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

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... ge 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 neutrosophy run length ( ) and neutrosophy power curve ( ) are established. The proposed chart's performance in a neutrosophic environment is also evaluated to the existing model. Results from this comparative analysis reveal that the suggested Vchart outperforms its current equivalent in terms of neutrosophic statistical power. Finally, a charting structure of proposed design for service life of ball bearings data is considered with a view to support implementation procedure of the proposed neutrosophic design in real-world scenarios. INDEX TERMS Neutrosophic logic, Rayleigh model, control chart, neutrosophic parameters Z. Khan et.al.: Neutrosophic Rayleigh model with some basic characteristics and engineering applications VOLUME XX, 2017 7