36 Int. J. Reliability and Safety, Vol. 9, No. 1, 2015 Copyright © 2015 Inderscience Enterprises Ltd. Probabilistic re-analysis of nonlinear systems when energy of excitation changes Mahdi Norouzi* Department of Physics and Engineering, Frostburg State University, 101 Braddock Road, Frostburg, MD 21532, USA Email: mah.norouzi@gmail.com *Corresponding author Efstratios Nikolaidis Mechanical Industrial and Manufacturing Engineering Department, The University of Toledo, 4006 Nitschke Hall, Toledo, OH 43606, USA Email: enikolai@eng.utoledo.edu Abstract: A reliability study of nonlinear mechanical systems under random dynamic loads often requires Monte Carlo simulation in the time domain with hundreds of thousands of replications. The uncertainties involved in design make such analyses necessary for various admissible loads, which can be impractical. The authors have already developed a methodology that reduces the computational cost of Monte Carlo simulation when the load is represented by a Power Spectral Density (PSD) function. This method is based on a probabilistic re-analysis, which uses results from a simulation for a single PSD to estimate the reliability for other admissible PSDs. However, the methodology was limited to PSDs with the same energy content. This paper proposes an approach to extend the applicability of the above method to cases in which the energy content of the PSD functions changes. Keywords: Monte Carlo simulation; probabilistic re-analysis; random vibration; power spectral density function; probability of first-passage. Reference to this paper should be made as follows: Norouzi, M. and Nikolaidis, E. (2015) ‘Probabilistic re-analysis of nonlinear systems when energy of excitation changes’, Int. J. Reliability and Safety, Vol. 9, No. 1, pp.36–50. Biographical notes: Mahdi Norouzi is currently an Assistant Professor of Mechanical Engineering at the Department of Physics and Engineering at Frostburg State University in Maryland, USA. He received his PhD in Mechanical Engineering from the University of Toledo in Ohio in 2012. His research focuses on reliability-based design, stochastic mechanics, and wind energy. Efstratios Nikolaidis is a Professor of Mechanical Engineering in the Mechanical, Industrial and Manufacturing Engineering Department at the University of Toledo, in Toledo, Ohio, USA. Since 1980, he has studied reliability design of aircraft, turbines and ocean structures. His research focuses on the decision-based design of engineering systems when there is limited