Abstract: Nonparametric profile monitoring (NPM) is for monitoring, over time, a functional relationship between a response variable and one or more explanatory variables when the relationship is too complicated to be specified parametrically. It is widely used in industry for the purpose of quality control of a process. Existing NPM approaches require the assumption that design points within a profile are deterministic, and are unchanged from one profile to another. In practice, however, different profiles can have different design points and, in some cases, they are random. NPM is particularly challenging in such cases because it is difficult to properly combine data in different profiles purposes of data smoothing and process monitoring. In this paper, we propose an exponentially weighted moving average (EWMA) control chart for handling this problem based on local linear kernel smoothing. In the proposed chart, the exponential weights used in the EWMA scheme at different time points are integrated into a nonparametric procedure for smoothing individual profiles. Because of certain properties of the charting statistic, this control chart is fast to compute, easy to implement, and efficient in the detection of profile shifts. Some numerical results show that it works well.
Key words and phrases: Bandwidth selection, EWMA, local linear kernel smoothing, nonparametric regression, profile monitoring, self-starting, statistical process control.