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The reflected power function distribution (RPFD) has increasing importance in practical life due to its application in diversified fields of life. Organisations often face difficulty monitoring operations to identify and remove errors during production. That is why there is a need to introduce control charts that effectively monitor the processes, mainly when the number of errors follows RPFD and the manufacturing process is in control. The current study suggested memory-based control charts as a solution to the problem. The control charts are based on the estimation methods and play a remarkable role in enhancing the machine process reliability. The parameters of RPFD are evaluated through the percentile estimator (PE) and modified maximum likelihood estimator methods (MMLM). Further, we create memory-based control charts, i.e., hybrid exponentially weighted moving average (HEWMA) and extended exponentially weighted moving average (EEWMA), using the PE and MMLM. The findings reflect that HEWMA control charts based on PE provide a better result in estimating the defects. The implications of the study will be helpful for practitioners and policy makers from reliability engineering, management sciences, and statisticians. [ABSTRACT FROM AUTHOR]