Biomanufacturing plays an important role in supporting public health and the growth of the bioeconomy. Modeling and studying the interaction effects among various input variables is very critical for obtaining a scientific understanding and process specification in biomanufacturing. In this paper, we use the ShapleyOwen indices to measure the interaction effects for the policy-augmented Bayesian network (PABN) model, which characterizes the risk- and science-based understanding of production bioprocess mechanisms. In order to facilitate efficient interaction effect quantification, we propose a sampling-based simulation estimation framework. In addition, to further improve the computational efficiency, we develop a non-nested simulation algorithm with sequential sampling, which can dynamically allocate the simulation budget to the interactions with high uncertainty and therefore estimate the interaction effects more accurately under a total fixed budget setting.