In order to reduce the time spent on tolerance analysis, it is necessary to correctly identify and prioritize the key characteristics of the product. For multiple-state mechanisms, a systematic procedure for doing this is lacking. We present a new complexity metric for multiple-state mechanisms based on the product behavior, describing the impact of geometrical variation. The sequence of the structural state transitions is linked to the product composition, enabling a clear prioritization of variation-critical states and interfaces. The approach is applied on an industrial case and verified based on a comparison with the company-specified priority tolerance calculations.