The science of engineering is soiled by uncertainties. The experimental data cost. The design stumbles at random. The objective of the design is to maximize the chances of success of a dimensioning. The objective of this work is to allow the users to understand the main methods. This volume is centered on a vast range of statistical distributions met in reliability. The aim is to run statistical measures, to present a report of enhanced measures in mechanical reliability and to evaluate the reliability of the repairable or not repairable systems. To reach these purposes, we present an approach theory /practice based on these themes: Criteria of failures; Bayesian Applied Probability; Chains of Markov; Simulation of Monte Carlo and finally many solved cases of studies.