Reliability of dynamic systems in random environment by extreme value theory

• Reliability estimates for random vibration problems by the extreme value theory.
• Reliability estimates that extend Monte Carlo estimates beyond data.
• MATLAB functions for estimating system reliability under Gaussian/non-Gaussian inputs.

A practical method is developed for estimating the performance of highly reliable dynamic systems in random environment. The method uses concepts of univariate extreme value theory and a relatively small set of simulated samples of system states. Generalized extreme value distributions are fitted to state observations and used to extrapolate Monte Carlo estimates of reliability and failure probability beyond data. There is no need to postulate functional forms of extreme value distributions since they are selected by the estimation procedure. Our approach can be viewed as an alternative implementation of the method in [7] for estimating system reliability. Numerical examples involving Gaussian and non-Gaussian system states are used to illustrate the implementation of the proposed method and assess its accuracy.