An algorithm for arranging response surface designs in small blocks

• Published in: Computational statistics & data analysis Vol. 33; no. 1; pp. 25 - 43
• Main Authors: Trinca, Luzia A., Gilmour, Steven G.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 28-03-2000; Elsevier Science; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Blocking; Box–Behnken design; Central composite design; Exact sciences and technology; Experimental design; Interchange algorithm; Mathematics; Probability and statistics; Sciences and techniques of general use; Scores; Second-order model; Statistics; Weighted mean efficiency factor; Central composite design; Box–Behnken design; Weighted mean efficiency factor; Blocking; Scores; Second-order model; Interchange algorithm; Score test; Experimental design; Composite design; Efficiency factor; Box Behnken design; Algorithm
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/S0167-9473(99)00033-X

We consider the problem of blocking response surface designs when the block sizes are prespecified to control variation efficiently and the treatment set is chosen independently of the block structure. We show how the loss of information due to blocking is related to scores defined by Mead and present an interchange algorithm based on scores to improve a given blocked design. Examples illustrating the performance of the algorithm are given and some comparisons with other designs are made.