Reliability assessment and replacement for machine tools under wear deterioration

This paper considers a problem of reliability assessment and determination of optimal replacement time for a machine tool under wear deterioration. Traditional models classifying a tool's condition use binary states, with working (success) or failure (1 or 0), to evaluate its reliability and decide its optimal replacement time; however, as most machine tools deteriorate over time, a multi-state discrete model is reported as a more realistic classification for quantifying the tool wear condition. In this paper, we propose a nonhomogeneous continuous-time Markov process (NHCTMP) for modeling the tool wear process, representing the length of time the tool stays in a certain state, which depends not only on its current state but also on how long it has remained in the current state. According to this model, we first develop reliability assessment for the tool with the multi-state deterioration. Then, we derive an average expected cost function of the tool operating over the manufacturing period and optimize it to find the optimal replacement time of the tool. The optimization of the average value of the expected cost over tool replacement time emerges as a classical tradeoff idea, balancing between increasing the average cost of tool replacement and decreasing the average cost of tool deterioration. A real application is illustrated throughout the paper.