Problem Management is the process responsible for managing the lifecycle of all problems. The primary objectives of problem management are to prevent problems and resulting incidents from happening, to eliminate recurring incidents and to minimize the impact of incidents that cannot be prevented.
Problems are not incidents. An incident can raise a problem, especially if there is a high possibility that the incident might happen again. In the case of a server crash after office hours, the crash is a problem. This is a high priority problem because if this problem is not resolved, this will become an incident.
An incident does not become a problem. A problem may be raised because of an incident and, a problem may cause an incident.