Abstract: Many industrial process variables have the characteristics of non-Gaussian and Gaussian mixture distribution.Independent factor analysis (IFA) algorithm utilizes one dimension Gaussian mixture model to approximate any factor distribution such that it can address the problem of the Gaussian and non-Gaussian mixture.Although the variational IFA with given factors can reduce the modeling-time,it still takes a lot of time to determine an optimal number.Especially,an inappropriate number may make the information of partial factors be remained in the residuals of the observed variables,which will result in the poor monitoring performance on the GSPE index.Aiming at the above problem in the application of IFA,this paper proposes a combined method of IFA and FA.Firstly,FA algorithm is used in determining the independent factor number so as to reduce the modelling time of IFA.And then,FA is further utilized to re-process the residual of IFA so that the remained partial factors' information in residual can be fully employed.Finally,the monitoring experiment in the Tennessee-Eastman (TE) process and the ethylene cracking furnace verifies the validity of the proposed method.