Analyzing uncertainties in model response using the point estimate method: Applications from railway asset management

Predicting current and future states of rail infrastructure based on existing data and measurements is essential for optimal maintenance and operation of railway systems. Mathematical models are helpful tools for detecting failures and extrapolating current states into the future. This, however, inherently gives rise to uncertainties in the model response that must be analyzed carefully to avoid misleading results and conclusions. Commonly, Monte Carlo simulations are used for such analyses which often require a large number of sample points to be evaluated for convergence. Moreover, even if quite close to the exact distributions, the Monte Carlo approach necessarily provides approximate results only. In contrast to that, the present contribution reviews an alternative way of computing important statistical quantities of the model response. The so-called point estimate method, which can be shown to be exact under certain constraints, usually (i.e. depending on the number of input variables) works with only a few specific sample points. Thus, the point estimate method helps to reduce the computational load for model evaluation considerably in the case of complex models or large-scale applications. To demonstrate the point estimate method, five academic but typical examples of railway asset management are analyzed in more detail: (a) track degradation, (b) reliability analysis of composite systems, (c) terminal reliability in rail networks, (d) failure detection/identification using decision trees, and (e) track condition modeling incorporating maintenance. Advantages as well as limitations of the point estimate method in comparison with common Monte Carlo simulations are discussed.