The binary response experiments are often used in many areas. In many investigations, different kinds of optimal designs are discussed under an assumed model. There are also some discussions on optimal designs for discriminating models. The main goal in this work is to find an optimal design with two support points which minimizes the maximal probability differences between possible models from two types of symmetric location and scale families. It is called the minimum bias two-points design, or the $mB_2$ design in short here. D- and A-efficiencies of the $mB_2$ design obtained here are evaluated under an assumed model. Furthermore, when the assumed model is incorrect, the biases and the mean square errors in evaluating the true probabilities are computed and compared with that by using the D- and A-optimal designs for the incorrectly assumed model.

This paper is concerned with the problem of finding an experimental design for discrimination between two rival models and for model robustness that minimizing the maximum bias simultaneously in binary response experiments. The criterion for model discrimination is based on the $T$-optimality criterion proposed in Atkinson and Fedorov (1975), which maximizes the sum of squares of deviations between the two rival models while the criterion for model robustness is based on minimizing the maximum probability bias of the two rival models. In this paper we obtain the optimum designs satisfy the above two criteria for some commonly used rival models in binary response experiments such as the probit and logit models etc.