Published

2018-07-01

On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution

Sobre la fiabilidad en un modelo multicomponente de resistencia al estrés con distribución de power Lindley

DOI:

https://doi.org/10.15446/rce.v41n2.69621

Keywords:

Bayesian inference, Bootstrap condence interval, Maximum likelihood estimation, Stress-strength model (en)
Inferencia bayesiana, intervalo de conanza Bootstrap, estimaci ón de máxima verosimilitud, modelo de resistencia al estrés (es)

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Authors

  • Abbas Pak Department of Computer Sciences, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran.
  • Arjun Kumar Gupta Department of Mathematics and Statistics, Bowling Green State University, Bowling Green,OH 43403-0221, USA.
  • Nayereh Bagheri Khoolenjani Department of Statistics, Isfahan University, Isfahan, Iran.
In this paper  we study the reliability of a multicomponent stress-strength model assuming that the components follow power Lindley model.  The maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval are obtained. Applying the parametric Bootstrap technique, interval estimation of the reliability is presented.  Also, the Bayes estimate and highest posterior density credible interval of the reliability parameter are derived using suitable priors on the parameters. Because there is no closed form for the Bayes estimate, we use the Markov Chain Monte Carlo method to obtain approximate Bayes  estimate of the reliability. To evaluate the performances of different procedures,  simulation studies are conducted and an example of real data sets is provided.

En este trabajo, estudiamos la fiabilidad de un modelo multicomponente de resistencia al estrés suponiendo que los componentes siguen el modelo Lindley de potencia. Se obtiene la estimación de máxima verosimilitud del parámetro de confiabilidad y su intervalo de confianza asintótico. Aplicando la técnica Bootstrap paramétrica, se presenta la estimación de intervalo de la confiabilidad. Además, la estimación de Bayes y el intervalo creíble de la densidad posterior más alta del parámetro de confiabilidad se obtienen utilizando

los antecedentes adecuados sobre los parámetros. Debido a que no existe una forma cerrada para la estimación de Bayes, utilizamos el método de Markov Chain Monte Carlo para obtener una estimación aproximada de Bayes de la confiabilidad. Para evaluar el rendimiento de diferentes procedimientos, se realizan estudios de simulación y se proporciona un ejemplo de conjuntos de datos reales.

References

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How to Cite

APA

Pak, A., Gupta, A. K. and Khoolenjani, N. B. (2018). On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution. Revista Colombiana de Estadística, 41(2), 251–267. https://doi.org/10.15446/rce.v41n2.69621

ACM

[1]
Pak, A., Gupta, A.K. and Khoolenjani, N.B. 2018. On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution. Revista Colombiana de Estadística. 41, 2 (Jul. 2018), 251–267. DOI:https://doi.org/10.15446/rce.v41n2.69621.

ACS

(1)
Pak, A.; Gupta, A. K.; Khoolenjani, N. B. On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution. Rev. colomb. estad. 2018, 41, 251-267.

ABNT

PAK, A.; GUPTA, A. K.; KHOOLENJANI, N. B. On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution. Revista Colombiana de Estadística, [S. l.], v. 41, n. 2, p. 251–267, 2018. DOI: 10.15446/rce.v41n2.69621. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/69621. Acesso em: 19 apr. 2024.

Chicago

Pak, Abbas, Arjun Kumar Gupta, and Nayereh Bagheri Khoolenjani. 2018. “On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution”. Revista Colombiana De Estadística 41 (2):251-67. https://doi.org/10.15446/rce.v41n2.69621.

Harvard

Pak, A., Gupta, A. K. and Khoolenjani, N. B. (2018) “On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution”, Revista Colombiana de Estadística, 41(2), pp. 251–267. doi: 10.15446/rce.v41n2.69621.

IEEE

[1]
A. Pak, A. K. Gupta, and N. B. Khoolenjani, “On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution”, Rev. colomb. estad., vol. 41, no. 2, pp. 251–267, Jul. 2018.

MLA

Pak, A., A. K. Gupta, and N. B. Khoolenjani. “On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution”. Revista Colombiana de Estadística, vol. 41, no. 2, July 2018, pp. 251-67, doi:10.15446/rce.v41n2.69621.

