Abstract: Principal component analysis (PCA) is a powerful tool in chemical process monitoring and product quality control. The number of principal components (PCs) is the essential parameter of PCA and ultimately determines the performance of this useful statistical method. Traditional selection methods are very subjective due to the monotonically increasing or decreasing indices they adopt. By exploring the minimum detectable fault magnitudes in the PCs space and residual space simultaneously, a new index of optimal critical fault magnitude (OCFM) was introduced and the number of PCs was selected by optimizing a function of the OCFM. The proposed method could incorporate the PCA fault diagnosing performance with the PCs selection procedure effectively, and has the advantages of forecasting PCA detection behavior of a specific fault and estimating the fault magnitude. The acquired results were then illustrated and verified by monitoring a simulated double-effect evaporator.