Most scheduling algorithms developed for soft and firm real-time systems lack the ability to enforce constraints on the upper limit of misses. Unbounded consecutive time constraint violations may occur without such an enforcement. Realistically, if consecutive instances of a task fail to complete before their deadlines, then the system will eventually suffer from a failure. This indicates that there are additional constraints. These constraints express the minimum degree of timeliness that must be enforced for firm real-time tasks. This is the subject of this chapter.