Phase I monitoring with nonparametric mixed‐effect models

In many real-life applications, the quality of products from a process is monitored by a functional relationship between a response variable and one or more explanatory variables. In these applications, methodologies of profile monitoring are used to check the stability of this relationship over time. In phase I of profile monitoring, historical data points that can be represented by curves (or profiles) are collected. In this article, 2 procedures are proposed for detecting outlying profiles in phase I data, by incorporating the local linear kernel smoothing within the framework of nonparametric mixed-effect models. We introduce a stepwise algorithm on the basis of the multiple testing viewpoint. Our simulation results for various linear and nonlinear profiles display the superior efficiency of our proposed monitoring procedures over some existing techniques in the literature. To illustrate the implementation of the proposed methods in phase I profile monitoring, we apply the methods on a vertical density profile dataset.