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The fundamentals of neutrosophic statistics provide a new basis for working with indeterminate data problems. In this study, the notion of the neutrosophic Rayleigh distribution has been introduced. The neutrosphic extension of the classical Rayleigh model with several application areas is highlighted. The major characteristics of the proposed distribution are described in a way that suggested model can be utilized in different situations involving undetermined, vague and fuzzy data. The usage of proposed distribution notably in the domain of statistical process control is considered. The classical structure of -chart is not capable of capturing uncertainty on studied variables. The mathematical structure of the -chart based on the proposed neutrosophic distribution has been developed. The neutrosphic parameters of the proposed -chart with other related performance metrics such as …