Bayes estimation of a Stochastic Index For Reliability and Quality Assessment of Transportation Systems

The paper address the topic of an efficient evaluations of the performances of transportation systems in terms of both Quality and Reliability, by means of an “ad hoc” developed mathematical index which puts the two aspects in close connection. This relationship is in accordance with the current state of art of the studies on the transportation Systems, and takes advantage of recent developments in the stochastic process theory, as well as risk and safety analysis. The two aspects of Quality and Reliability are indeed closely related, especially if dynamic aspects in system’s behavior are taken into account. According to this philosophy, the authors discuss the main features of the proposed index, and illustrate the adoption of a suitable Bayesian method for its estimation, which is based upon prior (or “a priori”) information, which should be easily available. For this purpose, the Beta and the Gamma distribution are chosen as prior models on the parameters, implying a Negative Log-Gamma for the index. Finally, the summary of a large set of numerical simulations is presented, which show the high efficiency of such Bayesian estimation methodology. In particular, its superiority with respect to the “classical” Maximum Likelihood (ML) estimation methods, traditionally adopted for such systems, is illustrated.