The electromechanical coupling property of piezoelectric transducers gives rise to a promising class of structural fault diagnosis methods often referred to collectively as impedance-based approaches. One active line of research in the related literature is the development of data-driven methods that can leverage the available experimental impedance measurements to accurately pinpoint the location and severity of structural faults. In this article, we offer a new perspective to the problem by casting the impedance-based fault diagnosis into a statistical calibration formulation, which has gained a wide popularity in the industrial statistics community in the past two decades. Specifically, we decide to estimate the values of the fault attributes (e.g. location and severity) that achieve the closest match between the outputs from a finite element model and those experimentally solicited from the host structure. We further propose to couple this statistical formulation with a pre-screening procedure to reduce the calibration search space and mitigate parameter identifiability issues. In addition to the merit of capably diagnosing structural faults, the proposed approach extends various useful concepts from the statistical calibration literature to the structural health monitoring applications, such as the construction of surrogate models for modeling and predicting impedance changes, the explicit use of a bias function to correct for inherent inadequacies in finite element models, as well as the ability to produce continuous probability distributions for quantifying a faults severity. These additional benefits substantially enhance both the fault diagnosis capability and computational efficiency. We demonstrate the effectiveness of the proposed approach using two simulated and two experimental case studies from the literature.