For the analysis of survival data including covariates whose effects vary in time, the multiprocess discount survival model is proposed. The parameter vector modeling the time-varying effects of covariates is to vary between time intervals and its evolution between time intervals depends on the perturbation of the next time interval. The recursive estimation of the parameter vector can be obtained at the end of each time interval. The retrospective estimation of the survival function and the forecasting of the survival function of individuals of the specific covariates also can be obtained based on the information gathered until the end of the time interval.