A framework for nonparametric profile monitoring

Control charts have been widely used for monitoring the functional relationship between a response variable and some explanatory variable(s) (called profile) in various industrial applications. In this article, we propose an easy‐to‐implement framework for monitoring nonparametric profiles in both Phase I and Phase II of a control chart scheme. The proposed framework includes the following steps: (i) data cleaning; (ii) fitting B‐spline models; (iii) resampling for dependent data using block bootstrap method; (iv) constructing the confidence band based on bootstrap curve depths; and (v) monitoring profiles online based on curve matching. It should be noted that, the proposed method does not require any structural assumptions on the data and, it can appropriately accommodate the dependence structure of the within‐profile observations. We illustrate and evaluate our proposed framework by using a real data set.