Stochastic Analysis

In general, sources of uncertainties in engineering analysis problems are broadly divided into four; physical uncertainties, model uncertainties, human error, and estimation error. Human errors represent the error involves in the stage of design, construction or operation. Finally, estimation errors which are statistical errors occur due to fluctuations in measurements, sampling and predictions. Simulation methods calculate the failure probability by employing sampling and estimation. The techniques work well with both implicit as well as explicit functions. The most popular method for reliability analysis is perhaps the Direct Monte Carlo simulation (MCS). MCS is a widely used method for computing multivariate integral in statistical physics. The overarching goal in engineering is to design a system/structure that is economical and safe. In reliability-based design optimization, the goal is to ensure that the optimized system is reliable enough. As a consequence, robust design optimization is computationally expensive.