Phase II Non-parametric and Semi-parametric Profile Monitoring

Abstract

The emergence of new technologies, as well as the availability of large amounts of information related to quality measurements, have shed the light to a new type of response characteristic called profile. Profiles are important when the quality of a large data process is represented by a relationship between the dependent variable and one or more independent variables. They are fitted using regression techniques and their performances are monitored by statistical process control (SPC). Most of the previous studies focused on monitoring the profiles assuming that, the model is correct with no model misspecification (parametric models). However, the parametric models may not perfectly fit the relationship of the dependent variable with the independent variable(s). Thus, this study considers profile monitoring via two nonparametric techniques and two semi-parametric techniques. The first non-parametric technique is the fitted values to the data, while the second is the fitted values to the residuals obtained from the parametric fit. Moreover, the first semi-parametric technique combines both parametric and of the non-parametric fits to the raw data (model robust regression technique 1 (MRR1), while the second one combines both parametric fit to the raw data and the non-parametric fit to the residuals obtained from the parametric fit (model robust regression technique 2 (MRR2). Also, according to the flexibility of linear mixed models (LMM), it was incorporated into different model fits. Thus, the initial portion of this research focuses on two methods for Phase II analysis, namely, MCUSUM and MEWMA statistics, to promote monitoring of the slope of LMM. Simulation study and real-data applications were carried out to compare the performances of the parametric charts with the proposed charts based on Average Run Length (ARL), standard deviation run length (SDRL) and Average Time to Signal (ATS) considering different profile sizes, sample sizes, and level of misspecifications for correlated and uncorrelated data. Furthermore, the overall abilities of the charts were evaluated by extra quadratic loss (EQL) criterion. The research demonstrates that the two proposed semi-parametric techniques had the best performances and higher sensitivities in detecting shifts.