Prediction of mean time between failures (MTBF) is an important aspect of the initial stage of system development. However, it is often difficult to predict system MTBF during a given time since the component failure processes are extremely complex. This paper presents a Monte Carlo simulation algorithm to calculate the MTBF during a given time of a binary coherent system. The algorithm requires the lifetime distributions of the components and the minimal path sets of the system. The MTBF for a specific time interval, eg, a month or a year, can be estimated. If the component lifetime distributions are unknown, then a lower bound of system MTBF can be estimated by using known constant failure rates for each component.