Assessment of national reference values for railway safety: a statistical treatment

We discuss the decision procedure used in the Commission Decision for national reference values. According to the safety directive, every year seven safety indicators have to be computed for every member state. In the decision, a fixed procedure has been presented for computing the safety indicators and to assess whether there is a possible deterioration in safety. In the safety assessment, the decision depends on a weighted sum in place of an arithmetic mean. It is then of interest how such a decision procedure would behave and what would be the advantages and disadvantages of the particular method. In this article, we study a slightly simplified version of the procedure by two means. First, we analyze the weighted sum and derive its characteristic as efficiency. Moreover, we compare it via a spread with an ordinary sample mean. We support the theoretical results with the help of a simple simulation study in order to estimate failure probabilities of the first and second kinds. In particular, we construct such alternative distributions that the decision procedure cannot distinguish.