Cross-Entropy Loss for Recommending Efficient Fold-Over Technique

Due to the limited resources and budgets in many real-life projects, it is unaffordable to use full factorial experimental designs and thus fractional factorial(FF) designs are used instead. The aliasing of factorial effects is the price we pay for using FF designs and thus some significant effects cannot be estimated. Therefore, some additional observations(runs) are needed to break the linages among the factorial effects. Folding over the initial FF designs is one of the significant approaches for selecting the additional runs. This paper gives an in-depth look at fold-over techniques via the following four significant contributions. The first contribution is on discussing the adjusted switching levels foldover technique to overcome the limitation of the classical one. The second contribution is on presenting a comparison study among the widely used fold-over techniques to help experimenters to recommend a suitable fold-over technique for their experiments by answering the following two fundamental questions:Do these techniques dramatically lessen the confounding of the initial designs, and do the resulting combined designs(combining initial design with its fold-over) via these techniques have considerable difference from the optimality point of view considering the markedly different searching domains in each technique? The optimality criteria are the aberration, confounding, Hamming distance and uniformity. Many of these criteria are given in sequences(patterns) form, which are inconvenient and costly to represent and compare, especially when the designs have many factors. The third innovation is on developing a new criterion(dictionary cross-entropy loss) to simplify the existing criteria fromsequence to scalar. The new criterion leads to a more straightforward and easy comparison study. The final contribution is on establishing a general framework for the connections between initial designs and combined designs based on any fold-over technique.