LAUSR

Abstract In our research work, the problem of how to construct the optimal design of collapse mixture model has been further explored and studied, and some new progress has been made. In this paper an abstract optimal criterion which is called normality optimality criteria is proposed by specifying some features of its equivalent matrix and invariant. And the optimality criteria, such as D-, A-, and R- etc., are proved to be normality optimality criteria. Meanwhile, the concept of collapsed homogeneous linear model is also proposed, and an inequality related to the collapsed homogeneous linear model is also proved. For multi mixture experiment, a concept of optimal weights for collapsed mixture model is also proposed first. For the so-called normality optimality criterion, an optimal weight for the collapsed homogeneous linear model is obtained by using these concepts and inequality mentioned above. The results obtained in this paper are not only applicable to the optimality criteria, such as D-, A-, and R- etc., but also applicable to the normal optimality criteria satisfying certain conditions.