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Estimation of multicomponent stress-strength reliability based on a bivariate Topp-Leone distribution

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Abstract

In this endeavour, we study the statistical inference of multicomponent stress-strength reliability when components of the system have two paired elements experiencing common random stress. The k strength variables \((X_1,Y_1),\ldots ,(X_k,Y_k)\) follow a bivariate Topp-Leone distribution and the stress variable which follows a Topp-Leone distribution. This system is unfailing when at least \(s(1\le s\le k)\) out of k components simultaneously activate. The maximum likelihood estimate along with its asymptotic confidence interval, the uniformly minimum variance unbiased estimate, and the exact Bayes estimate of stress-strength reliability are derived. Further, we determined the Bayes estimates of the stress-strength reliability via different methods such as the Tierney and Kadane approximation, Lindley’s approximation, and the Markov Chain Monte Carlo (MCMC) method, to compare their performances with the exact Bayes estimate. Also, the highest probability density credible interval is obtained using the MCMC method. Monte Carlo simulations are implemented to compare the different suggested methods. Ultimately, the analysis of one real data is investigated for illustrative purposes.

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References

  1. Kotz, S., Lumelskii, Y., Pensky, M.: The Stress-strength Model and Its Generalizations: Theory and Applications. World Scientific, Singapore (2003)

    Book  Google Scholar 

  2. Rao, G.S., Kantam, R., Rosaiah, K., Reddy, J.P.: Estimation of reliability in multicomponent stress-strength based on inverse Rayleigh distribution. J. Stat. Appl. Probab. 2(3), 261 (2013)

    Article  Google Scholar 

  3. Nadar, M., Kızılaslan, F.: Estimation of reliability in a multicomponent stress-strength model based on a Marshall-Olkin bivariate Weibull distribution. IEEE Trans. Reliab. 65(1), 370–380 (2015)

    Article  Google Scholar 

  4. Dey, S., Mazucheli, J., Anis, M.: Estimation of reliability of multicomponent stress-strength for a Kumaraswamy distribution. Commun. Statist.-Theory Methods 46(4), 1560–1572 (2017)

    Article  Google Scholar 

  5. Pandit, P.V., Joshi, S.: Reliability estimation in multicomponent stress-strength model based on generalized Pareto distribution. Am. J. Appl. Math. Stat. 6(5), 210–217 (2018)

    Article  Google Scholar 

  6. Kohansal, A.: On estimation of reliability in a multicomponent stress-strength model for a Kumaraswamy distribution based on progressively censored sample. Stat. Pap. 60, 2185–2224 (2019)

    Article  Google Scholar 

  7. Kohansal, A., Shoaee, S.: Bayesian and classical estimation of reliability in a multicomponent stress-strength model under adaptive hybrid progressive censored data. Stat. Pap. 62(1), 309–359 (2021)

    Article  Google Scholar 

  8. Ahmadi, K., Ghafouri, S.: Reliability estimation in a multicomponent stress-strength model under generalized half-normal distribution based on progressive type-II censoring. J. Stat. Comput. Simul. 89(13), 2505–2548 (2019)

    Article  Google Scholar 

  9. Rasekhi, M., Saber, M.M., Yousof, H.M.: Bayesian and classical inference of reliability in multicomponent stress-strength under the generalized logistic model. Commun. Stat.-Theory Methods 50(21), 5114–5125 (2020)

    Article  Google Scholar 

  10. Kayal, T., Tripathi, Y.M., Dey, S., Wu, S.-J.: On estimating the reliability in a multicomponent stress-strength model based on Chen distribution. Commun. Stat.-Theory Methods 49(10), 2429–2447 (2020)

    Article  Google Scholar 

  11. Kızılaslan, F.: Classical and bayesian estimation of reliability in a multicomponent stress-strength model based on the proportional reversed hazard rate mode. Math. Comput. Simul. 136, 36–62 (2017)

    Article  Google Scholar 

  12. Sauer, L., Lio, Y., Tsai, T.-R.: Reliability inference for the multicomponent system based on progressively type II censored samples from generalized pareto distributions. Mathematics 8(7), 1176 (2020)

    Article  Google Scholar 

  13. Kızılaslan, F., Nadar, M.: Estimation of reliability in a multicomponent stress-strength model based on a bivariate Kumaraswamy distribution. Stat. Pap. 59, 307–340 (2018)

