An efficient sampling technique for off-line quality control

The basic setting of this article is that of parameter-design studies using data from computer models. A general approach to parameter design is introduced by coupling an optimizer directly with the computer simulation model using stochastic descriptions of the noise factors. The computational burden of these approaches can be extreme, however, and depends on the sample size used for characterizing the parametric uncertainties. In this article, we present a new sampling technique that generates and inverts the Hammersley points (a low-discrepancy design for placing n points uniformly in a k-dimensional cube) to provide a representative sample for multivariate probability distributions. We compare the performance of this to a sample obtained from a Latin hypercube design by propagating it through a set of nonlinear functions. The number of samples required to converge to the mean and variance is used as a measure of performance. The sampling technique based on the Hammersley points requires far fewer samples to converge to the variance of the derived distributions. An application to off-line quality control of a continuous-stirred tank reactor illustrates that the Hammersley points require up to 40 times fewer samples to converge to the variance of the derived distribution.