I was recently asked to help with a design of experiment where the response Y is not a smooth function and has several discontinuities.within very narrow ranges of X values. Has anyone worked with this type of problem, and if so, how did you design and analyze the experiment?
You might consider using a space filling design, usually called for in computer experiments, to adequately sample the design space in which there might be large discontinuities in the response between design points. The usual design methods for the linear model (e.g., custom design) might be impractical and ineffective because they would require very high order polynomials that would still suffer from large degree of lack of fit.
You might use the Gaussian process model or an artificial neural network model for exploration and interpretation. In this case, if the original design space is only for screening, you might use the exploratory model to isolate a restricted region of the initial design space for a new experiment using a conventional design method in which you can rely on the linear model. Then again, these models can be quite accurate and further data collection might be unwarranted.
Thanks for the quick response! I have used the space filling design and the Gaussian process but not the neural net. I will follow your advice to see if I can isolate a restricted region. After that, I may have to do further space filling designs with much smaller intervals.
I would greatly appreciate if you or any one in the community have performed this type of work, especially if a paper, presentation, journal, etc. are available for sharing. Such references would help me convince management easier.
I hope that someone else might have a reference for you. I don't have any.
I have two cases where we successfully used this approach but I am not at liberty to divulge either one. I can say that both were successful.
In case it helps, you can think of this approach as a pre-screening. You know so little about the effect of the factors and the nature of the response to the factors is so complex that you cannot use any screening design until you know the productive factor ranges. This approach will identify that information for you.