Augmented Method For Supersaturated Design In The Case Of Adding New Factors

In many industrial experiments,people usually use sequential experiments to explore the relationship between factors and responses.In the initial stage of the experiment,a screening experiment is designed to understand a complex and expensive system by efficiently identifying the system’s most influential factors.Since the supersaturated designs are posited to effectively screen factors even when the number of runs is less than the number of considered factors,which greatly save time and economic costs.Therefore,the 2-level supersaturated design is often used as the screening design in the initial phase of the experiment.However,in the actual operations,some important factors may be ignored in the initial stage of the experiment for some reasons,and they need to be added in the next stage,so we need to augment the number of factors;because the initial design is a 2-level supersaturated design,it can only be used to study the linear effects of factors,if we want to further study the quadratic effects of certain factors,we need to augment the level of these factors;in addition,the experimental information accumulated in the initial stage and experts advice also have guiding significance for the next phase of the experiment.In view of the above requirements,according to the two situations where the newly added factors have different levels at the initial stage,based on two optimal criteria,we respectively propose two designs that both augment the number of factors and augment the level.When the newly added factors can be controlled at a certain level,and we will examine the influence of these new factors which level in the neiborhood area on the response in the next stage,according to the Bayesian D-optimal criteria,we propose Bayesian D-optimal column augment design;when the newly added factors level are allowed to change within a certain range and are unknown at the initial stage,we propose the integrated Bayesian D-optimal criteria,and the approximately integrated Bayesian D-optimal column augmented design can be obtained.In this paper,we take the E(s2)-optimal supersaturated designs as the initial design,and then use different variable selection methods to screen the active factors,the analysis results of the initial experiment would be used as valid prior information to conduct the next-stage design.Furthermore,the obtained column augmented design and the initial design are combined into a large design,and identify significant effects under the second-order model considering effect heredity principle and including block effect.Examples and simulation results show that the two augmented designs could effectively identify the latent factors effects and detect the curvature effects.