Reliability for Generalized Rayleigh of 1 Strength - 4 Stresses

Ahmed Haroon Khaleel

doi:10.37905/euler.v12i1.24175

Reliability for Generalized Rayleigh of 1 Strength - 4 Stresses

Ahmed Haroon Khaleel

Abstract

In this paper, the reliability of a one-component model is found where this component is subjected to four stresses with random variables Y1, Y2, Y3, Y4 and this component resists these stresses with its strength with random variable X and it was assumed that these variables follow a generalized Rayleigh distribution. The model's reliability was estimated by three different estimation methods (Percentile method, the Regression method, and the Least Squares method). A Monte Carlo simulation was performed to compare the results obtained from the estimate using two statistical criteria: the mean squares error criterion and the mean absolute percentage error criterion. The comparison showed that the best estimator of the reliability of the model is the favorable Percentile estimator.

Keywords

Generalized Rayleigh; Monte Carlo; Percentile; Regression; Stress-Strength

Full Text:

PDF

References

E. S. M. Haddad and F. S. M. Batah, “On Estimating Reliability of a Stress – Strength Model in Case of Rayleigh Pareto Distribution,” Iraqi J. Sci., vol. 62, no. 12, pp. 4847–4858, 2021, doi: https://dx.doi.org/10.24996/ijs.2021.62.12.23.

M. K. Jha, S. Dey, R. Alotaibi, G. Alomani, and Y. M. Tripathi, “Multicomponent Stress-Strength Reliability estimation based on Unit Generalized Exponential Distribution,” Ain Shams Eng. J., vol. 13, no. 5, p. 101627, 2022, doi: https://dx.doi.org/10.1016/j.asej.2021.10.022.

A. N. Salman and A. M. Hamad, “On estimation of the stress-Strength reliability based on lomax distribution,” IOP Conf. Ser. Mater. Sci. Eng., vol. 571, no. 1, 2019, doi: https://dx.doi.org/10.1088/1757-899X/571/1/012038.

A. M. Hamad and B. B. Salman, “On estimation of the stress-strength reliability on POLO distribution function,” Ain Shams Eng. J., vol. 12, no. 4, pp. 4037–4044, 2021, doi: https://dx.doi.org/10.1016/j.asej.2021.02.029.

L. Shang and Z. Yan, “Reliability estimation stress–strength dependent model based on copula function using ranked set sampling,” J. Radiat. Res. Appl. Sci., vol. 17, no. 1, p. 100811, 2024, doi: https://doi.org/10.1016/j.jrras.2023.100811.

H. Panahi, S. Asadi, Inference of stress-strength model for a lomax distribution, World Acad. Sci. Eng. Technol., v. 79, pp. 275–278, 2011. doi: https://doi.org/10.5281/zenodo.1080388.

A. M. Sarhan and A. H. Tolba, “Stress-strength reliability under partially accelerated life testing using Weibull model,” Sci. African, vol. 20, 2023, doi: https://dx.doi.org/10.1016/j.sciaf.2023.e01733.

K. Abbas and Y. Tang, “Objective bayesian analysis of the frechet stressstrength model,” Stat. Probab. Lett., vol. 84, no. 1, pp. 169–175, 2014, doi: https://dx.doi.org/10.1016/j.spl.2013.09.014.

N. S. Karam, S. M. Yousif, G. S. Karam, and Z. M. Abood, “Cascade Stress-Strength Reliability for P(X-Y-Z) of (1+1) and (2+1) Systems,” AIP Conf. Proc., vol. 2437, no. August, 2022, doi: https://dx.doi.org/10.1063/5.0109248.

P. Bhattacharya, R. Bhattacharjee, A study on Weibull distribution for estimating the parameters, Wind Eng. vol. 33, no. 5, pp. 469–476, 2009. doi: https://doi.org/10.1260/030952409790291163.

A. H. Khaleel and N. S. Karam, “Estimating the reliability function of (2+1) cascade model,” Baghdad Sci. J., vol. 16, no. 2, pp. 395–402, 2019, doi: https://dx.doi.org/10.21123/bsj.2019.16.2.0395.

N. S. Karam and A. H. Khaleel, “Generalized inverse Rayleigh reliability estimation for the (2+1) cascade model,” AIP Conf. Proc., vol. 2123, no. July, 2019, doi: https://dx.doi.org/10.1063/1.5116973.

N. Karam and A. Khaleel, “Weibull reliability estimation for (2+1) cascade model,” Int. J. Adv. Math. Sci., vol. 6, no. 1, p. 19, 2018, doi: https://dx.doi.org/10.14419/ijams.v6i1.9284.

A. H. Khaleel, “Exponential Reliability Estimation of (3+1) Cascade Model,” Iraqi. J. Sci., vol. 8, no. 2, pp. 46-54, 2021. doi: https://dx.doi.org/10.18081/2226-3284/5-10/46-54.

N. Karaday, B. Saracoglu and A. Pekgor, “Stress- strength reliability its estimation for a component which is Exposed two independent stresses”, Slcuk J. Appl. Math., Special Issue, pp.131-135, 2011.

J. B. Lewis and D. A. Linzer, “Estimating regression models in which the dependent variable is based on estimates,” Polit. Anal., vol. 13, no. 4, pp. 345–364, 2005, doi: https://dx.doi.org/10.1093/pan/mpi026.

DOI: https://doi.org/10.37905/euler.v12i1.24175