Reliability Exponential Distribution (1+3) Cascade Model
DOI:
https://doi.org/10.54153/sjpas.2026.v8i1.1264Keywords:
Unit, Monte Carlo, Percentile, Least Squares, and Exponential distributionAbstract
In this paper, a reliability formula was found for a cascade model containing four units (the first unit is basic and the other three units , , and are redundant standby). It was assumed that the two variables strength and stress follow the exponential distribution of the variables. The estimation of the exponential distribution parameters was found using three estimation methods (Maximum likelihood, Percentile, and Least Squares), these methods were used to estimate the reliability of the model. MATLAB was used in the Monte Carlo simulation and mean square errs was used to compare the simulation results and find which estimation methods are the best for reliability estimation. The simulation results proved that the estimator ML is the best for estimating the model's reliability.
References
1. Rahman, J. ul, Mohyuddin, M. R., Anjum, N., & Butt, R. (2016). Modelling of two Interconnected Spring Carts and Minimization of Energy. DJ Journal of Engineering and Applied Mathematics, 2(1), 7–11.
2. Siju, K. C., & Kumar, M. (2016). Reliability analysis of time dependent stress-strength model with random cycle times. Perspectives in Science, 8, 654–657.
3. Khaleel, A. H. Ahmed R Khlefha1,(2021).Reliability of (1+1) Cascade Model for Weibull Distribution. Highlights in Science, 1, 1-4.
4. Patowary, A. N., Hazarika, J., & Sriwastav, G. L. (2018). Reliability estimation of multi-component cascade system through Monte-Carlo simulation. International Journal of Systems Assurance Engineering and Management, 9(6), 1279–1286.
5. Khaleel, A. H. ,(2024).Reliability for Generalized Rayleigh of 1 Strength - 4 Stresses. JURNAL ILMIAH MATEMATIKA, SAINS DAN TEKNOLOGI, 12(1), 26-31.
6. Jebur, I. G., Kalaf, B. A., & Salman, A. N. (2020). On Bayesian Estimation of System Reliability in Stress - Strength Model Based on Generalized Inverse Rayleigh Distribution. IOP Conference Series: Materials Science and Engineering, 871(1).
7. Hassan, A. S., Nagy, H. F., Muhammed, H. Z., & Saad, M. S. (2020). Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values. Journal of Taibah University for Science, 14(1), 244–253.
8. Khaleel, A. H. ,(2024).Reliability Function of (1 Strength and 4 Stresses) for Rayleigh distribution. Basrah Journal of Sciences, 42(1), 13-22.
9. Kanaparthi, R., Palakurthi, J., & Narayana, L. (2020). Cascade reliability of stress-strength system for the new Rayleigh-Pareto Distribution, 5(2), 131–139.
10. Ashok, P., Devi, M. T., & Maheswari, T. S. U. (2019). Reliability of a cascade system of type (X
11. Chaturvedi, A., & Malhotra, A. (2020). On Estimation of Stress-Strength Reliability Using Lower Record Values from Proportional Reversed Hazard Family. American Journal of Mathematical and Management Sciences, 39(3), 234–251.
12. A. H. Khaleel,(2021). Reliability of one Strength-four Stresses for Lomax Distribution. J. Phys. Conf. Ser., 1879(3),1-10.
13. Khan, A. H., & Jan, T. R. (2014). Estimation of multi component systems reliability in stress-strength models. Journal of Modern Applied Statistical Methods, 13(2), 389–398.
14. Patowary, A. N., Hazarika, J., & Sriwastav, G. L. (2018). Reliability estimation of multi-component cascade system through Monte-Carlo simulation. International Journal of Systems Assurance Engineering and Management, 9(6), 1279–1286.
15. Salman, A. N., & Hamad, A. M. (2019). On estimation of the stress-Strength reliability based on lomax distribution. IOP Conference Series: Materials Science and Engineering, 571(1).
16. Khaleel, A. H. ,(2024). THE FRECHET RELIABILITY FOR (2+2) CASCADE MODEL. African Journal of Mathematics and Statistics Studies, 7(1), 50-63.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright Notice
Authors retain copyright and grant the SJPAS journal right of first publication, with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in Samarra Journal of Pure and Applied Science.
The Samarra Journal of Pure and Applied Science permits and encourages authors to archive Pre-print and Post-print items submitted to the journal on personal websites or institutional repositories per the author's choice while providing bibliographic details that credit their submission, and publication in this journal. This includes the archiving of a submitted version, an accepted version, or a published version without any Risks.
