The International Journal of Advanced Manufacturing Technology https://doi.org/10.1007/s00170-020-05222-z ORIGINAL ARTICLE On the effect of the measurement error on Shewhart t and EWMA t control charts Huu Du Nguyen 1 · Kim Phuc Tran 2 · Giovanni Celano 3 · Petros E. Maravelakis 4 · Philippe Castagliola 5 Received: 19 September 2019 / Accepted: 18 March 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020 Abstract 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. Keywords Measurement errors · t Char · EWMA chart · Markov chain · Statistical process control 1 Introduction Control charts are widespread statistical process control (SPC) means to perform online process monitoring. The  Kim Phuc Tran kim-phuc.tran@ensait.fr Huu Du Nguyen dunh@donga.edu.vn Giovanni Celano giovanni.celano@unict.it Petros E. Maravelakis maravel@unipi.gr Philippe Castagliola philippe.castagliola@univ-nantes.fr 1 Institute of Artificial Intelligence and Data Science, Dong A University, Danang, Vietnam 2 Ecole Nationale Sup´ erieure des Arts et Industries Textiles, GEMTEX Laboratory, 59056, Roubaix, France 3 Department of Civil Engineering and Architecture, Universit` a di Catania, Catania, Italy 4 Department of Business Administration, University of Piraeus, Piraeus, Greece 5 LS2N UMR CNRS 6004, Universit´ e de Nantes, Nantes, France implementation of a control chart requires the collection of a sample of n observations for a quality parameter to be monitored, the derivation of a proper sample statistic, and plotting this statistic vs. a control interval to state if the process is running in the in-control or the out-of-control state [1]. In SPC literature, several control charts have been proposed to monitor the mean and/or the dispersion of a single quality characteristic (see [2]). In 2009, Zhang et al. [3] showed that the ¯ X chart is not robust against errors in estimating the process standard deviation or in situations where the standard deviation is changing. Therefore, they developed the Shewhart t and EWMA t control charts using the T i statistic which is more robust than the classical mean ¯ X i statistic against changes in the process standard deviation. Then, the properties and design of t -type control charts have been thoroughly investigated by many authors. For further details, readers can do reference to, for instance, [4–8] and [9]. In these studies, the effect of measurement error on the Shewhart t and EWMA t control charts has not been investigated yet. But, in practice, the measurement process often adds errors which may adversely affect the performance of the implemented control charts. Generally, a measurement error exists when a measure X ∗ of the true but unobservable value X of the quality characteristic is collected during a sampling inspection. Measurement errors are known to affect the statistical