A Comparison of Three-Level Orthogonal Arrays in the Presence of Different Correlation Structures in Observations

Abstract

When the experimenter suspects that there might be a quadratic relation between the response variable and the explanatory parameters, a design with at least three points must be employed to establish and explore this relation (second-order design). Orthogonal arrays (OAs) with three levels are often used as second-order response surface designs. Generally, we assume that the data are independent observations; however, there are many situations where this assumption may not be sustainable. In this paper, we want to compare three-level OAs with 18, 27, and 36 runs under the presence of three specific forms of correlation in observations. The aim is to derive the best designs that can be efficiently used for response surface modeling.

Keywords:

• Change of variance functions
• Correlation in observations
• First-Order Autoregressive Disturbances
• First-Order Moving Average Disturbances
• Optimal Designs
• Orthogonal Arrays

Mathematics Subject Classification :

• 62K05
• 62K20
• 62M10