Control Chart For Monitoring Nonparametric Profiles With Arbitrary Design

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 a fundamental assumption that design points within a profile are deterministic (i.e., non-random) and they are unchanged from one profile to another. In practice, however, different profiles often have different design points, and in some cases they might even be random. NPM is particularly challenging in such cases because it is difficult to combine data in different profiles properly for data smoothing and for process monitoring. In this paper, we propose a novel 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 smoothing procedure for smoothing individual profiles. Because of certain good properties of the charting statistic, this control chart is fast to compute, easy to implement, and efficient to detect profile shifts. Some numerical results show that it works well in applications.