A semiparametric profile monitoring via residuals

Profile monitoring is a vast area of research underneath the statistical process monitoring (SPM). Several methods for univariate and multivariate process control are found in literature to monitor the profile data, including parametric, nonparametric, and some semiparametric methods. The main idea behind monitoring the linear profiles in mixed effects is to model the possible individual differences between similar set of profiles for future monitoring. In this paper, nonparametric and semiparametric approaches are proposed to model the profile data in a linear mixed effect setting by considering the residuals from a parametric model. A simulation study was carried out to compare the efficiency of the proposed methods. At first step, the residuals from a parametric linear mixed model are obtained. A nonparametric approach (NPR) is then used to model these residuals. Finally, a semiparametric method (MMRRPM) is proposed as a convex combination of the parametric (P) and nonparametric estimations based on the residuals (NPR) to model the profile data in mix effects. Two Hoteling's T 2 statistics were computed for each technique based on fitted values and the estimated random effects. The results show that the proposed methods are most effective to monitor the autocorrelated profile data compared with the state‐of‐the‐art.