Those systems are called critical systems which not only causes inconvenience, no or not-noticeable impact on time, money and life but also causes loss or injuries to life, economical destruction and such bigger impacts when the system fails.
For example, an word processor is meant to be used to type texts and if it fails somewhere mostly it will cause loss of few paragraphs you have written for the last few minutes. But if a system that associate air traffic controllers at an air-base fails for even few minutes, serious injuries and deaths, accidents may fall in.
Again, those system used in banks, if fails at a moment, loss of big amount of money exchange can take place.
Thus critical systems are systems on which the operators depend. Failure of critical systems are unavoidable but if fails, will cause serious loss to those which are supposed to be cared by the system or supposed to be assisting the operator in caring.