We address the problem of online detection of a change point via the online version of the CUSUM method. Change-point detection is based on the choice of a statistics and the threshold it must reach to report a change. CUSUM statistics is based on a sequential test of the likelihood ratio, which can be replaced by a score function in the non-parametric case and the classical method for selecting the detection threshold is based on Wald inequalities [Wald, A., D. J. (1945)]. In our work, we propose an empirical method for the selection of the detection threshold. We also suggest replacing the constant threshold with an instantaneous time-dependent threshold. In order to control the instantaneous false alarm rate (IFAR), the mean time between false alarms (MTBFA) and the average detection delay (ADD), we propose new procedures by correcting the stop rule usually used in the CUSUM approach. In order to evaluate and compare new different methods for selecting detection threshold and the new stop rules, we perform simulations to evaluate detection parameters in each case .