In a weak neutron source system, the neutron chains rarely overlap. It is necessary to describe this system using stochastic kinetics. Quantities of interest in the field of stochastic kinetics are Probability of Initiation (POI) and Probability of Survival (POS). The RMC code has the capability of calculating the POI in a static system. In this study, the calculation function of POS in dynamic systems is developed in RMC. The Monte Carlo direct simulation method is used for neutron transport in the program. The reactivity of the dynamic system changes with time through the linear interpolation method. The total number of simulated particles was controlled by the threshold and comb method. The benchmark calculated is proposed by the LANL. The calculation results of RMC and MCATK for POI are completely consistent. The calculation results of the two programs for POS are in good agreement except for 600sh(shake). Then the reason for the inconsistent between different calculation results of POS at time 600sh was analyzed and it can be found that the threshold setting in the comb method has a more significant impact on the calculation results of POS. This research is helpful for the further study of stochastic kinetics application.