At present. monitoring cutting tool wear becomes one of the most important problems to be solved urgently in automatic manufacturing. For this a new monitoring method is proposed using correlation of N dimensional Random Variables and cumulative power sum，namely comprehensively monitoring cutting tool wear and leakage by acquiring the correlation coefficient of vibration accelerations in three mutually perpendicular directions，and the cumulative power sum about torque of spindle or about any vibration acceleration. This method makes greater progress than the ones proposed before in the aspects of reliability and simplicity. So it has a bright future in application area. The theoretical basis of the method is strictly proved and some experimental results are given in this paper.