The mechanisms of some scientific phenomena are understood sufficiently well that useful mathematical models that flow directly from the physical mechanisms can be written down. Such models are not considered in this study. Response surface methodology in Schlaflian vectors and matrices representation for rotatability of experimental design points and optimal design theory in Kronecker product representation for measuring rotatability of experimental design points will be appropriate to the study of phenomena that are presently not sufficiently well understood to permit the mechanistic approach. These two techniques have three kinds of applications one approximate mapping of a surface within a limited region two choice of operating conditions to achieve desired specifications and three search for optimal conditions and area generalization of factorial designs emphasizing the concept of rotatability. The problem of fitting a curve to the relationship between the concentration of a stimulus and the proportion of individuals responding transforming proportions to the corresponding normal deviates for data from psychological experiments is the precursor of these techniques.
