ABSTRACT
In Commission Decision 2009/460, a set of so-called NRV (National Reference Values) for each member state of the EU is estimated from accident data for several years. This problem not only occurs on the member state level but is also faced by every railway safety agency and railway operator, where, for several event categories, data from a current period of time is compared from previous periods in order to answer the question: “Has safety performance significantly deteriorated?”, with respect to either reference values or previous periods. In this paper, we propose alternative decision procedures based on well-known statistical methods. They are based on the fact that accident data can be described as a Compound Poisson Process (CPP). A CPP can be decomposed into parts: the counting process itself and the height of the jumps describing the severity of accidents. In order to compare periods of the same duration, the maximum difference of the two CPP, which results in a random walk, can be evaluated in a distribution-free way and applied to inhomogeneous processes as well. Another approach is based on a classic decomposition approach from statistical test theory. We show that the combined test can be derived from the Neyman-Pearson lemma so that the test produced is the most powerful for particular distribution assumptions. The approaches are explained by an example.
