In this paper, $\overline{\mathrm{X}}$ charts based on robust scale estimators (known as $S_n$ and $Q_n$ 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 S_n, Q_n, 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, $S_n$, $Q_n$, 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, $S_n$, and D are suitable estimators for standard deviation for mean charts while $S_n$ and $Q_n$ are suitable estimators for standard deviation for dispersion charts for skewed and heavily tailed distributions.

中文翻译：

---

中值绝对偏差的性能以及偏斜和重尾过程的中值绝对偏差控制图的一些替代方案

在本文中， $\overline{\mathrm{X}}$ 基于稳健规模估计量的图表（称为 ${秒}_n$ 和 ${问}_n$估计量），并将基于中值绝对偏差 (MAD) 的控制图的性能与基于 MAD 的一些替代方案的性能进行比较，这些替代方案不需要任何位置估计，适用于正态分布、偏斜分布和重尾分布。由于其稳健性，MAD 在构建控制图时常被用作标准偏差的替代品。MAD 的三个替代方案，即S _n、Q _n和 Downton ( D ) 在本文中被视为无位置估计器。进行了模拟研究以评估基于 MAD 的控制图的性能，${秒}_n$, ${问}_n$, 和D估计量。平均游程长度 (ARL)、中位数游程长度 (MRL)、标准偏差游程长度 (SDRL) 和控制限区间 (CLI) 用于评估四个控制图的性能。结果表明，MAD、${秒}_n$, 和D是均值图标准差的合适估计量，而${秒}_n$ 和 ${问}_n$ 是偏斜和重尾分布的分散图的标准偏差的合适估计量。