To improve the detection and identification performance of the Statistical Quality Monitoring (SQM) system, a novel quality based Prioritized Sensor-Fault Detection (PSFD) methodology is proposed. Weighted by the V-p (variable importance in projection) index, which indicates the importance of the sensor variables to the quality variables, the new monitoring statistic, Q(v), is developed to ensure that the most vital sensor faults be detected successfully. Subsequently, the ratio between the Detectable Minimum Faulty Magnitude (DMFM) of the most important sensor and of the least important sensor is only V-pmin/V-pmax << 1. The Structured Residuals are designed according to the V-p index to identify and then isolate them. The theoretical findings are fully supported by simulation studies performed on the Tennessee Eastman process.