Sequential detection is based on a recursive statistic and a threshold it must reach toreport a change. In this paper, we consider the score-based CUSUM statistic and pro-pose to evaluate the detection performance of some thresholds on simulation data.Two thresholds come from the literature: the Wald’s constant and the Margavio’sinstantaneous, and three contribution thresholds built by a simulation-based proce-dure: the first one is constant, the second instantaneous and the third is a dynamicalversion of the previous one. The threshold’s performance are evaluated for severalscenarii, according to the detection objective and the real change in the data. The sim-ulation results show that Margavio’s threshold is the best at minimizing the detectiondelay while maintaining the given false alarm rate. But on real data, we suggest touse the dynamic instantaneous threshold because it’s the easiest to build for practical implementation.