On the Construction of third-order Rotatable Designs in Smaller Runs

Accepted - January 2024

Abstract

There may be situations in a product/process optimisation where a fitted second-order model fails to adequately represent the significance of the relationship between the input and response variables, ultimately leading to the estimation of parameters based on a higher (or third) order model. Sequential third-order response surface designs are beneficial for such situations, which allow for experimenting with a few additional runs and fitting a third-order model without discarding the first-stage experimental runs and generated responses. Sequential experimentation is useful in practice since it is more economical and requires fewer resources. For symmetric as well as mixed-level factors, methods of construction of sequential third-order design have been proposed in the paper that satisfy the necessary moment matrix requirement and ensure rotatability. Additionally, the proposed designs have smaller runs, making it more cost-effective to attain the best response. A comparison of the proposed design with existing sequential designs is also made on the basis of design size, G-efficiency and prediction capability using FDS and VDG plots.