I've been involved with DOE courses where the analysis (i.e., ANOVA) was run as if the response variable was continuous. However, what you cannot do is build a mathematical predictive model, but merely get an idea of the biggest contributing factors.
If you're referring to Taguchi designs, these are fractional factorials, and I don't think the smaller sample sizes and fractional nature lend themselves to a good experimental design with a binary response variable.
I am talking about fractional factorials. I can take pretty large samples in marketing application (direct marketing). Is it fair to design a test using DOE (as applied in most texts) and then analyze via logistic regression? I hear a lot of *BUZZ* about Taguchi applied to marketing like catalogs, web sites but never any how-to and how to estimate the main interest in these realms - namely response (0/1).
You can certainly design any experiment or study and apply logistic regression if the response is binary, but I am doubtful that the fractional factorials will give you useful, repeatable results. The Taguchi methods were HIGHLY fractional and fell out of favor in the QA / industrial / manufacturing world because they didn't do what they claimed....
For binary response variables are you pretty much left then with designing an experiment using the principles at least of DOE (controlling, blocks etc) and using sample sizes for proportions - ignoring the designs? Or using rules of thumbs for how many positive responses (response =1) per covariate? It seems like there is scant little literature about studies w/o continuous (normal) response variables.
The answer to your first question is basically yes. The reason for the lack of literature is that studies with binary responses require huge sample sizes, and therefore are kept pretty simple (at least that's the impression I got when we looked at this in grad school). Trying to design an experiment with multiple factors and studying the interactions with a binary DV would require enormous resources and costs (paying participants, etc.).