Designing robust modified R control charts for asymmetric distributions under ranked set and median ranked set sampling

Presence of outliers or contamination in the process control affect the construction of quality control limits badly. Therefore, more attention is to paid robust methods describing the data majority. The main focus of this study is to construct robust R charts by using ranked set sampling (RSS) and median ranked set sampling (MRSS) designs under contaminated skewed distributions such as Marshall–Olkin bivarite Weibull and Bivarite Lognormal distributions. Three robust methods named as robust modified Shewhart, robust modified weighted variance and robust modified skewness correction methods are introduced. An extensive simulation study is presented in order to analyse the efficiency of different sampling designs and robust modified R charts on the charts’ performance. These methods are evaluated in terms of their Type I risks (p). The simulation study showed that, in the contamination case, Shewhart, weighted variance and skewness correction charts based on classic estimators are affected from outliers under simple random sampling and RSS designs and cause the increase of the p values in the process. However using MRSS design is not affected by outliers. In the case of contamination, proposed robust MSC method under MRSS has the best performance for all cases. Moreover a real data application is conducted to show the superiority of proposed methods.