Well, I wouldn't call it a "method"; it's just a combination of a fault tree with an event tree diagram for a given hazard; both of which are the result of a corresponding analysis. Bow-tie diagrams appear a lot in Eurocontrol documents and standards since twenty years (e.g. in their safety assessment method); also the FAA seems to use them.
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> Well, I wouldn't call it a "method"; it's just a graphical way
“way” (in this sense, as opposed to say the sense of “road”) is a synonym for “method”.
I am an engineer and as most other engineers have a concrete idea of what "method" means; in any case, it is about much more than just painting something. However, I agree with you - if I interpret you correctly - that often the method how the result is developed is confused with a way of presenting the result. Since Merriam Webster indeed offers "a way of or for doing something" as a synonym for "a systematic procedure [...] employed by or proper to a particular discipline" I changed my statement a bit to avoid this (weak) ambiguity.
It's a method, a method of thinking, which connects event tree and fault tree. A powerful way of working with hazards and risks.
We certainly use this all the time.
Well, μέθοδος is derived from μετ᾽ (met᾽: towards,after) + ὁδός (hodós: road,way). So 'way' is a synonym in both senses.