Miscellanea: Probability-based Latin hypercube designs for slid-rectangular regions

Existing space-filling designs are based on the assumption that the experimental region is rectangular, while in practice this assumption can be violated. Motivated by a data centre thermal management study, a class of probability-based Latin hypercube designs is proposed to accommodate a specific type of irregular region. A heuristic algorithm is proposed to search efficiently for optimal designs. Unbiased estimators are proposed, their variances are given and their performances are compared empirically. The proposed method is applied to obtain an optimal sensor placement plan to monitor and study the thermal distribution in a data centre. © 2010 Biometrika Trust.