The Mandate of Heaven depends on whether an emperor is sufficiently virtuous to rule; if he does not fulfill his obligations as emperor, then he loses the Mandate and thus the right to be emperor. The Mandate of Heaven would then transfer to those who would rule best. The fact that a ruler was overthrown was taken by itself as an indication that the ruler had lost the Mandate of Heaven. In addition, it was also common belief that natural disasters such as famine and flood were other signs of heaven’s displeasure with the current ruler, so there would often be revolts following major environmental events as citizens saw these as signs of heaven's displeasure.
The Mandate of Heaven does not require that a legitimate ruler be of noble birth, and dynasties were often founded by people of common birth (such as the Han dynasty and Ming dynasty). The Mandate of Heaven had no time limitations, depending instead on the just and able performance of the ruler and his heirs. Throughout the history of China, times of poverty and natural disasters were often taken as signs that heaven considered the incumbent ruler unjust and thus in need of replacement.
https://en.wikipedia.org/wiki/Mandate_of_Heaven
http://www.islamreligion.com/articles/282/viewall/ones-who-perished/
Sahih International: And never would your Lord have destroyed
the cities until He had sent to their mother a messenger reciting to
them Our verses. And We would not destroy the cities except while their
people were wrongdoers.
Pickthall: And never did thy Lord destroy the townships,
till He had raised up in their mother(-town) a messenger reciting unto
them Our revelations. And never did We destroy the townships unless the
folk thereof were evil-doers.
Yusuf Ali: Nor was thy Lord the one to destroy a
population until He had sent to its centre a messenger, rehearsing to
them Our Signs; nor are We going to destroy a population except when its
members practise iniquity.
Shakir: And your Lord never destroyed the towns until He
raised in their metropolis a messenger, reciting to them Our
communications, and We never destroyed the towns except when their
people were unjust.
Muhammad Sarwar: Your Lord did not destroy the people of
the towns without first sending a Messenger to the mother town who would
recite His revelations to them. We did not want to destroy the towns if
the people therein were not unjust.
Mohsin Khan: And never will your Lord destroy the towns
(populations) until He sends to their mother town a Messenger reciting
to them Our Verses. And never would We destroy the towns unless the
people thereof are Zalimun (polytheists, wrong-doers, disbelievers in
the Oneness of Allah, oppressors and tyrants).
Arberry: Yet thy Lord never destroyed the cities until He
sent in their mother-city a Messenger, to recite Our signs unto them;
and We never destroyed the cities, save that their inhabitants were
evildoers.
http://corpus.quran.com/translation.jsp?chapter=28&verse=59
