A Part Is Born
Obviously very influenced by the scientific method that has been imprinted on my brain by a series of science teachers, here is a fairly realistic example of how a part is born at Ground Control.
Define the problem: Many BMW customers complain about having to change rear shock mounts frequently. 
Gather data: We rigged an E36 stock upper mount onto a stock shock on our Roehrig dyno. The deflection was more than we expected. E30 convertible mounts were not much better. 
Propose a hypothesis: The rear shocks on all E30, E36 and E46 cars have reduced effectiveness because the stock upper mounts deflect too much.
Test the hypothesis: We used the Motec data acquisition system from our race car to measure shock movement vs. chassis movement. 
Interpret the results: The stock mounts flex too much for performance shocks.
Propose a solution: If we could build a mount out of 6061-T6 billet aluminum, shock mount flex will no longer be a problem. 
Test the proposed solution: 