Product quality and operation cost control obtain increasing emphases in modern chemical system engineering. To improve the fault detection power of the partial least square (PLS) method for quality control,. a new Q(RPV) statistic is proposed in terms of the VP (variable importance in projection) indices of monitored process variables, which is significantly advanced over and different from the conventional Q statistic. Q(RPV) is calculated only by the residuals of the remarkable process variables (RPVs). Therefore, it is the dominant relation between quality and RPV not all process variables (as in the case of the conventional PLS) that is monitored by this new VP-PLS (VPLS) method. The combination of Q(RPV) and T-2 statistics is applied to the quality and cost control of the Tennessee Eastman (TE) process, and weak faults can be detected as quickly as possible. Consequently, the product quality of TE process is guaranteed and operation costs are reduced.