1st rear of rule death is most likely, if the 1st year is survived the danger gradually diminished to the 7th year. The safest years for an emperor are from 8th to 12th years of rule. After the 12th year the danger is increasing again. World politics in nutshell! In the study they compare Emperor's survival to a mechanical failure. I.e a car components are most likely to fail on it's first year. If first year is "survived" a car is "stable" till it's worn out on the 12th.
It is intuitive that chances of getting whacked are the highest on the 1st year. What is interesting are the other two markers 8th year the safest, 12th year is when the danger goes up again.