Neutrosophic Rayleigh Model With Some Basic Characteristics and Engineering Applications

Abstract

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 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.

A Review and Perspective on Neutrosophic Statistical Process Monitoring Methods

“…The graphical displays of f(Z, θ N ), and F (Z, θ N ) for the neutrosophic Rayleigh random variable Z with imprecise scale parameter θ N = [0.5, 0.75] are shown in Fig. 1, which was reproduced from Khan et al [2].…”

“…Khan et al [2] proposed a method for monitoring with an underlying neutrosophic Rayleigh distribution. The parameter of this distribution is a neutrosophic number.…”

“…N EUTROSOPHIC methods were first proposed by Smarandache [1]. As stated by Khan et al [2], "The idea of neutrosophic sets is a broader platform that expands the notions of the fuzzy and classical sets." Neutrosophic statistics was said by Albassam and Aslam [3] to be a generalization of traditional statistics that is used to analyze uncertain, unclear, vague, and incomplete data.…”

“…Almarashi and Aslam [33], Shawky et al [34], and Aslam et al [35] developed monitoring methods under the assumption of an underlying neutrosophic gamma distribution while Khan et al [2] assumed an underlying neutrosophic Rayleigh distribution. Aslam et al [36] and Arif et al [37] assumed an underlying neutrosophic Weibull distribution.…”

Closed-Form Sum-Rate Analysis of Interference Alignment with Limited Feedback Based on Scalar Quantization and Random Vector Quantization

“…The proposed IA performance analysis method can act as a guidance to determine the optimal feedback overhead in practical channel conditions. In the future, we may extend the analysis results by combining neutrosophic statistics in several directions, such as considering a more complicated neutrosophic Rayleigh model in the wireless channel [32], and reducing the approximation error by analyzing the distribution characteristics of different kinds of quantization errors [33][34][35].…”