Abstract: By the approaches of being linearly close to the workload of tasks in hard real-time system the closer response time upper bound can be used to decrease the running time.At the same time it is linear in time of complexity for the upper bound in the sufficient schedulable tests of task sets.In interactive system design tools，system optimization via search，and admission of new tasks into dynamic systems，this new linear upper bound can considerably improve efficiency of test.Further，it is wide in application for the scheduling model without the limit of deadline and jitter.The pertinent experiments show that the method of utilizing the approximate upper time has improved the efficiency of exact test of the schedulability.