Istrazivanja i projektovanja za privreduJournal of Applied Engineering Science


DOI: 10.5937/jaes0-28710 
This is an open access article distributed under the CC BY 4.0
Creative Commons License

Volume 19 article 878 pages: 980-988

M. O. Mohamed*
Zagazig University, Faculty of Science, Mathematical Department, Zagazig, Egypt

Ahmed H.A.Reda
Zagazig University, Faculty of Science, Mathematical Department, Zagazig, Egypt

This research paper aims to find the estimated values closest to the true values of the reliability function under lower record values, and to know how to obtain these estimated values using point estimation methods or interval estimation methods. This helps researchers later in obtaining values of the reliability function in theory and then applying them to reality which makes it easier for the researcher to access the missing data for long periods such as weather. We evaluated the stress–strength model of reliability based on point and interval estimation for reliability under lower records by using Odd Generalize Exponential–Exponential distribution (OGEE) which has an important role in the lifetime of data. After that, we compared the estimated values of reliability with the real values of it. We analyzed the data obtained by the simulation method and the real data in order to reach certain results. The Numerical results for estimated values of reliability supported with graphical illustrations. The results of both simulated data and real data gave us the same coverage.

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1. A. Chaturvedi and A. Malhotra, “On Estimation of Stress-Strength Reliability Using Lower Record Values from Proportional Reversed Hazard Family,” American Journal of Mathematical and Management Sciences, vol. 39, no. 3, pp. 234–251, Jul. 2020, doi: 10.1080/01966324.2020.1722299.

2. A. Hassan, H. Muhammed, and M. Saad, “Estimation of Stress-Strength Reliability for Exponentiated Inverted Weibull Distribution Based on Lower Record Values,” BJMCS, vol. 11, no. 2, pp. 1–14, Jan. 2015, doi: 10.9734/BJMCS/2015/19829.

3. A. S. Hassan, M. Abd-Allah, and H. F. Nagy, “Bayesian Analysis of Record Statistics Based on Generalized Inverted Exponential Model,” International Journal on Advanced Science, Engineering and Information Technology, vol. 8, no. 2, Art. no. 2, Mar. 2018, doi: 10.18517/ijaseit.8.2.3506.

4. B. Tarvirdizade and H. Kazemzadeh Garehchobogh, “Interval Estimation of Stress-Strength Reliability Based on Lower Record Values from Inverse Rayleigh Distribution,” Journal of Quality and Reliability Engineering, vol. 2014, pp. 1–8, 2014, doi: 10.1155/2014/192072.

5. A. Chaturvedi and A. Malhotra, “Estimation and testing procedures for the reliability functions of a family of lifetime distributions based on records,” Int J Syst Assur Eng Manag, vol. 8, no. S2, pp. 836–848, Nov. 2017, doi: 10.1007/s13198-016-0531-2.

6. A. Chaturvedi and S. Vyas, “Estimation and Testing Procedures for the Reliability Functions of Three Parameter Burr Distribution under Censorings,” Statistica, vol. Vol 77, pp. 207-235 Pages, Jan. 2018, doi: 10.6092/ISSN.1973-2201/6965.

7. F. Condino, F. Domma, and G. Latorre, “Likelihood and Bayesian estimation of $$P(Y{<}X)$$ P ( Y < X ) using lower record values from a proportional reversed hazard family,” Stat Papers, vol. 59, no. 2, pp. 467–485, Jun. 2018, doi: 10.1007/s00362-016-0772-9.

8. M. J. S. Khan and Mohd. Arshad, “UMVU Estimation of Reliability Function and Stress–Strength Reliability from Proportional Reversed Hazard Family Based on Lower Records,” American Journal of Mathematical and Management Sciences, vol. 35, no. 2, pp. 171–181, Apr. 2016, doi: 10.1080/01966324.2015.1134363.

9. A. Asgharzadeh, A. Fallah, M. Z. Raqab, and R. Valiollahi, “Statistical inference based on Lindley record data,” Stat Papers, vol. 59, no. 2, pp. 759–779, Jun. 2018, doi: 10.1007/s00362-016-0788-1.

10. A. Pak and S. Dey, “Statistical Inference for the power Lindley model based on record values and inter-record times,” Journal of Computational and Applied Mathematics, vol. 347, pp. 156–172, Feb. 2019, doi: 10.1016/

11. M. Z. Raqab, O. M. Bdair, and F. M. Al-Aboud, “Inference for the two-parameter bathtub-shaped distribution based on record data,” Metrika, vol. 81, no. 3, pp. 229–253, Apr. 2018, doi: 10.1007/s00184-017-0641-0.

12. A. Sadeghpour, M. Salehi, and A. Nezakati, “Estimation of the stress–strength reliability using lower record ranked set sampling scheme under the generalized exponential distribution,” Journal of Statistical Computation and Simulation, vol. 90, no. 1, pp. 51–74, Jan. 2020, doi: 10.1080/00949655.2019.1672694.

13. A. Iranmanesh, K. Fathi Vajargah, and M. Hasanzadeh, “On the estimation of stress strength reliability parameter of inverted gamma distribution,” Math Sci, vol. 12, no. 1, pp. 71–77, Mar. 2018, doi: 10.1007/s40096-018-0246-4.

14. C. Zhang and Y. Zhang, “Common cause and load-sharing failures-based reliability analysis for parallel systems,” EiN, vol. 22, no. 1, pp. 26–34, Dec. 2019, doi: 10.17531/ein.2020.1.4.

15. M. O. Mohamed, “Reliability with Stress-Strength for Poisson-Exponential Distribution,” j comput theor nanosci, vol. 12, no. 11, pp. 4915–4919, Nov. 2015, doi: 10.1166/jctn.2015.4459.

16. S. Vv, “New Odd Generalized Exponential - Exponential Distribution: Its Properties and Application,” BBOAJ, vol. 6, no. 3, Apr. 2018, doi: 10.19080/BBOAJ.2018.06.555686.

17. S. Kotz, Y. Lumelskii, and M. Pensky, The Stress-Strength Model and its Generalizations - Theory and Applications. World Scientific Publishing Co. Pte. Ltd., 2003.

18. “Smith, R.L. and Naylor, J. (1987) A Comparison of Maximum Likelihood and Bayesian Estimators for the Three-Parameter Weibull Distribution. Applied Statistics, 36, 358-369. - References - Scientific Research Publishing.” (accessed Sep. 16, 2020).