Factor Screening Design of Experiment with Nominal Response?

[#1]

Hi all,

I was wondering if there is a good strategy for designing a set of experiments to find the factors with the most effect on the response, which is nominal (yes/no, pass/fail type of response) instead of the typical continuous response? While for nominal response a logistic regression can be performed on available data, I doubt the usual factorial/fractional factorial design still works in this case (since they are meant for continuous response). What would be a suitable approach in this case? Kindly point me to any relevant terms/theories if anything comes to mind.

Thanks in advance.

[#2]

There is absolutely no apriori reason why a nominal response precludes or renders the sound practice of experimental design as an unsound path to discovery. All the principles of sound DOE methods still apply. As a JMP senior systems engineer (now retired) I called on numerous consumer product companies that use DOE as the lifeblood of their product design efforts. Industries and market segments as varied as candy/sweets, personal care/hygiene/cosmetics, to food additives/spices. Very often they would use sensory panels of product evaluators and almost universally the individuals who sit on these panels provide nominal type response data for the specific experimental designs that have been executed. In fact depending on the specific problem at hand you might find one of the more specialized designs that presume nominal responses supported by JMP such as Choice, Max Dif, or Covering Arrays. But there's no reason a good old fashioned 2 level fractional factorial or more modern design such as a D-optimal design couldn't be or shouldn't be used for screening purposes.

[#3]

Welcome to the community.  You are correct that having a nominal response posses some particular challenges, and Pete's advice is right on.  One of those challenges is the response may be the result of multiple failure mechanisms.  It lacks discrimination to separate those mechanisms (which might have different causal structures).

Of course you can use experimentation to better understand potential causal relationships between the independent variables and the dependent response variable(s). This is true regardless the response variable.  Now, experimentation may not be very resource efficient for nominal responses, but it will be effective none-the-less. My first set of advice would be to consider how to quantify the "phenomena" (response).  What does the response yes or pass mean?  Pass what?  As an example, Dr. Box describes an experiment on cracked springs in one of his papers ("The Scientific Context of Quality Improvement").  He was able to use the % good as a response and discover ways to improve the spring performance. Are there alternative ways to quantify the phenomena?  As suggested, if you are able to detect gradations or categories of "goodness", then you might be able to use an ordinal scale.  In my discussions with Dr. Taguchi, he always emphasized the importance of developing appropriate response variables...in many cases creating a new response variable to provide insight to the problem at hand.

In any case, let's assume you only have the nominal response.  What type of failure rate currently exists?  If the failure rate is high (perhaps >10%), then you aught to be able to detect a change in that rate fairly easily with experimentation.  If the failure rate is low (<5%), then experimentation could be inefficient as you might have to have large sample sizes to detect differences.  Also, given the nature of the response, make sure the design space is large (lots of potential factors set at bold levels).