Normally, tasks are classified into real time and non real time according to temporal constraints for the processing and transmitting of these tasks, consequently the worst-case response time and average performance should be focused on them. However, in practical engineering context, partly violated temporal constraints can be tolerated if the violation meets certain distribution. Nevertheless, the loss-rate (within real time region, an instance of a task is regarded as loss if it violates its temporal constraint) under stable state or statistical real time can solve the problem in some extent, it can't include the permitted distribution of violation. For completely solving the problem, weakly-hard real time schedule theory or window-constraint real time schedule theory, which is used to investigate the problem related to allowing violation of instances over a finite range, consecutive instances or a time window, is proposed. In order to effectively utilize the fact that a practical application can tolerate some violations of temporal constraint under certain distribution, the fundamental research must be done from the aspects of specification of temporal constraint, schedule and schedulibility, and implementation, which are explained in detail in this paper.