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In this article a new <inline-formula> <tex-math notation="LaTeX">$np$ </tex-math></inline-formula> control chart for the multiple dependent state sampling using the neutrosophic statistics has been introduced for the efficient monitoring of the number of defective items in any production process or the customer services agencies. The coefficients of the control limits of the proposed control chart have been determined using the neutrosophic algorithms. The efficiency of its quick performance has been determined by computing the neutrosophic average run lengths with respect to different false alarm rates under different process settings at different process shift levels. The comparison with the existing counterparts for the quick detecting ability of the proposed chart has also been conducted. The practical application of the proposed chart has been elucidated using a real-world example.