Response-Time Analysis (RTA) is a powerful, mature and well established schedulability analysis technique for real-time systems. In order to get better utilization of system resources, RTA should not overestimate the response time of tasks in the system. This paper addresses the problem of losing system wide information about precedence chains and overestimation found in response time of tasks when current RTA is applied to a system where precedence chain dependencies among tasks exist. We show that when there are precedence chains with one activating event in a real-time system, a task under analysis cannot experience Worst Case Execution Time of all interfering tasks at the same time when they all experience their maximum release jitter.