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This paper presents a fault detection method based on Dynamic Independent Component Analysis (DICA) with new statistics. These new statistics are statistical moments and first characteristic function that surrogate the norm operator to calculate the fault detection statistics to determine the control limit of the independent components (ICs). The estimation of first characteristic function by its series is modified such that the effect of series remainder on estimation is reduced. The advantage of using first characteristic function and moments, over second characteristic function and cumulants, as fault detection statistics is also presented. It is shown that the proposed method can detect a class of faults that the former methods cannot; in particular faults with small amplitude ICs that have either different probability density function or identical probability density function of the ICs, but different low order moments of the ICs compared with the normal performance. Simulation result are used to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]