In this article, we have extended the design structures of dual auxiliary information-based control charts under a variety of sampling strategies and runs rules schemes. We have considered the cases of known and unknown skewed distributions by using the skewness correction (SC) method. The design structures under the skewness correction method are based on the degree of skewness of the study variable, amount of correlation between study variable and auxiliary variable, and sample size. We have investigated the performance of the developed structures in terms of probability of signals, false alarm rate and average run length by considering the symmetrical distribution, skewed distributions, heavy tailed distributions and contamination environments. Outcomes of the current article showed that control charts based on extreme ranked set strategies have higher probability of detecting an out-of-control signal and are comparatively more robust than other control charts, especially for known distributions. Furthermore, control charts for unknown skewed process distributions under extreme ranked set strategies are relatively more robust for a small sample size, followed by other ranked set strategies-based control charts for a large sample size. Moreover, we have included a real-life example for the monitoring of ground water variables to highlight the application of our proposals.