Neoteric ranked set sampling for robust X¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{X}$$\end{document} and R control charts

Neoteric ranked set sampling (NRSS) is defined as an efficient sampling design compared to counterparts in the literature. NRSS differs from ranked set sampling (RSS) by selecting ordered sample units, and this design provides more accurate results for estimation of population parameters compared to RSS. This sampling design is firstly used by Koyuncu and Karagöz (Qual Technol Quant Manag 15(5):602–621, 2018) to construct control charts under bivariate asymmetric distributions. Robust control charts are another important topic for monitoring of process when the contamination exists. The novelty of this paper is that we have used NRSS design firstly in statistical process control to monitor robust control charts. Moving this direction, we have proposed to use NRSS design in modified robust methods to construct X¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{X}$$\end{document} and R charts under contaminated skewed distributions. The performances of the X¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{X}$$\end{document} and R control charts for monitoring the process by using NRSS are evaluated according to Type I risk probabilities. Based on the simulation study, the NRSS design in modified robust methods gives the most efficient results compared to existing methods.