Inference of fuzzy reliability model for inverse Rayleigh distribution

Mohamed A. H. Sabry; Ehab M. Almetwally; Osama Abdulaziz Alamri; M. Yusuf; Hisham M. Almongy; Ahmed Sedky Eldeeb; Mohamed A. H. Sabry; Ehab M. Almetwally; Osama Abdulaziz Alamri; M. Yusuf; Hisham M. Almongy; Ahmed Sedky Eldeeb

doi:10.3934/math.2021568

AIMS Mathematics

2021, Volume 6, Issue 9: 9770-9785. doi: 10.3934/math.2021568

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Research article

Inference of fuzzy reliability model for inverse Rayleigh distribution

1.
Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
2.
Faculty of Business Administration, Delta University for Science and Technology, Mansoura 11152, Egypt
3.
Statistics Department, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
4.
Mathematics Department, Helwan University, Egypt
5.
Faculty of Commerce, Mansoura University, Mansoura 35516, Egypt
6.
Department of Business Administration, College of Business, King Khaled University, Saudi Arabia
7.
Department of Statistics, Mathematics and Insurance, Alexandria University, Egypt

Received: 29 March 2021 Accepted: 22 June 2021 Published: 29 June 2021

In this paper, the question of inference of the reliability parameter of fuzzy stress strength ${R_F} = P(Y < X)$ is attached to the difference between stress and strength values when X and Y are independently distributed from inverse Rayleigh random variables. Including fuzziness in the stress-strength interference enables researchers to make more sensitive and precise analyses about the underlying systems. The maximum product of the spacing method for the reliability of fuzzy stress intensity inference has been introduced. As classical estimation methods and Bayesian estimation methods are used to estimate the reliability parameter $R_F$, the maximum product of spacing and maximum likelihood estimation methods is used. The maximum product of spacing under fuzzy reliability of stress strength model is introducing in this paper. Markov Chain Monte Carlo approach is used to obtain Bayesian estimators of traditional and fuzzy reliability of stress strength for inverse Rayleigh model by using the Metropolis-Hastings algorithm. Using an extensive Monte Carlo simulation analysis, the outputs of the fuzzy reliability and traditional reliability estimators are contrasted. Finally, for example, and to verify the efficiency of the proposed estimators, a genuine data application is used.
- fuzzy set,
- inverse Rayleigh distribution,
- reliability stress-strength,
- maximum likelihood,
- maximum product of spacing,
- Bayesian
Citation: Mohamed A. H. Sabry, Ehab M. Almetwally, Osama Abdulaziz Alamri, M. Yusuf, Hisham M. Almongy, Ahmed Sedky Eldeeb. Inference of fuzzy reliability model for inverse Rayleigh distribution[J]. AIMS Mathematics, 2021, 6(9): 9770-9785. doi: 10.3934/math.2021568

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Abstract

In this paper, the question of inference of the reliability parameter of fuzzy stress strength ${R_F} = P(Y < X)$ is attached to the difference between stress and strength values when X and Y are independently distributed from inverse Rayleigh random variables. Including fuzziness in the stress-strength interference enables researchers to make more sensitive and precise analyses about the underlying systems. The maximum product of the spacing method for the reliability of fuzzy stress intensity inference has been introduced. As classical estimation methods and Bayesian estimation methods are used to estimate the reliability parameter $R_F$, the maximum product of spacing and maximum likelihood estimation methods is used. The maximum product of spacing under fuzzy reliability of stress strength model is introducing in this paper. Markov Chain Monte Carlo approach is used to obtain Bayesian estimators of traditional and fuzzy reliability of stress strength for inverse Rayleigh model by using the Metropolis-Hastings algorithm. Using an extensive Monte Carlo simulation analysis, the outputs of the fuzzy reliability and traditional reliability estimators are contrasted. Finally, for example, and to verify the efficiency of the proposed estimators, a genuine data application is used.

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