Defining the process of type IRIS (Increasing Reward with Increasing Service) is one effort to get around the limitations of time available for execution. In this paper, the Double-Track Most Significant Operation First (DT-MSOF) strategy is proposed to improve system efficiency. In this strategy, the order of execution of the computing element according to their importance and the execution need only be done until the result is correct and/or acceptable. To know the performance of this strategy, two simulations are performed and an example of application is demonstrated. The simulation results show that the execution efficiency using DT-MSOF is better than DT-LSOF and DT-RSOF, measured by the percentage of executed computation. The demonstration indicates the possibility of implementation of this strategy on particular problem.