An efficient simulation method for reliability analysis of systems with expensive-to-evaluate performance functions

This paper proposes a novel reliability analysis method which computes reliability index, most probable point and probability of failure of uncertain systems more efficiently and accurately with compared to Monte Carlo, first-order reliability and response surface methods. It consists of Initial and Simulation steps. In Initial step, a number of space-filling designs are selected throughout the variables space, and then in Simulation step, performances of most of samples are estimated via interpolation using the space-filling designs, and only for a small number of the samples actual performance function is used for evaluation. In better words, doing so, we use a simple interpolation function called "reduced" function instead of the actual expensive-to-evaluate performance function of the system to evaluate most of samples. By using such a reduced function, total number of evaluations of actual performance is significantly reduced; hence, the method can be called Reduced Function Evaluations method. Reliabilities of six examples including series and parallel systems with multiple failure modes with truncated and/or non-truncated random variables are analyzed to demonstrate efficiency, accuracy and robustness of proposed method. In addition, a reliability-based design optimization algorithm is proposed and an example is solved to show its good performance.