Industrial elevator systems are commonly used software systems in our daily lives, which operate in uncertain environments such as unpredictable passenger traffic, uncertain passenger attributes and behaviors, and hardware delays. Understanding and assessing the robustness of such systems under various uncertainties enable system designers to reason about uncertainties, especially those leading to low system robustness, and consequently improve their designs and implementations in terms of handling uncertainties. To this end, we present a comprehensive empirical study conducted with industrial elevator systems provided by our industrial partner Orona, which focuses on assessing the robustness of a dispatcher, i.e., a software component responsible for elevators’ optimal scheduling. In total, we studied 90 industrial dispatchers in our empirical study. Based on the experience gained from the study, we derived an uncertainty-aware robustness assessment method (named \textit{UncerRobua}) comprising a set of guidelines on how to conduct the robustness assessment and a newly proposed ranking algorithm, for supporting the robustness assessment of industrial elevator systems against uncertainties.