Semiparametric MEWMA for Phase II profile monitoring

A control chart is one of the statistical process techniques that is used to monitor different processes. Some processes are characterized by functions or profiles, and a profile is a functional relationship between the dependent and independent variable(s) used to monitor the quality of the process. Several research studies were conducted on linear profiling where only fixed effects are considered. However, in this research, we focus on random effects as they represent the differences between profiles and thus are more proper for interpretation. Two approaches are proposed in this study for Phase II profile monitoring; the first approach is the nonparametric via residuals and the second is the semiparametric approach, where this technique combines the parametric estimates with a portion of the nonparametric estimates to the residuals. Usually, parametric estimations lead to biased estimates when the model is misspecified, whereas nonparametric estimates may give high variances, and thus semiparametric estimates are preferred. New nonparametric and semiparametric multivariate exponential weighted moving average (MEWMA) control charts are introduced and their performances compared to the parametric approach for different samples and shift sizes, and the correlation between and within profiles was considered. The average run length (ARL) and average time to signal (ATS) criteria are used for choosing the best approach. Simulation studies and real datasets were utilized for comparing the performance of the proposed MEWMA charts.