1. A system for predicting an occurrence of failure in a machine tool, comprising: a) first means for detecting a monitor data which is changed according to an operating situation in a series of working processes of the machine tool within an operating cycle, said first means including fifth means for detecting a position deviation variable of a tool as a result of rotation of a servomotor installed in the machine tool as the monitor data, the position deviation variable being defined as a deviation in position of the tool between contents of a movement instruction for the tool derived from a CPU to the servomotor and contents of an output pulse signal of a pulse encoder indicating an actual movement distance of the tool; b) second means for variably setting a prediction level of failure against the monitor data, the prediction level being varied according to different types of operating situations in the machine tool within the operating cycle; c) third means for comparing the monitor data detected by the first means with the prediction level set by the second means during a predetermined one of the series of working processes of the machine tool, said predetermined one of the series of working processes including the servomotor rotation, and outputting a failure prediction signal when the value of the monitor data exceeds the prediction level; and d) fourth means for informing the prediction of the occurrence of failure on the basis of the received failure prediction signal.