A health grade system against mechanical faults of power transformers has been little investigated compared to those for chemical and electrical faults. This paper thus presents a statistical health grade system against mechanical faults in power transformers used in nuclear power plant sites where the mechanical joints and/or parts are the ones used for constraining transformer cores. Two health metrics-root mean square (RMS) and root mean square deviation (RMSD) of spectral responses at harmonic frequencies-are first defined using vibration signals acquired via in-site sensors on fifty-four power transformers in several nuclear power plants in sixteen months. We then investigate a novel multivariate statistical model, namely copula, to statistically model the populated data of the health metrics. The preliminary study shows that the proposed health metrics and statistical health grade system are feasible to monitor and predict the health condition of the mechanical faults in the power transformers.