In the case of contamination for skewed distributions, the modified Shewhart, modified weighted variance, and modified skewness correction methods are newly introduced by Karagoz (Hacet J Math Stat 47(1):223-242, 2018). In this study, we propose to modify these methods by considering simple random sampling (SRS), ranked set sampling (RSS) and median ranked set sampling (MRSS) designs under the contaminated type I Marshall-Olkin bivariate Weibull and lognormal distributions. These bivariate distributions are chosen since they can represent a wide variety of shapes from nearly symmetric to highly skewed. We evaluate the performance of proposed modified methods based on different ranked set sampling designs by using Monte Carlo Simulation. The type I risks of (X) over bar charts for existing and newly proposed modified methods by using SRS, RSS and MRSS designs in the case of contamination for these distributions are obtained via simulation study. The proposed modified methods using RSS and MRSS designs for the (X) over bar chart can be a favorable substitute in process monitoring when the distribution is highly skewed and contaminated.