Inference of fuzzy reliability model for inverse Rayleigh distribution
Mohamed Sabry, Ehab M. Almetwally, Osama Abdulaziz Alamri, M. Yusuf, Hisham M. Almongy, Ahmed Sedky Eldeeb
Abstract
<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 <italic>X</italic> and <italic>Y</italic> 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. </abstract>