Stochastic kriging (SK) methodology has been known as an effective metamodeling tool for approximating a mean response surface implied by a stochastic simulation. In this paper we provide some theoretical results on the predictive performance of SK, in light of which novel integrated mean squared error-based sequential design strategies are proposed to apply SIC for mean response surface metamodeling with a fixed simulation budget. Through numerical examples of different features, we show that SIC with the proposed strategies applied holds great promise for achieving high predictive accuracy by striking a good balance between exploration and exploitation. Published by Elsevier B.V.

假設二元反應曲線為簡單線性羅吉斯迴歸模型(Simple Linear Logistic Regression Model)，在樣本數為偶數的前題下，所謂的最佳D型設計(D-Optimal Design)是直接將半數的樣本點配置在第17.6個百分位數，而另一半則配置在第82.4個百分位數。很遺憾的是，這兩個位置在參數未知的情況下是無法決定的，因此逐次實驗設計法(Sequential Experimental Designs)在應用上就有其必要性。在大樣本的情況下，本文所探討的逐次實驗設計法在理論上具有良好的漸近最佳D型性質(Asymptotic D-Optimality)。尤其重要的是，這些特性並不會因為起始階段的配置不盡理想而消失，影響的只是收斂的快慢而已。但是在實際應用上，這些大樣本的理想性質卻不是我們關注的焦點。實驗步驟收斂速度的快慢，在小樣本的考慮下有決定性的重要性。基於這樣的考量，本文將提出三種起始階段設計的方法並透過模擬比較它們之間的優劣性。 / The D-optimal design is well known to be a two-point design for the simple linear logistic regression function model. Specif-ically , one half of the design points are allocated at the 17.6- th percentile, and the other half at the 82.4-th percentile. Since the locations of the two design points depend on the unknown parameters, the actual 2-locations can not be obtained. In order to dilemma, a sequential design is somehow necessary in practice. Sequential designs disscused in this context have some good properties that would not disappear even the initial stgae is not good enough under large sample size. The speed of converges of the sequential designs is influenced by the initial stage imposed under small sample size. Based on this, three initial stages will be provided in this study and will be compared through simulation conducted by C++ language.

Fischer-Tropsch Synthesis (FTS) is a promising technology for the production of ultra-clean fuels and chemical feedstocks from biomass, coal, or natural gas. Iron catalysts are ideal for conversion of coal and biomass. However, precipitated iron catalysts used in slurry-bubble column reactors suffer from high attrition resulting in difficulty separating catalysts from product and increased slurry viscosity. Thus, development of an active and selective-supported iron catalyst to manage attrition is needed. This thesis focuses on the development of a supported iron catalyst and kinetic models of FTS on the catalyst using advanced statistical methods for experimental design and analysis. A high surface area alumina, modified by the addition of approximately 2 wt% lanthanum, was impregnated with approximately 20 wt% Fe and 1% Pt in a two step procedure. Approximately 10 wt% Fe and 0.5 wt% Pt was added in each step. The catalyst had a CO uptake of 702 μmol/g, extent of reduction of 69%, and was reduced at 450°C. The catalyst was stable over H2 partial pressures of 4-10 atm, CO partial pressures of 1-4 atm, and temperatures of 220-260°C. Weisz modulus values were less than 0.15. A Langmuir-Hinshelwood type rate expression, derived from a proposed FTS mechanism, was used with D-optimal criterion to develop experiments sequentially at 220°C and 239°C. Joint likelihood confidence regions for the rate expression parameters with respect to run number indicate rapid convergence to precise-parameter estimates. Difficulty controlling the process at the designed conditions and steep gradients around the D-optimal criterion resulted in consecutive runs having the same optimal condition. In these situations another process condition was chosen to avoid consecutive replication of the same process condition. A kinetic model which incorporated temperature effects was also regressed. Likelihood and bootstrap confidence intervals suggested that the model parameters were precise. Histograms and skewness statistics calculated from Bootstrap resampling show parameter-effect nonlinearities were small.