}, {10, 1} ), Add Term( {8, 1}, {11, 1} ),
	Add Term( {8, 1}, {12, 1} ), Add Term( {9, 1}, {10, 1} ),
	Add Term( {9, 1}, {11, 1} ), Add Term( {9, 1}, {12, 1} ),
	Add Term( {10, 1}, {11, 1} ), Add Term( {10, 1}, {12, 1} ),
	Add Term( {11, 1}, {12, 1} ), Center Points( 30 ), Set Sample Size( 114 ),
	Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
)

• However, when I create a design with the run order "Sort left to right", all my centre points are between rows 43 and 72, as you seem to have (see "Custom Design_Sorted" datatable). 

I hope this answer will help you,

[#3]

Hello @Victor_G ,

thank you very much for your quick reply! Unfortunately, your answer does not solve my problem. I am trying to avoid repeating the patterns [0,0,0,0,0,0,0,0,0,0,0,2]. I want the midpoint values to be randomly distributed over the entire data table to get the best mixing of values.

Do you know how i can do this?

Thanks a lot

Christopher Weiß

[#4]

Welcome to the community.  In the future, it helps expedite answers when you can attach your data table.  I must say I'm confused.  The first table Victor attached is certainly a possible random order of "center points".  Apparently you have some constraint regarding the particular center point where the discrete variable is at level 2?  So then you do not want a random order?  In any case, feel free to move the rows however you would like.  Most importantly, keep track of actual run order for later analysis.

OK, I must ask...why 30 center points?  That seems rather excessive.

[#5]

Hello @ChristopherWeiß,

As @statman writes, I'm getting also more and more confused as we clearly lack details. Are you already familiar with DoE or do you need more information/help on the concept itself ? There are a lot of ressources links we could send you.

I was thinking first that the problem was the randomization of centre points rows (and not the "pattern" of the centre points rows), but it doesn't seem to be the case.

So let's start from the beginning :

1. Have you already information/experiences done in the same factors ranges ? Or do you have information about the real practical feasability of the tests with the ranges provided ?
2. What's your objective ? Screening main effects, screening main effects + interactions, or a full Response Surface design for optimisation ? Something else ?
3. Why do you want middle levels (you call them "midpoints") for your factors ? Midpoints are often included in factorial designs to estimate quadratic effects (in Response Surface Design for example). Do you want to estimate/test these effects ?
4. Why do you want so many midpoints ? Are you concerned about variance in the centre of your experimental space (and you want to include centre points, but replicate runs could also be an alternative), or do you want to test curvature for all your main effects (and so, having three levels for each factor randomly distributed, as you would have if you include "Power, 2nd" terms in your model) ?
5. What is your experimental budget ?

Depending on your experimental budget, I think a sequential approach might be interesting for you, beginning with screening main effects, and then augmenting the design to search for interactions, to finally augment it and try to optimize your system with quadratic effects and additional runs.

Looking forward to reading your response, so we could provide more guidance, help and relevant information.