Abstract: In this paper, a new method of calculating parity vector is proposed. First, a performance criterion for robust fault detection is given. By using the theory of Generalized Eigenstructure, the criterion can be solved to obtain optimal redundancy relation for the system detection. An optimal isolation performance criterion and Mean Value Test method (MVT) is also proposed. The parity vector can be compensated by using non-linear filtering, and the parity vector compensation approach can reduce the influence of sensor errors such as input misalignments, scale factor errors, and biases, and allow to use a constant threshold. When only one sensor fails, both GLT and MVT method can detect and isolate the failure correctly; When more than two sensors fail simultaneously, GLT method can detect the failures, but can not isolate the failures. However, MVT method can not only detect failures but also isolate failures.