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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 powerplant sites where the mechanical joints and/or parts are the ones used for constraining transformer cores. Two health metrics-RMS and root mean square deviation of spectral responses at harmonic frequencies-are first defined using vibration signals acquired via insite sensors on 54 power transformers in several nuclear powerplants in 16 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.