  To identify the robust settings of the control factors, it is very important
to understand how they interact with the noise factors. In this article, we
propose space-filling designs for computer experiments that are more capable of
accurately estimating the control-by-noise interactions. Moreover, the existing
space-filling designs focus on uniformly distributing the points in the design
space, which are not suitable for noise factors because they usually follow
non-uniform distributions such as normal distribution. This would suggest
placing more points in the regions with high probability mass. However, noise
factors also tend to have a smooth relationship with the response and
therefore, placing more points towards the tails of the distribution is also
useful for accurately estimating the relationship. These two opposing effects
make the experimental design methodology a challenging problem. We propose
optimal and computationally efficient solutions to this problem and demonstrate
their advantages using simulated examples and a real industry example involving
a manufacturing packing line.
