Estimation of the Multicomponent Stress-Strength Reliability Model Under the Topp-Leone Distribution: Applications, Bayesian and Non-Bayesian Assessement
Abstract
The advantages of applying multicomponent stress-strength models lie in their ability to provide a comprehensive and accurate analysis of system reliability under real-world conditions. By accounting for the interactions between different stress components and identifying critical weaknesses, engineers can make informed decisions, leading to safer and more reliable designs. The primary emphasis of this research is placed on the Bayesian and classical estimations of a multicomponent stress-strength reliability model that is derived from the bounded Topp Leone distribution. It is presumable that both stress and strength follow a Topp Leone distribution, but the shape parameters of each variable differ, and the scale parameters (which determine where the variable is bounded) remain the same. Statisticians utilize approaches such as maximum likelihood paired with parametric and non-parametric bootstrap, as well as Bayesian methods, in order to evaluate the dependability of a system. Bayesian methods are also utilized. Simulation studies are carried out with the intention of establishing the degree of precision that may be achieved by employing the various methods of estimating. For the sake of this example, two genuine data sets are dissected and examined in detail.References
C. W. Topp, and F. C. Leone, A family of J-shaped frequency functions, Journal of the American Statistical Association, vol. 50, no.269, pp. 209–219, 1955.
M. E. Ghitany, S. Kotz and M. Xie On some reliability measures and their stochastic orderings for the Topp-Leone distribution, Journal of Applied Statistics, vol. 32, no. 7, pp. 715–722, 2005.
M. E. Ghitany Asymptotic distribution of order statistics from the Topp-Leone distribution, Int J Appl Math, vol. 20, pp.371–376, 2007.
A. I. Genc Moments of order statistics of Topp-Leone distribution, Stat Pap, vol. 53, no. 1, pp. 117–131, 2012.
S. M. T. K. MirMostafaee On the moments of order statistics coming from Topp-Leone distribution, Statistics and Probability Letters, vol. 95, pp. 85–91, 2014.
H. A. Bayoud Admissible minimax estimators for the shape parameter of Topp-Leone distribution, Communications in Statistics-Theory and Methods, vol. 45, no. 1, pp. 71–82, 2016a.
H. A. Bayoud Estimating the Shape Parameter of Topp-Leone Distribution Based on Progressive Type-II Censored Samples, REVSTAT, vol. 14, no. 4, pp. 415–431, 2016b.
H. M. Yousof and M. C¸ . Korkmaz Topp-leone Nadarajah-haghighi distribution, Istatistikciler Dergisi: Istatistik ve Aktuerya, vol. 10, no. 2, pp. 119–127, 2017.
H. Reyad, M. C¸ . Korkmaz, A. Z. Afify, G. G. Hamedani and S. Othman The Frechet Topp Leone-G family of distributions:
Properties, characterizations and applications, Annals of Data Science, vol. 8, pp. 345–366, 2021.
A. I. Genc Estimation of P(X>Y) with Topp-Leone distribution, Journal of Statistical Computation and Simulation, vol. 83, no. 2, pp. 326–339, 2013.
F. Condino, F. Domma and G. Latorre Likelihood and Bayesian estimation of Pr(Y < X) using lower record values from a proportional reversed hazard family, Stat Pap, vol. 59, pp. 467–485, 2016.
M. C . Korkmaz, H. M. Yousof, M. Alizadeh and G. G. Hamedani. The Topp-Leone generalized odd log-logistic family of distributions: properties, characterizations and applications, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2 1506–1527, 2019.
M. Rasekhi, M. M. Saber and H. M. Yousof Bayesian and classical inference of reliability in multicomponent stress-strength under the generalized logistic model, Communications in Statistics-Theory and Methods, vol. 50, no. 21, pp. 5114–5125, 2020.
M. M. Saber and H. M. Yousof Bayesian and Classical Inference for Generalized Stress-strength Parameter under Generalized Logistic Distribution, Statistics, Optimization and Information Computing, vol. 11, no. 3, pp. 541–553, 2023.
M. M. Saber, M. Mohie El-Din Marwa and H. M. Yousof Reliability estimation for the remained stress-strength model under the generalized exponential lifetime distribution, Journal of Probability and Statistics, pp. 1–10, 2021.
M. M. Saber , M. Rasekhi and H. M. Yousof Generalized Stress-Strength and Generalized Multicomponent Stress-Strength Models, Statistics, Optimization and Information Computing, forthcoming. 2022b.
M. M. Saber, G.G. Hamedani, H. M. Yousof, N. S. But and B. Ahmed A Family of Continuous Probability Distributions: Theory, Characterizations, Properties and Different Copulas, CRC Press, Taylor and Francis Group. 2022a.
M. M. Ali, H. M. Yousof and M. Ibrahim G Families of Probability Distributions: Theory and Practices, CRC Press, Taylor and Francis Group. 2022.
S. Kotz , Y. Lumelskii and M. Pensky The Stress-Stength Model and Its Generalizations., World Scientific, Singapore. 2003.
D. Bhattacharya and S. Roychowdhury Reliability of a coherent system in a multicomponent stress-strength model, American Journal of Mathematical and Management Sciences, vol. 32, no. 1, pp. 40–52, 2013.
G. K. Bhattacharya and R. A. Johnson Estimation of reliability in a multi-component stress-strength model, Journal of the American Statistical Association, vol. 69, no. 348, pp. 996–970, 1974.
S. Geman and D. Geman Stochastic relaxation, gibbs distributions, and the Bayesian restoration of images, IEEE Trans Pattern Anal Mach Intell, vol. 6, no. 6, pp. 721–741, 1984.
S. Dey, J. Mazucheli and M.Z. Anis Estimation of Reliability of Multicomponent Stress-Strength for a Kumaraswamy Distribution, Communications in Statistics-Theory and Methods, vol. 46, no. 4, pp. 1560–1572, 2017.
R. Dasgupta On the distribution of Burr with applications, Sankhya B, vol. 71, no. 1, pp. 1–19, 2011.
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