Abstract—In field or laboratory planned experiments, it is possible to observe vague, incomplete, or imprecise data due to known or unknown reasons. Thus, the analysis should take into consideration the imprecision in data vales. In recent past, researchers have proposed various approaches such as fuzzy, intuitionistic fuzzy and neutrosophic logic and analysis, which provide better understanding, analysis and interpretations of the imprecise data. Experimental design and analysis is a systematic, rigorous approach to problem solving that applies principles and techniques at the data collection stage so as to ensure the generation of valid, defensible, and supportable conclusions. Factorial designs are widely used in experiments that involve several factors and where it is necessary to study the joint effects of the factors on a response. Several special cases of the general factorial design are important because they are widely used in research work and also because they form the basis of other designs of considerable practical value. These designs are widely used in factor screening experiments as well. The most important of these special cases is that of k factors, each at only two levels. These levels may be quantitative or they may be qualitative. A complete replicate of such a design is called a 2^k-factorial design. In this paper, we consider the first design in the 2^k-series which is one with only two factors, say A and B, each run at two levels. The levels of the factors may be arbitrarily called low and high. This design is called a 2²-factorial design. For the imprecise response data, we will define a neutrosophic 2²-factorial design (N2²FD), neutrosophic model and neutrosophic analysis. As an illustration, we consider an investigation into the effect of the concentration of the reactant and the amount of the catalyst on the conversion (yield) in a chemical process. The objective of the experiment is to determine if adjustments to either of these two factors would increase the yield.

Keywords—Imprecise data, neutrosophic statistics, neutrosophic factorial design, neutrosophic analysis

Cite: Pranesh Kumar, "Neutrosophic 2²-Factorial Designs and Analysis," International Journal of Applied Physics and Mathematics, vol. 14, no. 2, pp. 59-66, 2024.

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