Basic 3 phases of an emergency:
Uncertainty
Alert
Distress
As an example, para 3 of the following document sets some specific limits for moving from one phase to another if a flight plan has been filed:
http://legacy.icao.int/SARafrica/doc..._Manual_en.pdf
Whether there are some internationally agreed limits or not I don't know. I expect IAMSAR would be the place to look.