Statistical Analysis of Various Optimal Latin Hypercube Designs

Among several Design of Experiments (DoEs), Latin Hypercube Design (LHD) is one of the most frequently used methods in the field of physical experiments and in the field of computer simulations to find out the behavior of response surface of the surrogate model with respect to design points. A good experimental design should have three important characteristics, namely (i) non-collapsing, (ii) space-filling and (iii) orthogonal properties. Though inherently LHD preserves non-collapsing property, but randomly generated LHDs have poor space-filling in terms of minimum pair-wise distance. In order to ensure the last two properties in LHD, researchers are frequently looking for finding optimal LHD in the sense of space-filling and orthogonal properties. Moreover, researchers are frequently encountered the question, which distance measure is the best in the case of optimal designs? In the literature, several types of optimal LHDs are available such as Maximin LHD, Orthogonal LHD, Uniform LHD, etc. On the other hand, two distance measures namely Euclidean and Manhattan distance measures are used frequently to find optimal DoEs. But which one of the two distance measures is better, is still unknown. In this article, intensive statistical analysis has been carried out on numerical instances to explore the deep scenario of each optimal LHD. The main goal of this research is to find out a scenario of the well-known optimal designs from statistical point of view. From this elementary experimental study, it seems to us that in the sense of space-filling, Euclidean distance measure-based Maximin LHD is the best. But if one needs space-filling along with better orthogonal property, then multi-objective (Maximin with approximate orthogonal)-based optimal LHD is relatively better than Maximin LHD.