In the last years it has been recognized the need for investigation into the reliability of accelerator systems.This requirement results from new applications of accelerators (e.g. High Power Proton Accelerators for Accelerator Production of Tritium and Accelerator Transmutation of Wastes, International Fusion Materials Irradiation Facility) demanding high availability and reliability. At present, although a significant history of accelerator operation has been accumulated over the past 50 or so years, there is a deficiency in reliability estimates of accelerator systems due to the fact that the reliability is not a major topic as far as most existing accelerators for scientific experiments, in the field of high energy physics, are concerned. The present paper intends to highlight the main issues concerning the reliability assessment of accelerator machines, focusing on the state of the art in this area and suggesting future directions for addressing the issues. In particular the topic is discussed referring mainly to Accelerator-Driven Reactor System concept, on which the effort of several research organization is focused aiming at its development.