Design based Global Sensitivity Analysis for Quantity-Permutation Models

Global sensitivity analysis (GSA) plays a pivotal role in elucidating the structural dependency of a black-box model on its input parameters. In recent years, a new class of models with inhomogeneous inputs is emerging in designed experiments for quality improvement, featuring “quantitative” and “permutable” factors that exert different influences on the output of interest. Traditional GSA methods designed for single-subject analysis are not applicable to these quantity-permutation (QP) models. To address this challenge, we propose an innovative method, called bidirectional-global sensitivity analysis (BGSA), for extracting key features in QP models. The BGSA method splits the model into two parts. One part is used to implement ANOVA decomposition to identify influential quantitative factors, while the other part undergoes symmetrical decomposition to learn about the symmetric pattern induced by the permutable factors. Theoretical properties of the proposed method are studied, and optimal designs for efficient data collection are developed. We demonstrate the effectiveness of the BGSA method by explaining different models and solving a practical problem.