Joint Research Conference
June 24-26, 2014
Novel Techniques for Phase I Profile Monitoring via Non-linear Mixed Models Profile monitoring is an approach in quality control best used where the process data follow a profile (or curve). The majority of previous studies in profile monitoring focused on the parametric modeling of either linear or non- linear profiles, with both fixed and random-effects, under the assumption of correct model specification. In many practical situations, the practitioner has some knowledge of the parametric form for a particular profile model. However, this model may be misspecified over a portion of the data or the relationship is too complicated to be described parametrically. We propose two novel alternative approaches for modeling nonlinear autocorrelated profile data, a nonparametric (NP) and a semiparametric procedure that combines both parametric (P) and NP profile fits. We refer to our semiparametric method as nonlinear mixed model robust profile monitoring (NMM- RPM). Initial simulation results show that our NP and NMMRPM methods perform well in terms of providing adequate fits to the nonlinear correlated profiles and in making decisions regarding outlying profiles when com- pared to a misspecified nonlinear mixed parametric model. In addition, however, the NMMRPM method is robust to model misspecification because it also performs well when compared to a correctly specified nonlinear mixed parametric model. The proposed control charts have excellent capability of detecting changes in Phase I data. We illustrate the proposed nonlinear mixed profile monitoring methods for two real applications, a bioassay dataset and the vertical density profiles of particle boards’ dataset.