Disallowed combinations and constraints

[#1]

Hi,

In my custom DOE design. If some combinations are feasible, but based on literature it will not be as effective, should I make it a disallowed combination? Will it have any negative impact to the design or analysis if I exclude the combination?

Ie. Out of seven factors, two factors (level 0 and 1) are said to work better together rather than alone, is there negative impact to excluding the combinations of (0,1) and (1,0)?

Assuming I do enough runs to get a prediction variance <1.

Thanks!

[#2 · Accepted solution]

You said, "If some combinations are feasible, but based on literature it will not be as effective, should I make it a disallowed combination?" That question demonstrates that you have a 'testing' mindset, not an 'experimenting' mindset. A test provides an answer. An experiment provides a model (lots of answers). It is not a matter of 'right or wrong.' It is a matter of being clear about your purpose. Either mindset might be right depending on your goal. You can keep testing until you find what you want ('trial and error'), or you can run a designed experiment, fit a model, and use the model to explore the space to find what you want.

You add constraints when some conditions in the regular design space are impossible, dangerous, or would change the phenomenon under study. Otherwise, you want to observed the entire design space as efficiently and effectively as possible. Because you want to estimate the model parameters.

A good experiment will illicit both good and bad responses. That way, you have a realistic model that can predict the entire range of outcomes.

You said, "Out of seven factors, two factors (level 0 and 1) are said to work better together rather than alone." This observation indicates that an interaction effect is important in the response. Eliminating the combinations of (0,1) and (1,0) will make it impossible to model that interaction. The data will be devoid of the necessary information without those combinations. 

[#3]

That makes sense. Thank you!

[#4]

Here's another thought on a similar topic. Say for a different two factors, it is infeasible at full scale to run them together and only feasible to run them as (0,1) or (1,0). However, it is feasible to perform those two factors together at small scale (1,1). If I constrain the design to disallow (1,1), it increases the prediction variance. So it makes sense to include the (1,1) combination in the screening design since I'll be performing it at small scale, correct?

[#5]

I assume that all the factors are continuous, including scale. You can use a linear constraint for this case. Use a simple factorial combination of the factors. For example, with just two factors involved, you would define the end points, for example, (0,1) and (1,0). Those two points define a line, a boundary, of which you want to remain on one side. You can get the coefficients that you need from fitting a linear model. Extend this approach to three factors.

[#6]

I've run into this topic once again! So I have to disallow certain combinations, BUT it decreases the prediction variance and power significantly. So how do I get around this? How will I be able to trust the results if power is so low and the prediction variance high?