aspg-21-2230-1791475926 20261008161206 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 1 Fuad S. Alduais Mathematics Department, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia; Business Administration Department, Administrative Scien Zahid Khan Department of Mathematics and Statistics, Hazara University Mansehra Pakistan Muhammad Waseem Department of Mathematics and Statistics, Hazara University Mansehra Pakistan The application of neutrosophic statistics provides a novel approach to dealing with uncertain and imprecise data problems. In this study, we present an improved method called neutrosophic Rayleigh exponential weighted moving average style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>REWMA style='mso-bidi-font-style:normal'> font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>N chart. The style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>REWMA style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>N chart is an extension of the traditional style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>V style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>NR model and can be applied in various fields. The proposed style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>REWMA style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>N scheme is designed to enhance the detection capability of the traditional style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>V style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>NR chart. The key features of the suggested chart are discussed, highlighting its capability to handle vague, indeterminate, and fuzzy data situations. We evaluate the performance of the proposed scheme by analyzing the designated limits and charting parameters for different sample sizes. Moreover, we establish the performance metrics of the style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>REWMA style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>N chart such as neutrosophic run length ( style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>ARL style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>N ) and neutrosophic power curve ( style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>PC style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>N ).Performance metrics demonstrate that the style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>REWMA style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman"'>N chart is highly sensitive to persistent shifts in the scaling parameter of the neutrosophic Rayleigh distribution. Monte Carlo simulations are conducted to compare the suggested scheme with the existing model. A comparative study indicates that the proposed chart outperforms the competing design, particularly in detecting smaller shifts. Finally, we provide a charting structure for the proposed design using daily average wind speed data, which can be used as a practical implementation guideline for real-world applications. 2024 59 72 2230 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230105 https://www.americaspg.com/journal/21/article/2230 https://www.americaspg.com/storage/91699965854.pdf