APPROXIMATION OF SYSTEM RELIABILITIES USING A SHOOTING MONTE-CARLO APPROACH

A new Monte Carlo based method is presented for estimating the system reliability of constraint bounded design spaces. The new method is fir st developed in its general form, which is applicable to any joint pro bability distribution. It is also demonstrated that this method can be used to concurrently estimate derivatives of tile system reliability (e.g., for use in gradient-based numerical optimization). The method i s then specialized to tile particular case of an n-dimensional Gaussia n (normal) distribution, which allows for a simpler form. An important property of probability distributions, the dead band effect, is also presented, and it is shown that this effect has important ramification s for the application of the shooting Monte Carlo approach. Finally, n umerical values are presented that demonstrate improved efficiencies o f up to orders of magnitude relative to the conventional Monte Carlo a pproach.