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Weighted Uniform Simulation (WUS) is recently presented as one of the efficient simulation methods to obtain structural failure probability and most probable point (MPP). This method requires initial assumptions of failure probability to obtain results. Besides, it has the problem of variation in results when it conducted with few samples. In the present study three strategies have been presented that efficiently enhanced capabilities of WUS. To this aim, a progressively expanding intervals strategy proposed to eliminate the requirement to initial assumptions in WUS, while low-discrepancy samples simultaneously employed to reduce variations in failure probabilities. Moreover, to improve the accuracy of MPP, a new simple local search method proposed and combined with the simulation that strengthened the method to obtain more accurate MPP. The capabilities of proposed strategies investigated by solving several structural reliability problems and obtained results compared with traditional WUS and common reliability methods. Results show that proposed strategies efficiently improved the capabilities of conventional WUS.