Augmenting a DSD matrix

[#1]

We ran a Definitive Screening Design matrix to explore 6 factors and have since found that due to process performance we need to adjust the range of one of the parameters downwards a bit from where it was targeted in the original DSD. The parameter in question does impact an output as a primary factor and as a 2-way interaction with 2 other factors per the original DSD analysis.

What's the best way forward here? A 6 run matrix to evaluate X1, X2, X3, X1*X2, X1*X3 or something more thoughtful?

We can only do about 10 more runs.

Thanks for any input.

[#2]

Here are my thoughts:

1. The purpose of the DSD is to find active factors not find the best levels.  It seems your DSD did that although you have not provided the entire analysis of the DSD.  Without any context for the factor, the situation or the response variables, it is difficult to provide advice.  Do you need further experiments?  Do you think changing the factor levels for the factor in question will invalidate the learnings from the DSD?

2. Were there any quadratic effects for any of the factors?  Did you simplify the model and save the prediction formula?  Perhaps just run some confirmatory runs with the factor in question at the "better" levels.

3. Did you have any strategy to handle noise in your experiment?  Perhaps some sampling of the model over time would be good to validate the consistency/predictability of the factor effects.

[#3]

We were using DSD to characterize a step; meaning we had targets that were previously determines and acceptable operating ranges that are largely determined by the capability of control in the process. We were checking to see if the step was sensitive to that level of variation. The range on one of the parameters needed to be adjusted to accommodate where the step was actually running in production, so we were trying to think of a way to do that.

Thanks for your input!

[#4 · Accepted solution]

To add my two cents to the issues and questions raised by @statman here's my thought. Forget about augmenting the DSD design. The augmented DSD would no longer be a DSD...but what I used to call a Frankenstein design. DSDs have some very special concepts behind them (effect heredity and sparsity but two) and specific characteristics such as the foldover property that would be rendered moot by analyzing it as a Frankenstein DSD...and I'm pretty sure the Fit Definitive Screening Design analysis platform would not like the Frankenstein design and you might get error messages galore. Here's my thought. Since you've got 3 factors you'd like to study further, with some very specific model terms you'd like to estimate, why not run a D-optimal design in the 10 runs you say you have available, specifying the exact model you wrote, and analyze it as such. In 10 runs you've still got a few degrees of freedom leftover for error estimation for the specified model. Then take away the practical conclusions from both experiments and see where that leads either to solving the problem at hand or additional trials. All this is consistent with the sequential design of experiments problem solving process.

[#5]

You are absolutely correct. Going about adding to a DSD without doing a complete foldover would be a mess.