SAMS: Stochastic Analysis With Minimal Sampling—A Fast Algorithm for Analysis and Design Under Uncertainty

Design of processes and devices under uncertainty calls for stochastic analysis of the effects of uncertain input parameters on the system performance and process outcomes. The stochastic analysis is often carried out based on sampling from the uncertain input parameters space, and using a physical model of the system to generate distributions of the outcomes. In many engineering applications, a large number of samples—on the order of thousands or more—is needed for an accurate convergence of the output distributions, which renders a stochastic analysis computationally intensive. Toward addressing the computational challenge, this article presents a methodology of $S̱$tochastic $A̱$nalysis with $M̱$inimal $S̱$ampling (SAMS). The SAMS approach is based on approximating an output distribution by an analytical function, whose parameters are estimated using a few samples, constituting an orthogonal Taguchi array, from the input distributions. The analytical output distributions are, in turn, used to extract the reliability and robustness measures of the system. The methodology is applied to stochastic analysis of a composite materials manufacturing process under uncertainty, and the results are shown to compare closely to those from a Latin hypercube sampling method. The SAMS technique is also demonstrated to yield computational savings of up to 90% relative to the sampling-based method.