I've neglected to mention the importance of measurement in problem solving. The Six Sigma process emphasizes measurements and statistics to make sense of those measurements. Unless you measure the current state, and the state after implementing changes or improvements, you cannot claim success. Measurement is the foundation of problem solving. Before you can visualize, or model, or even brainstorm solutions, you must be able to characterize the current state.
Remember when you were a kid and your parents would mark your height on something so you could track your growth? Measurement must be done to show progress. Perhaps you've gone on a diet. Sure you feel better as you lose weight, but you don't go by those feelings alone, you check your weight (and perhaps your waistline) frequently to track your progress.
Without measurement, you are blind to your current situation and how it may (or may not) change.