Space-filling properties are important in designing computer experiments. The traditional maximin and minimax distance designs consider only space-filling in the full-dimensional space; this can result in poor projections onto lower-dimensional spaces, which is undesirable when only a few factors are active. Restricting maximin distance design to the class of Latin hypercubes can improve one-dimensional projections but cannot guarantee good space-filling properties in larger subspaces. We propose designs that maximize space-filling properties on projections to all subsets of factors. We call our designs maximum projection designs. Our design criterion can be computed at no more cost than a design criterion that ignores projection properties.

ZnO nanowires (NWs), an outstanding member of the family of onedimensional nanostructures, 1Ϫ3 have found many applications in fabricating electronic, optoelectronic, electrochemical, and electromechanical devices, such as ultraviolet (UV) lasers, 4 light-emitting diodes, 5 field emission devices, 6,7 solar cells, 8 as well as piezo-nanogenerators. 9,10 In general, ZnO NWs are typically manufactured by two methods, namely, physical vapor deposition and hydrothermal decomposition. In contrast to the physical vapor deposition, synthesized via the wet chemical method, the ZnO NWs are of low aspect ratio typically of 10 to 15, 11,12 which greatly limits their applications in which flexible and high surface to volume ratio ZnO NWs are needed. There has been a few reports that the aspect ratio of the ZnO NWs could be increased by adding some external capping agents, such as ethylenediamine (En) 13 and polyethylenimine (PEI); 8 however, at the same time, these capping agents might also introduce some undesirable impurities into the ZnO NWs, which would greatly undermine their applications for which untainted ZnO NWs are required.In most existing literature, synthesis of nanomaterials lacks of theoretical guidance for achieving high quality and reproducible nanomaterials. The practical requirements for nanomaterial synthesis are morphology control, dimensionality control, and orientation control. In this study, as guided by statistical methods, we performed a sequence of experiments toward growing aspect ratio enhanced ZnO NW arrays. Classic statistical analysis did not suit this application due to the uncontrollable variation in the process and complex interactions among various factors. In this work, we use pick-the-winner rule 14 and one-pair-at-a-time main effect analysis 15 to identify optimal reaction settings. By controlling the hydrothermal reaction parameters, for instance, the precursor concentration, the reaction time, and temperature, the aspect ratio of the ZnO NWs can be improved to almost twice that of the regular ZnO NWs. Furthermore, the antireflection properties were also improved dramatically with increased aspect ratio of the ZnO NW arrays, which shows great potential applications as antireflection coating layer for solar cells. RESULTS AND DISCUSSIONReaction Mechanism and Statistical Design of Experiments. The annealing process helped the as-deposited Au layer to form a uniform crystalline thin layer on the surface of the Si substrate, which was critical to the oriented growth of aligned ZnO NWs. The chemistry of the growth has been well-

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the second one models local details. The new predictor also incorporates a flexible variance model, which makes it more capable of approximating surfaces with varying volatility. Compared to the commonly used stationary Gaussian process model, the new predictor is numerically more stable and can more accurately approximate complex surfaces when the experimental design is sparse. In addition, the new model can also improve the prediction intervals by quantifying the change of local variability associated with the response. Advantages of the new predictor are demonstrated using several examples.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS570 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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