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The machining industry raises an ever-growing concern for the significant cost of cutting tools in the production process of mechanical parts, with a focus on the replacement policy of these inserts. While an early maintenance induces lower tool return on investment, scraps and inherent costs stem from late replacement. The framework of this paper is the attempt to predict the tool inserts Mean Up Time, based solely on the value of a cutting parameter (the cutting speed in this particular turning application). More specifically, the use of the Cox Proportional Hazards (PH) Model for this prediction is demonstrated. The main contribution of this paper is the analytic approach that was conducted about the relevance on data transformation prior to using the Cox PH Model. It is shown that the logarithm of the cutting speed is analytically much more relevant in the prediction of the Mean Up Time through the Cox PH model than the raw cutting speed value. The paper also covers a numerical validation designed to show and discuss the benefits of this data transformation and the overall interest of the Cox PH model for the lifetime prognosis. This methodology, however, necessitates the knowledge of an analytical law linking the covariate to the Mean Up Time. It also shows how the necessary data for the numerical experiment was obtained through a gamma process simulating the degradation of cutting inserts. The results of this paper are expected to help manufacturers in the assessment of tool lifespan.

An Analytic Approach to the Cox Proportional Hazards Model for Estimating the Lifespan of Cutting Tools