Designing a multivariate exponentially weighted moving average control chart with measurement errors

Control chart is one of the useful tools of statistical process control, which monitor the processes over time. In most of the designed control charts, it is assumed that the measurement errors do not exist in the measurement system, while this assumption is usually violated in practice as well. The presence of measurement errors leads to poor performance of the control charts. In this paper, a multivariate exponentially weighted moving average control chart is designed by considering measurement errors in Phase II. To decline the effect of measurement errors on the performance of the proposed control chart, multiple measurements method is applied. Also, sensitivity analysis about the effect of the number of measurements on the ARL performance of the proposed control chart is conducted. Note that different scenarios for the variance-covariance matrix are considered in simulation studies, including Case 1. Uncorrelated case with equal variances. Case 2. Negatively correlated case with equal variances. Case 3. Uncorrelated case with unequal variances. Case 4. Positively correlated case with unequal variances. Moreover, the performance of the proposed control chart is compared with the performance of Hotelling's T2 control chart. Results show the admissible performance of the proposed method in decreasing the effect of measurement errors.