A generalized likelihood ratio test for monitoring profile data

Profile data emerges when the quality of a product or process is characterized by a functional relationship among (input and output) variables. In this paper, it is assumed that each profile has one response variable Y, one explanatory variable x, and the functional relationship between these two variables can be rather arbitrary. We propose a general method based on the Generalized Likelihood Ratio Test (GLRT) to perform Phase II monitoring of profile data. Unlike existing methods in profile monitoring area, the proposed method uses nonparametric regression to estimate the on-line profiles and thus does not require any functional form for the profiles. Both Shewhart-type and EWMA-type control charts are considered. The average run length (ARL) performance of the proposed method is studied by using a nonlinear profile dataset. It is shown that the proposed GLRT-based control chart can efficiently detect both location and dispersion shifts of the on-line profiles from the baseline profile. An upper control limit (UCL) corresponding to a desired in-control ARL value is constructed.