Mathematical Sciences: Studies in Optimal and Efficient Design of Experiments

这项研究是关于构建析因实验设计，它对时间趋势具有健壮性，并且误差更普遍地相关。这些问题包括(I)当观测数据自相关时用于比较处理的最优和有效的区块和行列设计，(Ii)估计或预测相关误差区域上的响应面的最佳和有效的设计，以及(Iii)以尽可能少的运行生成满足特定实验需要的部分析因设计的系统方法。这项研究属于统计学的一个子领域，称为实验设计，它涉及制定有效分配资源的计划。这项工作将扩展目前关于实验设计的理论，以更好地适应在一段时间内收集数据的实验，而不是同时收集所有数据。

This research is on the construction of factorial experimental designs which are robust against time trends and where errors are more generally correlated. The problems include (i) optimal and efficient block and row-column designs for comparing treatments when the observations are autocorrelated, (ii) optimal and efficient designs for estimating or predicting a response surface over a region for correlated errors and (iii) systematic methods of generating fractional factorial designs to meet specific experimental needs with as few runs as possible. This research is in a subfield of statistics called experimental design which involves the development of plans for allocating resources efficiently. This work will extend the current theory on experimental design to more appropriately accommodate experiments in which data is collected over a period of time, rather than all at the same time.