On the other hand, we have places like Japan, that remained pretty much in calm order after a national disaster.
There are a number of variables that effect how long an area would maintain order after a disaster. The biggest of these, in my opinion, is the overall culture and moral quality of the population. Are the people going to stay clam, band together and help one another get through the ordeal with morals intact? Or are they going to turn into packs of wolves, taking every opportunity to loot, rob and worse while the Law is distracted? Some will use even relatively small, localized disasters to go wild.
You can't control the moral fiber of the general population, but you can control where you live. Obviously, stay away from high crime areas; if crime is bad in normal times, it will get a hundred times worse with "po-po" out of the equation.
Unfortunately, there are morally bankrupt people in most every community. Heck, even many self-proclaimed survivalists/preppers have little more than a bunch of guns, ammo, and a plan to take what they need after a collapse. You'll need to be prepared to deal with people who want to take what you have, no matter how nice and pleasant your community is.
Aside from social norms/morals, there are a host of other variables that will affect how long order remains. The length, scale and severity of the disaster, the overall level or preparedness, the level of outside aid/support and similar. Most of these come down to desperation--will people become so hungry/thirsty/sick that they take desperate measures? How long would that take? While moral people will not engage in looting and other crimes of opportunity post disaster, they may be forced to take desperate measures if the situation is bad enough and lasts long enough. While some people will just lie down and starve, many won't. And when it's a matter of survival, people will take desperate measures to live to see another day.
As a broad generalization, I would expect to see looting and crimes of opportunity within the first 24 hours of a major disaster wide enough to disrupt the normal rule of law, with varying levels depending on the culture/moral quality of the impacted communities. If there is no outside aide or intervention, this level of crime will increase on an exponential basis as the disaster drags on. During the initial few days of the disaster, the average decent person may engage in looting, but only for needed supplies--groceries and similar--once they've realized how dire the situation is. I would expect the average decent person to hold out maybe three days after their food has run out, before becoming desperate enough to resort to other measures. Maybe that's a bit pessimistic, maybe it's a bit optimistic. What do you think?