Estimation of representation of trunned orthogonal subdesigns of the full factor experiment design

A generally accepted and widely used approach to solving the problem of analyzing a system of the "composition - property" type consists in identifying and selecting a set of factors that presumably affect the value of a certain response function. Such a function characterizes the efficiency of the system's functioning and is usually formalized in the form of a regression equation that is nonlinear in terms of factors, but linear in terms of parameters. Under the conditions of a large number of influencing factors, it is difficult to solve practical problems of this type due to insufficient experimental data. If by artificial orthogonalization of a passive experiment it is possible to solve the problem of independent estimation of the degree of influence of factors and their interactions, then there is no guarantee that the interaction of factors in the selected subdesign of the experiment design is orthogonal to the factors and to each other. The degree of preference for the subdesign will be the higher, the smaller the number of interactions of factors is not orthogonal to factors and to each other. In this regard, it is important to have a substantiated criterion for assessing the quality of a truncated orthogonal subdesign of the design of a full factorial experiment, which characterizes the level of mixing of the influences of factors and their interactions. It is this criterion that is introduced in this work. The proposed technology for the formation of a representative truncated orthogonal subdesign is described on a specific example of a full factorial experiment design N = 26 formed by artificial orthogonalization. As a result, it is shown that the degree of preference for the design is the higher, the higher the order of interaction of factors mixed with the main factors and the smaller the total number of pairs of non-orthogonal columns. The result of the work was the addition of the traditional set of criteria that are usually used when choosing one of the many possible truncated orthogonal subdesigns of the full factorial experiment design with one more criterion that significantly characterizes the quality of the truncated subdesign. The introduced criterion determines the level of mixing of the influences of factors and their interactions on the value of the response function