Robust profile monitoring for phase II analysis via residuals

Many studies were conducted for fitting models using parametric and non-parametric techniques; in fact, their fits may be biased and have inflated the estimated variances when the model is misspecified, respectively. Thus, semi-parametric techniques are used for fitting models as they combine the advantages of parametric and non-parametric fits. In this study, we introduce model robust regression technique-2 (MRR2) for Phase II profile monitoring, namely, the semi-parametric approach, where it is a combination of the parametric fit with a portion of a non-parametric residuals fit. Multivariate CUSUM (MCUSUM) chart unitized for monitoring the slope of the linear mixed models in Phase II based on the random-effects. A comprehensive simulation study was performed to evaluate the proposed approach for correlated and uncorrelated profiles assuming different profile sizes, sample sizes, and several model misspecification levels. Average run length (ARL) and average time to signal (ATS) criteria were used for comparing the performances of the parametric, non-parametric, and semi-parametric MCUSUM charts. The results showed that the semi-parametric chart had the best performance in detecting different shifts. Also, a real data application was conducted, where it showed that the semi-parametric chart had the highest sensitivity for the out-of-control scenarios.