DOI: https://doi.org/10.15588/1607-3274-2020-4-6

### THE METHOD OF BUILDING PLANS OF MULTIFACTORIAL EXPERIMENTS WITH MINIMAL NUMBER OF FACTOR LEVELS MEASUREMENTS AND OPTIMAL BY COST (TIME) EXPENSES

#### Abstract

Context. Relevant task of developing the method of plans building for multifactorial experiments was solved with minimal number of factor levels measurements and optimal by cost (time) expenses.

Objective. To develop method and means of synthesis the plans of multifactorial experiment with minimal number of factor levels measurements and optimal by cost (time) expenses.

Methods. Methods of experiment planning gives possibility to reduce cost (time) expenses when researching different technological processes, devices and systems.

Quantity of factor levels measurements minimization during the process of building the plans of multifactorial experiments also leads to cost (time) reduction on their implementation.

Suggested earlier method of building the plans of multifactorial experiments, based on Grey code application, provides a possibility to minimize number of factor levels measurements. But such plans are not always optimal in relation to cost (time) expenses. That’s why the task appears to develop a method and means of synthesis the plans of multifactorial experiment with minimal number of factor levels measurements and optimal by cost (time) expenses.

Essence of a suggested method consists of: generation of permutations with minimal number of transpositions for neighbor elements; number of factor level variations is determined for each obtained plan by calculating the distance after Hamming for neighbor pairs of binary words; recording the plan with minimal number of factor levels measurements into set D; analysis of binary codes that enter set D, among which codes, received form Grey code by E, H and (E, H) transformations are present; searching among modified Grey codes G(E, H) such codes, that are optimal by cost (time) expenses.

Results. Software which performs the suggested method of building the plans with minimal number of factor levels measurements and optimal by cost (time) expenses was developed. Software allows to synthesize optimal plans of experiment with k = 3,…, 4 number of factors.

Conclusions. Computer experiments, that were carried out to build optimal plans to research such an objects as production of pieces by hot press forming technological process and a tracking system proved workability and effectiveness both of the developed method and software for its performance.

Scientific novelty is represented by method, that allows to synthesize plans of multifactorial experiments with minimal number of factor levels measurements and optimal by cost (time) expenses.

Practical importance of the results is that developed software can find wide application for technological processes, devices and systems researching, if it is possible to implement active experiment.

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Copyright (c) 2020 N. D. Koshevoy, V. A. Dergachov, H. V. Pavlyk, O. V. Zabolotnyi, I. I. Koshevaya, Е. М. Kostenko

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