In addition to the quick detection of abnormal changes in a multivariate process, it is also critical to provide an accurate fault identification of responsible components following an out-of-control signal. In line with the work of Tan and Shi for diagnosing shifts in the mean vector, this paper develops a Bayesian approach for diagnosing shifts in the covariance matrix. The simulation comparisons favor the proposed approach. A real example is also presented to demonstrate the implementation of the proposed method.