In this paper, a systematic approach that employs novel parameter similarities is proposed to detect, isolate, and identify multiplicative faults in a multi-input multi-output (MIMO) dynamic system. These multiplicative faults are usually difficult to deal with using conventional statistics-based methods. Similarity measures based on impulse response sequences of dynamic elements are defined. By using the proposed similarity measures, the overall and local faults, including dead time, gain, and other dynamic parameters in a multivariate process, can be detected and isolated. The method has the potential to be used for on-line fault diagnosis. Simulated numerical and industrial examples are used to demonstrate the methodology.