Based on the traditional ranked set sampling (RSS), Al-Nasser and Al-Omari [1] have recently presented a cost-effective sampling technique called MiniMax RSS (MMRSS). However, MMRSS has some drawbacks when the distribution is asymmetric. To overcome this situation, in this article, we consider developing a modified version of MMRSS (MMMRSS). Monte Carlo simulations from numerous symmetric and asymmetric distributions are employed to assess the performance of the suggested MMMRSS mean estimator. Simulation findings demonstrated that MMMRSS estimator is more efficient than their counterparts using simple random sample (SRS) and MMRSS for all distributions considered in this article. Moreover, we have constructed Quality control charts to monitor the process mean based on the suggested MMMRSS. The performance of the average run length (ARL) of these new charts was compared with the control charts based on several sampling techniques. The results, based on a simulation study, indicate that our suggested MMMRSS control charts performed the best in detecting changes in process mean in most simulated scenarios. A real-life application concerning the global temperature is also provided as an illustration of the suggested charts.