Run Orders of Central Composite Designs with Correlated Observations and Block Structure

[[abstract]]In this thesis, we are interested in finding the run orders of central composite designs for rotatability with correlated structures. Based on the rotatable conditions in Das (1997), run order of central composite design is studied for two different inter-class correlated structures. Given a central composite design that contains 2^k full factorial design; 2^(k-1)+k+2 center points and 2k star points with alpha=2^(k/4), the rotatable run order are determined. Then for any central composite design, we transform the rotatable run order problem as an maximization problem according to the rotatable measure proposed by Das (1999). To solve this maximization problem, a simulate annealing algorithm in Zhou (2001) is modified for searching the corresponding optimal run order.(2001) is modified for searching the corresponding optimal run order