Adaptive combined space-filling and D-optimal designs

In the beginning of sequential experimentation, space-filling designs are more appropriate for exploring process behaviour since they do not require any assumptions about the underlying model. In the latter stages of sequential experimentation, however, when data are collected and more knowledge about the process behaviour is gathered, model-based optimal designs may be more appropriate. This article proposes an adaptive combined design (ACD) balancing the characteristics of both design criteria at different stages of the sequential experiments. The tuning parameter associated with the ACD adaptively gauges the amount of process knowledge gain, which is used to improve the estimation of model parameters while still allowing for the exploration of model uncertainties. Rather than employing the weighted-sum method, an ϵ$ \epsilon $-constraint method is proposed to balance the two design criteria. Property investigation shows that the ACD provides better estimation of parameters over the space-filling design, and yet is more robust against model misspecification when compared to optimal designs. Simulated and real-life nanofabrication examples illustrate the needs of the ACD and the interesting features of the tuning parameter in searching for the process optimum.