Phase I control chart study of profile monitoring using linear quantile mixed models

Addressing the challenge of monitoring profiles in the context of the phase I linear quantile mixed model, this paper assumes that binary profiles obtained from fixed samples collected over time adhere to a normal distribution. We then introduce a control chart grounded in the linear quantile mixed model, aimed at tracking changes in regression coefficients and exploring the robustness of the F-test estimation coefficient. Simulation results demonstrate that the proposed control chart offers a robust tool for statistical process control.