Turabian

Pak, Abbas, Arjun Kumar Gupta, and Nayereh Bagheri Khoolenjani. “On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution”. Revista Colombiana de Estadística 41, no. 2 (July 1, 2018): 251–267. Accessed April 19, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/69621.

Vancouver

1.
Pak A, Gupta AK, Khoolenjani NB. On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution. Rev. colomb. estad. [Internet]. 2018 Jul. 1 [cited 2024 Apr. 19];41(2):251-67. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/69621

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CrossRef citations16

1. Hossein PASHA-ZANOOSİ, Ahmad POURDARVİSH. (2022). Multicomponent stress-strength reliability based on a right long-tailed distribution. Hacettepe Journal of Mathematics and Statistics, 51(2), p.559. https://doi.org/10.15672/hujms.880993.

2. Abbas Pak, Arjun Kumar Gupta, Nayereh Bagheri Khoolenjani. (2018). On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution. Revista Colombiana de Estadística, 41(2), p.251. https://doi.org/10.15446/rce.v41n2.69621.

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5. Anita Kumari, Indranil Ghosh, Kapil Kumar. (2024). Bayesian and likelihood estimation of multicomponent stress–strength reliability from power Lindley distribution based on progressively censored samples. Journal of Statistical Computation and Simulation, 94(5), p.923. https://doi.org/10.1080/00949655.2023.2277331.

6. Mayank Kumar Jha, Sanku Dey, Refah Alotaibi, Ghadah Alomani, Yogesh Mani Tripathi. (2022). Multicomponent Stress-Strength Reliability estimation based on Unit Generalized Exponential Distribution. Ain Shams Engineering Journal, 13(5), p.101627. https://doi.org/10.1016/j.asej.2021.10.022.

7. Vikas Kumar Sharma, Sanku Dey. (2019). Estimation of reliability of multicomponent stress-strength inverted exponentiated Rayleigh model. Journal of Industrial and Production Engineering, 36(3), p.181. https://doi.org/10.1080/21681015.2019.1646032.

8. Alaa M. Hamad, Bareq B. Salman. (2021). On estimation of the stress-strength reliability on POLO distribution function. Ain Shams Engineering Journal, 12(4), p.4037. https://doi.org/10.1016/j.asej.2021.02.029.

9. Mayank Kumar Jha, Yogesh Mani Tripathi, Sanku Dey. (2021). Multicomponent stress-strength reliability estimation based on unit generalized Rayleigh distribution. International Journal of Quality & Reliability Management, 38(10), p.2048. https://doi.org/10.1108/IJQRM-07-2020-0245.

10. A R Mezaal, A I Mansour, N S Karm. (2020). Multicomponent stress-strength system reliability estimation for generalized exponential-poison distribution. Journal of Physics: Conference Series, 1591(1), p.012042. https://doi.org/10.1088/1742-6596/1591/1/012042.

11. Hossein Pasha-Zanoosi. (2023). Reliability of stress–strength model for exponentiated Teissier distribution based on lower record values. Japanese Journal of Statistics and Data Science, https://doi.org/10.1007/s42081-023-00229-8.

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13. Ahmed Ibrahim Shawky, Khushnoor Khan. (2022). Reliability Estimation in Multicomponent Stress-Strength Based on Inverse Weibull Distribution. Processes, 10(2), p.226. https://doi.org/10.3390/pr10020226.

14. Refah Mohammed Alotaibi, Yogesh Mani Tripathi, Sanku Dey, Hoda Ragab Rezk. (2020). Bayesian and non-Bayesian reliability estimation of multicomponent stress–strength model for unit Weibull distribution. Journal of Taibah University for Science, 14(1), p.1164. https://doi.org/10.1080/16583655.2020.1806525.

15. Kazem Fayyaz Heidari, Einollah Deiri, Ezzatallah Baloui Jamkhaneh. (2021). Using the best two-observational percentile and maximum likelihood methods in a multicomponent stress-strength system to reliability estimation of inverse Weibull distribution. Life Cycle Reliability and Safety Engineering, 10(3), p.255. https://doi.org/10.1007/s41872-021-00166-z.

16. Lauren Sauer, Yuhlong Lio, Tzong-Ru Tsai. (2020). Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions. Mathematics, 8(7), p.1176. https://doi.org/10.3390/math8071176.

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