Abstract:
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Profile monitoring is an approach in quality control best used where the process data follow a profile (or curve). A number of previous studies in profile monitoring focused on the nonlinear parametric (P) modeling of profiles, with both fixed and random-effects, under the assumption of correct nonlinear model specification. More recently, in the absence of an obvious nonlinear P model, nonparametric (NP) methods have been employed in the profile monitoring framework. We propose a semiparametric (SP) procedure that combines both nonlinear P and NP profile fits for cases where a nonlinear P model is adequate over part of the data but inadequate of the rest. We refer to our semiparametric procedure as the nonlinear mixed robust profile monitoring (NMRPM) method. These three methods (P, NP, and NMRPM) can account for the autocorrelation within profiles and treat the collection of profiles as a random sample from a common population. For each approach, we propose a version of Hotelling's T2 statistic for use in Phase I analysis to determine abnormal profiles based on the estimated random effects and obtain the corresponding control limits. The performance of the proposed method is evaluated using a real data set. The results show that, the NMRPM method is robust to model misspecification and performs well when compared to a correctly specified nonlinear P model. The proposed control charts have excellent capability of detecting changes in Phase I data and has control limits that are simple to calculate.
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