For large-scale dynamic railway traffic control systems, the reliability analysis and risk assessment are important for system evaluation, decision making and enforcement of performance-based safety-critical standards. The Axiomatic Safety-Critical Assessment Process (ASCAP) developed at the University of Virginia's Center of Rail Safety-Critical Excellence provides a dynamic Monte Carlo simulation methodology for the quantitative risk assessment of large-scale rail systems. An appropriate reliability model is critical for effective and valid ASCAP simulation results. In reliability engineering, it is know that the electrical and mechanical equipment, such as switch machines, track circuits and trip-stops in railway infrastructure, usually manifest deterioration and/or improvement in reliability over time. A constant failure rate, which entails an exponential distribution of the object's life-time, may not be sufficient and appropriate. A time-varying fatigue rate is adopted in the reliability probabilistic model, which is presented in this paper. The Weibull distribution is one of the most widely used distributions for modeling lifetimes and the Weibull process is particularly suitable for modeling reparable systems because of their flexibility in shaping and scaling time-varying failure rates over time. The algorithm of the Weibull model and the Monte Carlo simulation are presented and the numerical results from applying the method are also provided.