1. A method of detecting faults, comprising: receiving, by a computing device, process data that includes a plurality of process variables; adapting one or more multivariate statistical models by the computing device according to the process data, wherein adapting includes applying a change to at least one univariate statistic of the one or more multivariate statistical models if the change is greater than a threshold value, wherein one or more statistics for a first subset of process variables from the plurality of process variables is adapted, and wherein one or more statistics for a second subset of process variables from the plurality of process variables is not adapted; and using the one or more adapted multivariate statistical models to analyze subsequent process data to detect faults.