EVOLUTION OF 2K FACTORIAL DESIGN: EXPANSION AND CONTRACTION OF THE EXPERIMENTAL REGION WITH A FOCUS ON FUZZY LEVELS

Abstract

This research presents a novel approach of an evolution of the 2^k factorial design (E2kFD) which is based on a fuzzy search heuristic technique. Moreover, this approach allows multiple horizontal and vertical exploration spaces, expanding and contracting the experimental region within the region of operability. It can be achieved by defining a variable position for each point or treatment of study factors in its geometric representation, as an alternative to the conventional 2^k factorial design in which fixed positions at the vertices of its geometric representations are defined. In general, the main disadvantage of model-based DoE methods is the requirement for fast and reliable decision making in setting the deterministic value for each level. It is often that the value of the levels is unknown in advance inducing imprecision and vagueness when these are determined by experts based on their heuristic knowledge. For this reason, the proposed method combines the main advantages to use values with uncertainty for each one of the levels and to be able to explore inside and outside of the experimental region to assign variables positions to coded levels, and therefore the method works iteratively. Moreover, in the proposed fuzzy search heuristic technique approach the high and low levels of each factor are considered as linguistic variables. These are classified into three linguistic labels in a simple and clear language as: regular, major and minor which are used as an indicator of strength. A maximum fuzzy operator in the implication and aggregation stages are used to search the highest membership value and their position to assign feasible fuzzy levels as one of the scientific contributions of the present investigation. The method is demonstrated with a simulation, which shows the potential of the proposed approach. Additionally, the traditional 2^k factorial and our evolved E2kFD expert designs were validated conducting the experimental tests in a textile company in southern Guanajuato, Mexico. Finally, by comparing the results between the traditional and our proposed designs, it will be shown that better explanation and prediction models for the response variables under study are obtained with the E2kFD proposed design.