Time-varying failure rate for system reliability analysis in large-scale railway risk assessment simulation

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 SafetyCritical 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 known 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 lifetime, may not be sufficient and appropriate. A time-varying failure rate is adopted in our reliability probabilistic model. The Weibull distribution is one of the most widely used distributions for modeling lifetimes and the Weibull process is particularly suitable for modeling repairable systems due to their flexibility in shaping and scaling time-varying failure rates over time. The Weibull shape parameter determines the trend of reliability variation, however, the repair and scheduled maintenance may also contribute to a rise or fall of the failure rate at the repair time. To represent the physical failure characteristics, a so-called piecewise Weibull process model is proposed. The likelihood function is derived and used to estimate the Weibull parameters with maximum likelihood. We demonstrate the use of the piecewise Weibull model by applying it to evaluate the reliability of transit signaling devices in a large-scale railway system. The algorithm of the model implementation and Monte Carlo simulation is presented. The numerical results from applying the method are also provided.