A robust two-stage sequential design for estimating the effective range based on binary responses

The estimation of the effective range of the logic signal devices which have good application prospects in the development of intelligent information transmission equipments, is a significant problem. Numerous studies concentrate on models to estimate this range based on collected data. However, a design that can enable efficient data collection is a crucial factor that has received scant attention. To overcome this problem, this study proposes a two-stage sequential design. The first stage utilizes a modified binary search strategy to quickly correct the rough estimations of the parameters, and the second stage employs a maximum likelihood estimation (MLE) iteration strategy that converge the experimental sequences at endpoints of the effective range. The new method is robust to the model assumptions and initial guesses and can address the cold-start problem experienced by the local D-optimal method. A theoretical analysis denotes that the proposed method is asymptotically consistent. Some simulation studies have demonstrated the superiority of the proposed method over the local D-optimal method in the terms of mean square error and computational time; furthermore, the simulation study based on real gap-null gate experiment data confirms that the new method is more efficient for saving materials and resources, which is of great benefit in applications.