As a purely practical measure, for really important occasions, I'll often plan in an activity at second-to-last which is actually unimportant and can be dropped. So, for example, if I have a job interview, my plan will be that, after I've found the entrance to the company office and there is as little left to go wrong as possible, I'll then, as a second-to-last activity, do something like go for a relaxed lunch at a nearby cafe, and then just stroll in at the ideal time.

On the day everything goes to pot, I can use up the time I planned for the second-to-last activity. So I should hopefully still have time to go back for the forgotten briefcase, hire a taxi from my broken-down car, replace my torn shirt, and still get to the interview hungry rather than two hours late.

This is a good plan for anything with a hard start time - weddings, theatre trips, plane trips - add a pleasant activity that you can delete if needed at second-to-last. Of course the length of this optional activity should be at least as long as the number of sigmas you need for the important one. The result is that you arrive on-time and de-stressed (almost) every time.