# Attribute input factors for CCD

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• #27494

Anonymous
Participant

Recently, I was asked to recommend how to design a central composite using continuous and attribute input factors. Attribute input factors being choices, e.g. yes/ no. I instructed the team to use MiniTab to layout the design assuming all factors were continuous. Then add rows to the design to accomodate all the combinations of attribute factors to the center points and alpha levels. I also instructed them to convert any alpha levels for attribute factors to +/- 1.

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#67472

anon
Participant

What is meant by, “convert(ing) any alpha levels for
attribute factors to +/- 1?” Why are use suggesting a CCD, are you planning to develop a model of the process using attribute inputs? If so, perhaps you should consider using a Logistic model for the inputs… One assumption of this approach is that all inputs are independent. Is that a reasonable assumption for these inputs? Is there a way of setting categorical levels for these inputs? If you can get to about 5 levels per inputs, then you can considered a loosely a continuous variable.

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#67479

Terry Harris
Member

It sounds like you are augmenting the CCD to accommodate the factorial combinations of attribute facts. Is this correct? Will you delete the runs selected by MINITAB that require your attributes be other than +/-1? Remember, the CCD is a crossed, 4 level design with a center point (5 levels). If so you will not have a CCD but something else.
You can think of a combination attribute/continuous experimental design as a full or fractional design of continuos factors in n blocks determined by the full or fractional factorial combination of attribute factors. Such designs are not uncommon and are best chosen either D-optimally if the factors are not balanced or factorially if they are. In either case models can be generated that support a complete second order response in continuous factors with main effects and interactions of the attribute factors. However, no second order effects can exist for attributes at two levels. I am referring to squared terms when I refer to second order and not interactions which are mathematically second order.
I am often asked to recommend an experimental design by various scientists and engineers and have found that although they have a good idea of what they would like to achieve, they have little idea of what specific questions their experimental effort should or can answer. Typically they would like to achieve a non-linear process model, which I consider a third level goal without passing through the first two goals; factor screening and main effects modeling.
For instance, they might like to increase the yield from a distillation column and optimize the process without knowing what process or material factors are significant and how they are related. Do the raw materials entering the process or the process control factors vary and if so why, how much and to what effect? What is the effect of the nominal value of each on the output and do they interact? Also, little if any consideration is given to the measurement of the outputs or the inputs of the process. Are the measurement systems available capable or even sufficient?
These walk first questions are vitally important and in my experience generally controversial. Any collection of seasoned professionals studying a problem will undoubtedly tell us they understand these things and want to get to the optimization model and yet there can be much disagreement between them when pressed to quantify any response to these queries. In fact if they knew as much as they would have us believe there would be no need for an optimization experiment. Their great process knowledge blinds them to what might be.
I only mention these observations because your group asked you to recommend how to design a CCD when it seems inappropriate. They seem to want to run long before they can walk. My advice would be to question at great length any request for something more complex than the bread and butter two level factorials.

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#67480

Neil Polhemus
Participant

I second Terry Harris’ suggestions. Anything beyond a two-level factorial makes no sense for the yes/no input factors. It might be simpler to go with a modified Box-Behnken design where you split the centerpoints amongst the levels of the attribute factors. I would not just go in and adjust the star points in the CCD. The resulting design will be considerably larger than necessary.

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#67482

John Noguera
Participant

I agree with Neil, but you might want to also consider a D-Optimal design.  Note that regardless of the design type, you will not be able to estimate a squared term for the categorical factor, and you will lose  orthogonality, rotability, and uniform precision.
Having said all of that, if the runs are not expensive, then your original design wins for simplicity.

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#67483

John Noguera
Participant

Oops, I meant rotatability.

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#67492

Murray
Participant

You are using a bad choice of design. What advice are you getting from the Master Black Belts? Attribute input and CCD do not go together

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#67507

Anonymous
Participant

I agree with you. But, and I guess there is always a but, how do I combine the linear effect of the attribute factors and the non linear impact of the continuous variables?

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