Overview of reliability estimation methods for mechanical systems under operating conditions

The estimation of reliability of mechanical systems under variable constraints needs the knowledge of the failure modes to which the system is subjected. These mechanical systems are generally complex, that is why this article first presents two MATLAB libraries Reliabilitix and Simulatrix developed to estimate reliability of such systems. Two methods, used to determine reliability parameters, are detailed and implemented in the libraries: the regression method and the maximum likelihood estimator (MLE) method. Second, this article studies the reliability relative to the fatigue failure mode, which is established combining the distribution of the endurance limit and the Wöhler’s law. For that, two reliability models, which are function of operating variables, are presented and applied to fatigue. The first one considers that the parameters of the reliability distribution depend of the operating variables and the second is Cox’s proportional hazards model. Both can be used to identify the reliability of a mechanical equipment subject to fatigue, but the first one is more adapted because it depends on the failure mode. Keywords—Reliability, Fatigue, Lognormal, Cox’s PHM