In the traditional parity relation based fault detection approach, a lower order parity vector means a simpler online realization but a poorer performance index, while a higher order parity vector brings a better performance index but leads to a higher computational. load and a higher rate of misdetection. In this noted by introducing the so-called stationary wavelet transform into the residual signal, a new kind of parity relation based residual generator and the corresponding optimization approach are proposed. The residual generator of the new approach can ensure a good performance index, a satisfactory low misdetection rate kind a suitable response speed to faults with a low order parity vector and a simple online implementation form. The method is compared with three existing parity relation based approaches.