During a surveillance mode, the system receives present time-series signals gathered from sensors in the power transformer. Next, the system uses an inferential model to generate estimated values for the present time-series signals, and performs a pairwise differencing operation between actual values and the estimated values for the present time-series signals to produce residuals. The system then performs a sequential probability ratio test on the residuals to produce alarms having associated tripping frequencies (TFs). Next, the system uses a logistic-regression model to compute a risk index for the power transformer based on the TFs. If the risk index exceeds a threshold, the system generates a notification that the power transformer needs to be replaced. The system also periodically updates the logistic-regression model based on the results of periodic dissolved gas analyses for the transformer to more accurately compute the index for the power transformer.