Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 676923, 19 pages
Research Article

Time-Variant Reliability Assessment and Its Sensitivity Analysis of Cutting Tool under Invariant Machining Condition Based on Gamma Process

School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, Liaoning Province, China

Received 28 April 2012; Revised 24 September 2012; Accepted 8 October 2012

Academic Editor: Mohammad Younis

Copyright © 2012 Changyou Li and Yimin Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The time-variant reliability and its sensitivity of cutting tools under both wear deterioration and an invariant machining condition are analyzed. The wear process is modeled by a Gamma process which is a continuous-state and continuous-time stochastic process with the independent and nonnegative increment. The time-variant reliability and its sensitivity of cutting tools under six cases are considered in this paper. For the first two cases, the compensation for the cutting tool wear is not carried out. For the last four cases, the off-line or real-time compensation method is adopted. While the off-line compensation method is used, the machining error of cutting tool is supposed to be stochastic. Whether the detection of the real-time wear is accurate or not is discussed when the real-time compensation method is adopted. The numerical examples are analyzed to demonstrate the idea of how the reliability of cutting tools under the invariant machining condition could be improved according to the methods described in this paper.