Statistical inference of the stress-strength reliability and mean remaining strength of series system with cold standby redundancy at system and component levels
A real data set is analyzed for the purpose of illustration.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:In this study, we consider the stress-strength reliability and mean remaining strength of a series system with cold standby redundancy at the component and system levels.
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Temel Bulgular & Veri:We perform Monte Carlo simulations to compare the performance of proposed estimates.
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Sonuç & Katkı:A real data set is analyzed for the purpose of illustration.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Stress-strength reliability · mean remaining strength · cold standby
Abstract
In this study, we consider the stress-strength reliability and mean remaining strength of a series system with cold standby redundancy at the component and system levels. Classical and Bayesian approaches are studied in order to obtain the estimates when the underlying stress, strength and standby components follow the exponential distribution with different parameters. Bayes estimates are approximated by using Lindley’s approximation and Markov Chain Monte Carlo methods. Asymptotic confidence intervals and highest probability density credible intervals are constructed. We perform Monte Carlo simulations to compare the performance of proposed estimates. A real data set is analyzed for the purpose of illustration.
Cüran, G., Kızılaslan, F. (2021). Statistical inference of the stress-strength reliability and mean remaining strength of series system with cold standby redundancy at system and component levels. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 6. https://doi.org/10.15672/hujms.804070
K. Ahmadi and S. Ghafouri, 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.
F.G. Akgül, Reliability estimation in multicomponent stress–strength model for ToppLeone distribution, J. Stat. Comput. Simul. 89 (15), 2914-2929, 2019.
E.K. AL-Hussaini, M.A.M.A. Mousa and K.S. Sultan, Parametric and nonparametric estimation of P(Y Y ) in ranked set sampling, SORT 40 (2), 243-266, 2016.
R. Nojosa and P.N. Rathie, Stress-strength reliability models involving generalized gamma and Weibull distributions, Int. J. Qual. Reliab. 37 (4), 538-551, 2020.
R Core Team R, A language and environment for statistical computing, Vienna, Austria, R Foundation for Statistical Computing, 2020.
C.R. Rao, Linear Statistical Inference and Its Applications, Wiley, 1965.
T.R. Rasethuntsa and M. Nadar, Stress-strength reliability of a non-identicalcomponent-strengths system based on upper record values from the family of Kumaraswamy generalized distributions, Statistics 52 (3), 684-716, 2018.
K. Shen and M. Xie, The effectiveness of adding standby redundancy at system and component levels, IEEE Trans. Rel. 40 (1), 53-55, 1991.
K.C. Siju and M. Kumar, Estimation of stress-strength reliability of a parallel system with active, warm and cold standby components, J. Ind. Prod. Eng. 34 (8), 590-610, 2017.
L. Tierney, Markov chains for exploring posterior distributions, Ann. Statist. 22 (4), 1701-1728, 1994.
R. Yan, B. Lu and X. Li, On Redundancy allocation to series and parallel systems of two components, Comm. Statist. Theory Methods 48 (18), 4690-4701, 2019.
P. Zhao, Y. Zhang and L. Li, Redundancy allocation at component level versus system level, European J. Oper. Res. 241 (2), 402-411, 2015.
Z.W. Birnbaum and B.C. McCarty, A distribution-free upper confidence bounds for P r(Y < X) based on independent samples of X and Y, Ann. Math. Statist. 29 (2), 558-562, 1958.