We propose an approach to constructing nested Latin hypercube designs. Such designs are useful for conducting multiple computer experiments with different levels of accuracy. A nested Latin hypercube design with two layers is defined to be a special Latin hypercube design that contains a smaller Latin hypercube design as a subset. Our method is easy to implement and can accommodate any number o...

Latin Hypercube Sampling (LHS) and Jittered Sampling (JS) both achieve better convergence than standard Monte Carlo Sampling (MCS) by using stratification to obtain a more uniform selection of samples, although LHS and JS use different stratification strategies. The “Koksma-Hlawka-like inequality” bounds the error in a computed mean in terms of the sample design’s discrepancy, which is a common...

Uncertainty quantification in numerical simulations generally relies on applying sampling techniques to select input parameters for a suite of deterministic calculations and then combining the results of the calculations into output distributions. Several approaches, including metamodeling and Latin Hypercube Sampling, are prevalent today. This paper will focus on the comparison of several comm...

Manufactured parts differ from ideal shape. Therefore tolerances are used in product development in order to constrain the admissible deviations. The impact of tolerances is analyzed in different ways. It is common to employ Monte Carlo Sampling in order to obtain a statistical result by the iterative evaluation of the functional relationship. In contrast to this, Robust Design has established ...

This paper provides an updated review of Monte Carlo simulation. The use of random sampling, its consequences in simulation, the use of descriptive sampling, its advantages, its limits and its improvement upon the precision of simulation estimates: Refined descriptive sampling. This state of the art gives also an insight into other sampling procedures used in the literature, like Ranked set sam...