On the effect of the measurement error on Shewhart t and EWMA t control charts

In the industrial practice, control charts are frequently implemented assuming that the quality characteristic of interest can be accurately measured without errors. In general, this assumption is not realistic: measurement error always exists in quality control applications and may considerably affect the performance of control charts in detecting the occurrence of an out-of-control condition. In this paper, the effect of measurement error on the statistical performance of Shewhart t and EWMA t control charts is investigated. Several tables are provided to show how the statistical performance of these control charts changes with different sources of the measurement error. The obtained results show that the measurement errors have a significant influence on the performance of both the Shewhart t and EWMA t control charts. Two examples in the analytical chemistry and food industry are presented to illustrate the use of the proposed charts.