Sequential detection is based on a recursive statistic and a threshold it must reach to report a change. In this paper, we consider the score-based CUSUM statistic and propose to evaluate the detection performance of some thresholds on simulated data. Three thresholds come from the literature: the Wald's constant, the empirical constant and the conditional empirical instantaneous (the latter two are built by a simulation-based procedure). Two new thresholds are built by a simulation-based procedure: the first one is instantaneous, the second is a dynamical version of the previous one. The thresholds' performance measured by an estimation of the Mean Time Between False Alarm (MTBFA) and the Average Detection Delay (ADD), are evaluated on independent and autocorrelated data for several scenarii, according to the detection objective and the real change in the data. The simulations allow us to compare the difference between the thresholds' results and to see that their performances prove to be robust when a parameter of the pre-change regime is misestimated or when the data independence assumption is violated. We found also that the conditional empirical threshold is the best at minimizing the detection delay while maintaining the given false alarm rate. However, on real data, we suggest to use the dynamic instantaneous threshold because it's the easiest to build for practical implementation.