RESEARCH OF MULTIPLE PLANS IN MULTI-FACTOR EXPERIMENTS WITH A MINIMUM NUMBER OF TRANSITIONS OF LEVELS OF FACTORS

Abstract

Contex. The actual problem of reducing the set of plans for multivariate experiments in searching for the best in price costs has been solved. Objective is the synthesis and study of a variety of experimental plans with a minimum number of transitions of factor levels. Methods. The use of experimental design methods allows reducing the price and time costs in the study of various technological processes, devices and systems. Minimizing the number of transitions of levels of factors in terms of the experiment, in turn, leads to a decrease in the cost (time) of its implementation. One of the methods for reducing the number of transitions of levels of factors is the use of the Gray code when constructing a plan of an experiment. It is shown that multi-factor experiments plans constructed using the Gray code have a minimum number of transitions of factor levels, but are not always optimal in terms of the cost (time) of the experiment. For the synthesis of many experimental plans with a minimum number of transitions of levels of factors in searching for the optimal plan for cost (time) costs, a method based on the generation of binary code variants is proposed. Analysis of their characteristics and the choice of sequences that meet specified requirements were conducted. The formation of test plans for an experiment is carried out according to the method based on the generation of variants for constructing plans, determining equivalence classes with respect to a given group P of transformations and forming a set of typical representatives for the selected equivalence classes. Results. Software that implements the proposed methods, which is used in the construction of a set of experimental plans for the number of factors K = 3 with the minimum number of level transitions was developed. Conclusions. The experiments, which were carried out, confirmed the efficiency of the proposed methods and the software implementing them makes it possible to reduce the set of experiment plans for finding the optimal one. The scientific originality of the research is presented by the methods which allow to synthesize many plans of multifactor experiments to reduce the search for optimal plans in price (time) cost. The practical significance of the research results is in the developed software which implements the proposed methods. It can be widely used in the study of technological processes, devices and systems, on which the implementation of an active experiment is possible.