In this paper, trueX¯ charts based on robust scale estimators (known as Sn and Qn estimators) are proposed, and the performance of control charts based on median absolute deviation (MAD) is compared with those based on some alternatives to MAD, which do not need any location estimate, for normal, skewed, and heavily tailed distributions. MAD is often used as a substitute for standard deviation in constructing control charts due to its robustness. Three alternatives to MAD namely the Sn, Qn, and Downton (D) are considered in this paper as location‐free estimators. A simulation study was carried out to appraise the performance of the control charts based on the MAD, Sn, Qn, and D estimators. The average run length (ARL), median run length (MRL), standard deviation run length (SDRL), and control limits interval (CLI) were used to assess the performance of the four control charts. The results showed that MAD, Sn, and D are suitable estimators for standard deviation for mean charts while Sn and Qn are suitable estimators for standard deviation for dispersion charts for skewed and heavily tailed distributions.