Monitoring disturbances in process dispersion using control chart is mostly based on the assumption that the quality characteristic follows normal distribution, which is not the case in many real‐life situations. This paper proposes a set of new dispersion charts based on the homogeneously weighted moving average (HWMA) scheme, for efficient detection of shifts in process standard deviation (σ). These charts are based on a variety of σ estimators and are investigated for normal as well as heavy tailed symmetric and skewed distributions. The shift detection ability of the charts is evaluated using different run length characteristics, such as average run length (ARL), extra quadratic loss (EQL), and relative ARL measures. The performance of the proposed HWMA control charts is also compared with the existing EWMA dispersion charts, using different design parameters. Furthermore, an illustrative example is presented to monitor the vapor pressure in a distillation process.

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.

Many studies were conducted for fitting models using parametric and nonparametric techniques; in fact, their fits may be biased and have inflated the estimated variances when the model is misspecified, respectively. Thus, semiparametric 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 semiparametric 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 semiparametric 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.