![]() However, the run size n of any design in the former three references must be a power of two (n=2c) or a power of two plus one (n=2c+1), which is a rather severe restriction. (2009) and Georgiou (2009) all have this property. LHDs constructed by Ye (1998), Cioppa and Lucas (2007), Sun et al. When second-order effects are present, it is desirable that an orthogonal LHD satisfies the property that the sum of elementwise products of any three columns (whether distinct or not) is 0. ![]() A number of methods have been proposed to construct LHDs with orthogonality among main-effects. Latin hypercube designs (LHDs) have recently found wide applications in computer experiments. They also rate comparably to maximin Latin hypercube designs by the minimum interpoint distance criterion used in the latter's construction. These rotated factorial designs are very easy to construct and preserve many of the attractive properties of standard factorial designs: they have equally-spaced projections to uni-variate dimensions and uncorrelated regression eeect estimates (orthogonality). This paper presents a new class of designs developed from the rotation of a two-dimensional factorial design in the plane. A number of alternative designs have been proposed, but many can be burdensome computationally. Standard factorial designs are inadequate in the absence of one or more main eeects, their replication cannot be used to estimate error but in-stead produces redundancy. However, to use these models for scientiic inves-tigation, their generally long running times and mostly deterministic nature require a special designed experiment. Some newly constructed orthogonal Latin hypercube designs are tabulated for practical use.Ĭomputer models can describe complicated physical phenomena, such as performance characteristics of integrated circuits. In addition, we provide a method to construct a new class of orthogonal Latin hypercube designs with multi-dimensional stratifications by rotating regular factorial designs. Besides orthogonality, the resulting designs also preserve better space-filling property than those constructed by using the existing methods. The newly constructed column-orthogonal designs ensure that the estimates of all linear effects are uncorrelated with each other and even uncorrelated with the estimates of all second-order effects (quadratic effects and bilinear effects) when the rotated orthogonal arrays have strength larger than two. In this paper, we propose some methods to construct column-orthogonal designs with multi-dimensional stratifications by rotating symmetric and asymmetric orthogonal arrays. However, they usually do not achieve maximum stratifications in multi-dimensional margins. The orthogonal Latin hypercube design and its relaxation, and column-orthogonal design, are two kinds of orthogonal designs for computer experiments.
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