Construction of orthogonal Latin hypercube designs with flexible run sizes

Fasheng Sun, Min Qian Liu, Dennis K.J. Lin

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


Latin hypercube designs (LHDs) have recently found wide applications in computer experiments. A number of methods have been proposed to construct LHDs with orthogonality among main-effects. 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. The orthogonal LHDs constructed by Ye (1998), Cioppa and Lucas (2007), Sun et al. (2009) and Georgiou (2009) all have this property. 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. In this paper, we construct orthogonal LHDs with more flexible run sizes which also have the property that the sum of elementwise product of any three columns is 0. Further, we compare the proposed designs with some existing orthogonal LHDs, and prove that any orthogonal LHD with this property, including the proposed orthogonal LHD, is optimal in the sense of having the minimum values of ave(t), tmax, ave(q) and qmax.

Original languageEnglish (US)
Pages (from-to)3236-3242
Number of pages7
JournalJournal of Statistical Planning and Inference
Issue number11
StatePublished - Nov 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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