International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

Frequency: 12

line decor
  
line decor

 Volume 9, Issue 8 (August 2022), Pages: 92-99

----------------------------------------------

 Original Research Paper

Estimation of reliability function based on the upper record values for generalized gamma Lindley stress–strength model: Case study COVID-19

 Author(s): M. O. Mohamed *

 Affiliation(s):

 Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

  Full Text - PDF          XML

 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0003-0792-3919

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2022.08.012

 Abstract:

In this paper, the problem of estimation when X and Y are two independent upper record values from gamma Lindley distribution is considered. Maximum likelihood and the Bayesian estimator methods were used to set the best-estimated reliability function. The importance of this research is because this model, when applied, can obtain reliability values that depend on upper record values, which is an interesting problem in many real-life applications. Also, based on WHO data on the COVID-19 pandemic, a stress-strength model was applied based on the upper recorded values for Mont-Carlo simulation data.

 © 2022 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Stress-strength reliability, Upper record values, Generalized gamma Lindley function, COVID-19

 Article History: Received 14 February 2022, Received in revised form 3 May 2022, Accepted 20 May 2022

 Acknowledgment 

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Mohamed MO (2022). Estimation of reliability function based on the upper record values for generalized gamma Lindley stress–strength model: Case study COVID-19. International Journal of Advanced and Applied Sciences, 9(8): 92-99

 Permanent Link to this page

 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4

 Tables

 Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 

----------------------------------------------    

 References (14)

  1. Abd-Elfattah AM and Mohamed MO (2011). Bayesian censored data viewpoint in Weibull distribution. Life Science Journal, 8(4): 828-837.   [Google Scholar]
  2. Ahsanullah M (2004). Record values-theory and applications. University Press of America. Maryland, USA.   [Google Scholar]
  3. Arnold BC, Balakrishnan N, and Nagaraja HN (1992). A first course in order statistics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA.   [Google Scholar]
  4. Bai X, Shi Y, Liu Y, & Liu B (2019). Reliability inference of stress–strength model for the truncated proportional hazard rate distribution under progressively Type-II censored samples. Applied Mathematical Modelling, 65: 377-389. https://doi.org/10.1016/j.apm.2018.08.020   [Google Scholar]
  5. Baklizi A (2008a). Estimation of Pr (X< Y) using record values in the one and two parameter exponential distributions. Communications in Statistics-Theory and Methods, 37(5): 692-698. https://doi.org/10.1080/03610920701501921   [Google Scholar]
  6. Baklizi A (2008b). Likelihood and Bayesian estimation of Pr (X< Y) using lower record values from the generalized exponential distribution. Computational Statistics and Data Analysis, 52(7): 3468-3473. https://doi.org/10.1016/j.csda.2007.11.002   [Google Scholar]
  7. Baklizi A (2014). Interval estimation of the stress–strength reliability in the two-parameter exponential distribution based on records. Journal of Statistical Computation and Simulation, 84(12): 2670-2679. https://doi.org/10.1080/00949655.2013.816307   [Google Scholar]
  8. Chandler K (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society: Series B (Methodological), 14(2): 220-228. https://doi.org/10.1111/j.2517-6161.1952.tb00115.x   [Google Scholar]
  9. Hassan AS, Muhammed HZ, and Saad MS (2015). Estimation of stress-strength reliability for exponentiated inverted Weibull distribution based on lower record values. British Journal of Mathematics and Computer Science, 11(2): 1-14. https://doi.org/10.9734/BJMCS/2015/19829   [Google Scholar]
  10. Jamal QA, Arshad M, and Khandelwal N (2019). Multicomponent stress strength reliability estimation for Pareto distribution based on upper record values. https://doi.org/10.48550/arXiv.1909.13286   [Google Scholar]
  11. Laribi D, Masmoudi A, and Boutouria I (2021). Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics. Mathematica Slovaca, 71(2): 455-474. https://doi.org/10.1515/ms-2017-0481   [Google Scholar]
  12. Lindley DV (1980). Approximate bayesian methods. Trabajos de Estadística y de Investigación Operativa, 31(1): 223-245. https://doi.org/10.1007/BF02888353   [Google Scholar]
  13. Mohamed MO (2015). Reliability with stress-strength for Poisson-exponential distribution. Journal of Computational and Theoretical Nanoscience, 12(11): 4915-4919. https://doi.org/10.1166/jctn.2015.4459   [Google Scholar]
  14. Teimouri M and Gupta AK (2012). On the Weibull record statistics and associated inferences. Statistica, 72(2): 145-162.   [Google Scholar]