No abstract

In some statistical process control applications, the quality of a process is described by a linear relationship between the response variable(s) and the independent variable(s), which is called a linear profile. Process capability is a significant issue in statistical process control. The ability of a process to meet customer specifications or standards is measured by the process capability indices (PCIs). There are several attempts for studying the process capability in linear profiles. In this research, two robust PCIs for multiple linear profiles are proposed. In the suggested robust PCIs, the process capability is estimated using the M‐estimator and the Fast‐τ‐estimator. Performances of the proposed robust PCIs in comparison with the classical PCIs in the absence and presence of contamination are evaluated. The results show that the robust PCIs proposed in this research perform as well as the classical PCIs in the absence of contamination and much better in the presence of contamination. The proposed PCIs, using Fast‐τ‐estimator, perform better in small shifts, and the proposed PCIs, using M‐estimator, perform better in large shifts. Introduction of robust indices for multivariate multiple linear profiles is an area for further research.

No abstract

In many applications of statistical process control, the quality of a product or a process is described by the relationship between the response variable and one or more independent variables which is called a profile. A profile could be either linear or nonlinear. The control limits of a chart, used to monitor a profile, are functions of model parameters. The classical estimators used to estimate the parameters, are defined under certain hypotheses such as the normality of the error terms. Deviation from any of these assumptions may cause contamination. Whenever contamination exists, the classical estimators are not robust, and the resulting control charts are not accurate when monitoring the profiles. In this research, a robust estimator of the model error term variance is introduced and evaluated using MSE. Then the robust estimators of the slope and the intercept along with the robust estimator of the error term variance are used to define the control limits for the process profile under consideration. Simulation results indicate that the out of control ARL of the proposed control charts is smaller than the ARL of the classical control charts in the presence of contamination.

No abstract