This is the first in a series of examples where I explain how you can use the solving problem method I described earlier.
You're walking through a local supermarket pushing a cart full of your weekly shopping supplies and bump into your old friend Adam, who you haven't seen since college.
The first thing he says is: "Oh my God, you're fat!".
The conversation ensues and later ends, but the thought never actually leaves your head. After getting past the initial uncomfortableness of hearing it, you return the extra tub of ice-cream you'd impulsively picked up while walking through the frozen aisle and start to wonder if you should hit the gym -- or start running more.
This is typical of how our "normal" problem-solving approach is -- we jump straight to solutions. Eating less, running more or hitting the gym are all solutions, but which should we do? The reason for our confusion is that we're skipping steps: we've yet to actually *Define* the problem.
The DMAIC approach
What is the problem, exactly? You may think this is obvious: you've obviously gained weight since the last time you'd seen Adam and it may seem sufficient, but it's not: let's dig more.
> Problem v0: "I've gained weight since college"
Unless Adam was carrying a weighing scale around with him, he didn't actually weigh you. He made a judgement based on how you looked. This is important.
> Problem v1: "I look fatter than I did in college"
To move forward, we need to know how the judgement was formed. What caused Adam to say you looked fat? So, we track him down in the organic food aisle and ask him. After looking at you strangely, he answers that it was your waist.
> Problem v2: "The size of my waist has grown since college"
This is obviously better than the previous two. Even though we're not even close to looking at solutions yet, we can start to sense that the increased clarity in the problem definition would favor weight-loss techniques that target the actual problem area (waist size) over others
We'd typically spend the majority of our time on Define. Yes, the most important step of the process is also the step that most people skip entirely! Since this is the first example though, we won't dwell on this much longer. Onwards.
Simply put: You can't improve what you can't measure. Here, we take the problem definition and sprinkle some numbers on.
You may not recall what your waist size was in college (it would actually be weird if you did). Instead, we can compare against benchmarks (e.g. the "normal" waist size for adults of your age/gender). A bit of research here would go a long way; the heart foundation, you are at risk if your waist size is greater than 94cm (or 80cm if you're female).
Lo and behold, you pick up a tape measure and you get 100cm. Now we know there's a problem (and we're not relying on Adam's random judgement any more).
There's alot more to say about measure (e.g. do you know that the tape measure is ok, what specific area are you measuring, etc) but this post is getting too long already.
You can't adjust your waist size directly (i.e. just chop off the extra 6cms). Instead, you'd have to do other things that affect the waist size. We call these "X's" (it's a math thing, since formulas follow the form Y = f(x) and changing your X's, or inputs, affects the Y, or outcome).
Here, we identify these X's and focus on the ones that have the greatest impact on our Y (reducing waist size). Once more, Google is your friend -- and the first result for "reduce waist size" tells us:
1. Eating the right foods
3. Lifestyle changes
...all have a direct impact on waist size.
Next, we weigh the impact of each one to identify our "critical" X's - the ones that matter most. Reasearch has shown that #1 has the greatest impact, followed by #2 and #3 (in that order).
You can spend alot more time on this and consider things like interaction among the various X's, etc but we've done enough for this simple example. We'll peel back the covers in future examples.
We finally get to improve things now! At this point, we've got a good idea for what the overall goal is and what factors we'd like to target to achieve an improvement. Here, we systematically apply the improvements (in the order of importance). Since this is a simple example, we'll keep it at that for now (though in future examples we'll talk more about how to verify which X's matter more than others).
Even after implementing the solution, we're not done yet! We need to lock it in to ensure that the improvement is lasting -- and not a one time affair. On a personal level, this would include replacing bad eating habits with healthy ones (e.g. keeping vegetable snacks around the house, drinking water frequently, etc.).
In the end..
That's it! Congratulations on successfully going from a single comment ("You're fat!") to a well defined, problem, solution and ultimately a lasting system of change. Stay tuned for juicier, more complex problems soon!
 If this seems like we're putting unwarranted emphasis on Adam's opinion, it's good to remember that (doing nothing)™ is also an option in the problem solving world.