TITLE:
Use of Statistical Distance T2 and ARL to Detect Cutting Tool Drift
AUTHORS:
Boukar Abdelhakim, Awat Atteib Abderahim, Aslain Brisco Ngnassi Djami
KEYWORDS:
Tool Offsets, Machine Setting, Machine Steering, Hotelling’s T2
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.15 No.12,
December
30,
2025
ABSTRACT: This article exploits the statistical distance T2 for the detection of cutting tool drift in the case of CNC machine tools. We present a control approach based on the T2 chart and inertial control in a multivariate process. Inertial control is an approach for controlling CNC machine tools developed in recent years. Its principle is to link measurable parameters of the part to adjustable parameters on the machine (tool coordinators). In the case of machining mechanical parts by CNC machine tools, it involves linking tool offsets on the machine to deviations in dimensions measured on the part. This produces an incidence matrix representing the influence of machine parameters on product characteristics. When a tool offset affects several dimensions of the part, there is a correlation between these dimensions and the tool offset. The T2 chart allows us to take this correlation into account to detect cutting tool misalignment, and inertial control will calculate the tool offset values to correct this misalignment. Furthermore, we use the ARL (Average Run Length) measurement to evaluate the performance of T2 in comparison with the Shewhart control chart. ARL is commonly used to monitor processes and detect changes in their behavior. A comparative result based on ARLs of these charts is presented in the article. An example of a simple 1D part in which a tool offset is maximal in three dimensions is presented in this article to illustrate our point.