Asserting the provenance of an item is an essential validation in any supply chain process. Unfortunately, counterfeit objects continue to proliferate as these networks grow in size and complexity. Anything from consumer luxury items to safety-critical subsystem components are targeted by counterfeiters. The reliable assertion of an item's origin and build quality remains an open problem that is expected to cost the global economy trillions of dollars (USD) in coming years. While institutional economic disparity is a concern, poor quality counterfeits infiltrating mission-critical systems, such as flight controllers, pose a tangible and physical risk to society. To address this issue, we propose a novel approach for detecting counterfeit items using piezoelectric signatures which result from actuating piezoelectric sensors and observing the electromechanical response. We demonstrate that the collision rate (percentage of parts that are counterfeit and probability of part type signal overlap) of piezoelectric signatures can be analytically estimated and tuned in relation to desired parameters such as a minimal false positive rate.