In the monitoring of manufacturing and service processes, it is sometimes necessary to measure the parameters of interest. One critical and often overlooked issue is the presence of measurement error.

In this study, we propose the application of sampling methods based on Ranked Set Sampling (RSS) to mitigate the impact of measurement error.

In this paper, the performance of the T2-Hotelling’s control chart for monitoring multivariate normal processes in the presence of measurement error is initially investigated using the classical additive model in Phase II. Subsequently, to mitigate the effect of measurement error in multivariate processes, novel sampling approaches based on Ranked Set Sampling (RSS) are proposed. The methods employed include standard RSS and Neoteric RSS (NRSS), which are extended to multivariate processes in this study, with ranking performed based on principal component scores.

The performance of the proposed approaches is evaluated through simulation. The results indicate that the presence of measurement error significantly deteriorates the performance of the control chart due to a substantial increase in both the average run length (ARL) and the standard deviation of the run length (SDRL). Overall, the results demonstrate that the performance of the control chart using the proposed method based on standard RSS and NRSS is superior, due to lower ARL and SDRL values under out-of-control conditions, compared to the control chart performance in the presence of measurement error using simple random sampling. Furthermore, the performance of the proposed standard RSS and NRSS method improves with increasing sample size n as well as increasing the correlation coefficient between variables.

Considering that the process is multivariate and there is correlation among the variables, this study proposes the use of principal component scores for ranking the correlated variables when applying the proposed RSS-based methods. The results also show that ranking based on the first principal component generally leads to better outcomes, as evidenced by lower ARL and SDRL values, compared to ranking based on the second principal component. Therefore, it is recommended that, in the proposed approaches, ranking be performed according to the first principal component.