Joe - For me, it's binary logistic regression.  BLR is a bit of an obscure tool, but it allows for establishing a relationship between an attribute output and either variable or attribute predictors.  I find it useful when there is an unknown specification limit.  For example, when I hold a customer clinic, I can ask the participants whether they are satisfied with the performance of a given feature, or if they would bring the system back for warranty.  I record this as a 1 or 0--the result is binary--they are either satisfied or not (or they will or will not return the system fr warranty).  I can then use the measurements taken on that part or system and determine above or below what value I can guarantee that x% of the customers will be satisfied.  I have been very successful with this tool in DFSS project and also in DMAIC projects.

I do like Binary Logistic Regression as well.  It is a very powerful tool.

However, often with two simple tools (process mapping and FMEA) I feel like a Belt can get 50% towards a solution. Obviously some situations are much more complex and require more powerful tools. 

I absolutely love a good box plot! I'm a visual learner so that picture of the data really helps me see what is going on.