This paper discusses on-line detection and prediction problems of the failure or life of stochastic systems by using autoregression (AR) models. We regard the change of the equipment from an ordinary state to failure as a variation of the characteristics of a time aeries signal. An AR model is fitted to the time aeries signal and the change is detected by variations of the model. Using four types of performance index of the variations, we detect the failure of a cutting tool of a lathe and predict the width of flank wear.