A Low-Complexity Algorithmic Method for Constructing Balanced and Near-Orthogonal 3k-p Fractional Factorial Designs with 5 to 10 Factors

3k experimental designs are very useful in industry and research. However, their application is limited because increasing the number of factors exponentially expands the required experimental runs. A standard alternative to mitigate this issue is the implementation of 3k-p designs. The proposed method offers a lightweight, deterministic alternative to traditional experimental construction approaches, which typically rely on three methodologies: the traditional one using algebraic generators, which ceases to be practical after exceeding five factors; the use of existing fractions catalogs, which depends on their availability and restricts the experiment to the pre-established fraction; and advanced optimization methods to identify the desirable fractions, which require high technical specialization and consume excessive computational and economic resources before starting the research. This study proposes a simple, computationally efficient method to generate fractions of 3k-p designs with five to 10 factors with good balance and orthogonality properties for main effects, as well as a low level of factor confounding. This method boasts high efficiency by selectively identifying which experimental runs to execute in each iteration. The generated fractions were validated against Xu’s orthogonal arrays, demonstrating excellent performance. Therefore, the proposed method is software-independent due to its highly intuitive, user-centric design, allowing it to be used in a wide range of scenarios within industry and research, whether for a process or product improvement, or for research purposes.