Neutrosophic Rayleigh Model With Some Basic Characteristics and Engineering Applications

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
$\left ({{RD}_{N} }\right)$
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
$\left ({SPC }\right)$
is considered. The classical structure of
$V_{SQR}$
-chart is not capable of capturing uncertainty on studied variables. The mathematical structure of the
$V_{NR}$
-chart based on the proposed neutrosophic distribution has been developed. The neutrosphic parameters of the proposed
$V_{NR}$
-chart with other related performance metrics such as neutrosophy run length
$\left ({{ARL}_{N} }\right)$
and neutrosophy power curve
$\left ({{PC}_{N} }\right)$
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
$\mathrm {V}_{\mathrm {NR}}$
-chart 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.