I'm looking for a reference to the following. I commonly hear that one-third of a projects time will be spent in design, one-third in implementation, and one-third in testing. The three phases of development seems to be derived from the waterfall model. But, where did the time division originate (1/3, 1/3, 1/3)? Is there a paper or book that this is from?
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The rule of thumb you're describing sounds extremely similar to Brooks' rule of thumb, as presented in the Mythical Man-Month:
I don't know where exactly your rule of thumb comes from, but it certainly looks like a derivative of Brooks' rule of thumb.