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This paper investigates the fault detection problem of instruments in process industry. Considering the difficulty of fault identification and the problems of multivariable and large computation complexity based on traditional kernel principal component analysis (KPCA), this paper presents a new method for fault detection and identification, which combines the coupling analysis with kernel principal component for multivariable fault detection and employed the local outlier factor (LOF) for multivariable fault identification. The new method consists of three parts. Firstly, according to nonlinear correlation of multivariable, coupling analysis and module division of variables based on detrended cross-correlation analysis (DCCA) are considered to reduce false alarm rate (FAR) and missed detection rate (MDR) in fault detection and identification. Secondly, KPCA is employed to detect fault in each sub-module of variables. Finally, for the sub-module which has the fault detected in second step, the LOF is adopted to calculate abnormal contribution of each variable in sub-modules to realize fault identification. To prove that the new method has the better capability of processing multivariable fault detection and the more accuracy rate on fault detection and identification than the conventional methods of KPCA, a case study on Tennessee process is carried out at the end. [ABSTRACT FROM AUTHOR]