A MODIFIED CLASS OF COMPOSITE DESIGNS FOR THE RESPONSE MODEL APPROACH WITH NOISE FACTORS - Oh, Jinho (International Journal of Industrial Engineering: Theory, Applications and Practice, 2023)
A class of composite designs involves factorial, axial, and center points. Factorial points are with a variance-optimal design for a first-order or interaction model, and axial points provide information about the existence of curvature. The center points allow for efficient estimation of the pure quadratic terms. From these properties, a class of composite designs is recommended if resources are readily available and a high degree of precision of parameter estimate is expected and evolves from their use in sequential experimentation. However, there are often cost constraints imposed on experiments. Previous studies show that resolution, orthogonal quadratic effect property, and saturated or near-saturated design reduce the number of experiments. This study extends the response model approach with noise factors to composite designs satisfying these properties. These modified composite designs are further discussed and examined in terms of scaled prediction error variance and extended scaled prediction variance, which provides a good distribution of the prediction variance of the response. Based on these criteria, the best performance design is suggested according to the number of control and noise factors. As a result, we show that the modified designs showing robustness to noise factors and stability of predictive variance are a class of modified small composite designs and modified augmented-pair designs.