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The concept of neutrosophic statistics is applied to propose two monitoring schemes which are an improvement of the neutrosophic exponentially weighted moving average (NEWMA) chart. In this study, two control charts are designed under the uncertain environment or neutrosophic statistical interval system, when all observations are undermined, imprecise or fuzzy. These are termed neutrosophic double and triple exponentially weighted moving average (NDEWMA and NTEWMA) control charts. For the proficiency of the proposed chart, Monte Carlo simulations are used to calculate the run-length characteristics (such as average run length (ARL), standard deviation of the run length (SDRL), percentiles (P 25 , P 50 , P 75 )) of the proposed charts. The structures of the proposed control charts are more effective in detecting small shifts while these are comparable with the other existing charts in detecting moderate and large shifts. The simulation study and real-life implementations of the proposed charts show that the proposed NDEWMA and NTEWMA charts perform better in monitoring the process of road traffic crashes and electric engineering data as compared to the existing control charts. Therefore, the proposed charts will be helpful in minimizing the road accident and minimizing the defective products. Furthermore, the proposed charts are more acceptable and actual to apply in uncertain environment.

The New Neutrosophic Double and Triple Exponentially Weighted Moving Average Control Charts