Michael Bierut of Design Observer admits his real design process is different than the one put on proposals. And the real process is very true of anyone who makes things.
When I do a design project, I begin by listening carefully to you as you talk about your problem and read whatever background material I can find that relates to the issues you face. If you're lucky, I have also accidentally acquired some firsthand experience with your situation. Somewhere along the way an idea for the design pops into my head from out of the blue. I can't really explain that part; it's like magic. Sometimes it even happens before you have a chance to tell me that much about your problem! Now, if it's a good idea, I try to figure out some strategic justification for the solution so I can explain it to you without relying on good taste you may or may not have. Along the way, I may add some other ideas, either because you made me agree to do so at the outset, or because I'm not sure of the first idea. At any rate, in the earlier phases hopefully I will have gained your trust so that by this point you're inclined to take my advice. I don't have any clue how you'd go about proving that my advice is any good except that other people — at least the ones I've told you about — have taken my advice in the past and prospered. In other words, could you just sort of, you know...trust me?
This design process is discussed in the book Artful Making: What Managers Need to Know about How Artists Work, written by Harvard Business School professor Rob Austin and Swarthmore College Theater professor Lee Devin. They advocate a process similar to Bierut's based on producing a play.
The authors take pains to point out that they're not advocating a "loose" process or one that lacks rigor. "A theater company," Austin and Devin point out, "consistently delivers a valuable, innovative product under the pressure of a very firm deadline (opening night, eight o'clock curtain). The product, a play executes again and again with great precision, incorporating significant innovations every time, but finishing within 30 seconds of the same length every time." They are careful to identify the defining characteristics of this kind of work: allowing solutions to emerge in a process of iteration, rather than trying to get everything right the first time; accepting the lack of control in the process, and letting the improvisation engendered by uncertainty help drive the process; and creating a work environment that sets clear enough limits that people can play securely within them. They call this artful making: in short, "any activity that involves creating something entirely new." This includes not just the obvious "arty" things, but, for instance, "a successful response to an unexpected move by a competitor" or "handling a sudden problem caused by a supplier."