Modeling and monitoring the nonlinear profile of heat treatment process data by using an approach based on a hyperbolic tangent function

摘要

In this article, a new approach is proposed which uses the hyperbolic tangent function to model and monitor vacuum heat treatment process data. The proposed hyperbolic tangent function approach is compared to the smoothing spline approach. The latter serves as the benchmark when the vacuum heat treatment profile is investigated. The vector of the obtained parameter estimates is monitored by using Hotelling's method for the hyperbolic tangent function approach, and the metrics method used for the smoothing spline approach. For the purposes of verification, data from a real aluminum alloy heat treatment process is used to illustrate the proposed approach. In Phase I, the modified hyperbolic tangent function and the smoothing spline are first utilized to fit the process data. The proposed approach provides a better fitting result than the smoothing spline approach. In Phase II, the proposed approach produces a much better out-of-control average run length (ARL) performance than the smoothing spline approach when the heat treatment profile shows process abnormalities.