Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for incipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal component analysis. In this approach, mutual information estimation and Bayesian information criterion (BIC) are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation (BP) network is applied whose input is multivariate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis (LKPCA) model for incipient fault prognosis. The new method has been exemplified in a simple nonlinear process and the complicated Tennessee Eastman (TE) benchmark process. The results indicate that the new method has superiority in the fault prognosis sensitivity over other traditional fault prognosis methods. (C) 2016 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.