In this paper, on-line batch process monitoring is developed on the basis of the three-way data structure and the time-lagged window of process dynamic behavior. Two methods, DPARAFAC (dynamic parallel factor analysis) and DTri-PLS (dynamic trilinear partial least squares), are used here depending on the process variables only or on the process variables and quality indices, respectively. Although multivariate analysis using such PARAFAC (parallel factor analysis) and Tri-PLS (trilinear partial least squares) models has been reported elsewhere, they are not suited for practicing on-line batch monitoring owing to the constraints of their data structures. A simple modification of the data structure provides a framework wherein the moving window based model can be incorporated in the existing three-way data structure to enhance the detectability of the on-line batch monitoring. By a sequence of time window of each batch, the proposed ethodology is geared toward giving meaningful results that can be easily connected to the current measurements without the extra computation for the estimation of unmeasured process variables. The proposed method is supported by using two sets of benchmark fault detection problems. Comparisons with the existing two-way and three-way multiway statistical process control methods are also included.