    Article  Google Scholar 

  14. Topp, C.W., Leone, F.C.: A family of J-shaped frequency functions. J. Am. Stat. Assoc. 50(269), 209–219 (1955)

    Article  Google Scholar 

  15. Genç, A.I.: Estimation of \(P(X>Y)\) with Topp-Leone distribution. J. Stat. Comput. Simul. 83(2), 326–339 (2013)

    Article  Google Scholar 

  16. Akgül, F.G.: Reliability estimation in multicomponent stress-strength model for Topp-Leone distribution. J. Stat. Comput. Simul. 89(15), 2914–2929 (2019)

    Article  Google Scholar 

  17. Bhattacharyya, G., Johnson, R.A.: Estimation of reliability in a multicomponent stress-strength model. J. Am. Stat. Assoc. 69(348), 966–970 (1974)

    Article  Google Scholar 

  18. Ghitany, M., Al-Mutairi, D.K., Aboukhamseen, S.: Estimation of the reliability of a stress-strength system from power Lindley distributions. Commun. Stat.-Simul. Comput. 44(1), 118–136 (2015)

    Article  Google Scholar 

  19. Tierney, L., Kadane, J.B.: Accurate approximations for posterior moments and marginal densities. J. Am. Stat. Assoc. 81(393), 82–86 (1986)

    Article  Google Scholar 

  20. Lindley, D.V.: Approximate bayesian methods. Trabajos de estadísticay de investigación operativa 31, 223–245 (1980)

    Article  Google Scholar 

  21. Chen, M.-H., Shao, Q.-M.: Monte Carlo estimation of Bayesian credible and HPD intervals. J. Comput. Graph. Stat. 8(1), 69–92 (1999)

    Google Scholar 

  22. Irshad, M., D’cruz, V., Maya, R.: The exponentiated unit Lindley distribution: properties and applications. Ricerche di Matematica, 1–23 (2021)

  23. Sharma, V.K., Singh, S.V., Shekhawat, K.: Exponentiated teissier distribution with increasing, decreasing and bathtub hazard functions. J. Appl. Stat. 49(2), 371–393 (2022)

    Article  Google Scholar 

  24. Yadav, A.S., Saha, M., Tripathi, H., Kumar, S.: The exponentiated XGamma distribution: a new monotone failure rate model and its applications to lifetime data. Statistica 81(3), 303–334 (2021)

    Google Scholar 

  25. El-Morshedy, M., Aljohani, H.M., Eliwa, M.S., Nassar, M., Shakhatreh, M.K., Afify, A.Z.: The exponentiated Burr-Hatke distribution and its discrete version: reliability properties with csalt model, inference and applications. Mathematics 9(18), 2277 (2021)

    Article  Google Scholar 

  26. Pal, A., Samanta, D., Mitra, S., Kundu, D.: A simple step-stress model for Lehmann family of distributions. Adv. Stat.-Theory Appl.: Honoring Contributions Barry C. Arnold Stat. Sci., 315–343 (2021)

  27. Demiray, D., Kızılaslan, F.: Stress-strength reliability estimation of a consecutive k-out-of-n system based on proportional hazard rate family. J. Stat. Comput. Simul. 92(1), 159–190 (2022)

    Article  Google Scholar 

  28. Seo, J.I., Kim, Y.: Note on the family of proportional reversed hazard distributions. Commun. Stat.-Simul. Comput. 51(10), 5832–5844 (2022)

    Article  Google Scholar 

  29. Demiray, D., Kızılaslan, F.: Reliability estimation of a consecutive k-out-of-n system for non-identical strength components with applications to wind speed data. Qual. Technol. Quant. Manag., 1–36 (2023)

  30. Sadeghpour, A., Nezakati, A., Salehi, M.: Comparison of two sampling schemes in estimating the stress-strength reliability under the proportional reversed hazard rate model. Stat. Optim. Inform. Comput. 9(1), 82–98 (2021)

    Article  Google Scholar 

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Funding

This work was supported by the Khorramshahr university of marine science and technology with Grant Number 1401.

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  1. Department of Basic Sciences, Faculty of Economics and Management, Khorramshahr University of Marine Science and Technology, Khorramshahr, Iran

    Hossein Pasha-Zanoosi

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  1. Hossein Pasha-Zanoosi
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HP-Z: Methodology, conceptualization, writing, methodology and simulation.

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Correspondence to Hossein Pasha-Zanoosi.

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Pasha-Zanoosi, H. Estimation of multicomponent stress-strength reliability based on a bivariate Topp-Leone distribution. OPSEARCH (2023). https://doi.org/10.1007/s12597-023-00713-5

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