Methods For Estimating R_((S,K)) Based On Rayleigh-Pareto Distribution
Keywords:
Rayleigh-Pareto, Multicomponent Reliability, Stress-Strength, Least squares Method, and Ridge Regression MethodAbstract
This paper considers with the reliability of a multicomponent system of k components estimation problem of a stress-strength model. is obtained when the strength and stress variables have the two-parameters Rayleigh-Pareto distribution . is the known scale parameter and ( ) is an unknown shape parameter for stress - strength distribution of Rayleigh-Pareto. The system contains (K) components with its strength ( , which represent random variables distributed independently and symmetrically, and each component suffers from random stress is (X). The system regards as active system only if at least strength components exceed the stress. Parameter estimation using Least Squares (LS) , Relative Least Squares RLS , Wight Least Squares (WLS) and Ridge Regression Method (RRM) have discussed. The estimating of reliability parameters obtained from all the approaches above are compared with the Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) criteria based on Monte-Carlo simulation experiment. Significantly, WLS and LS estimators have shown better performance compared with other methods.
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References
[2] Birnbaum, Z. W. and McCarty, B.C. (1958). "A distribution-free upper confidence bounds for Pr(Y < X) based on independent samples of X and Y". The Annals of Mathematical Statistics, 29(2), 558-562.
[3] Bhattacharyya, G.K., Johnson, R.A., (1974)."Estimation of Reliability in a Multi-Component Stress-Strength Model", Journal of the American Statistical Association, 69(348), 966-970.
[4] Swain J, Venkatraman S, Wilson J. (1988) ."Least squares estimation of distribution function in Johnson’s translation system", Journal of Statistical Computati-on and Simulation, 29(4),271–297.
[5] Afify, E.E. ,(2003) ."Comparison of estimators of parameters for the Rayleigh distribution.",http://jscs.stat.vt..Edu/interstat/articles/abstracts/u0300I.htmlssi.Online text.
[6] Hassan A. S. and Basheikh H. M., (2012), "Estimation of Reliability in Multi-Component Stress-Strength Model Following Exponential Pareto Distribution", The Egyptian Statistical Journal, Institute Of Statistical Studies & Research, Cairo University, vol. 56(2), 82-95.
[7] Pandit, P. V. and Kantu, Kala, J.(2013). "System reliability estimation in multicomponent exponential stress-strength models". International Journal of Reliability and Applications, 14(2), 97-105.
[8] Nada Sabah Karam, Hind Husham Jani (2016) . Estimation of Reliability in Multi-Component Stress-Strength Model Following Burr-III Distribution, 1(1) , 329-342.
[9] Rao,G.S.; Aslam, M.; Arif, O.H. (2017), "Estimation of Reliability in Multicomponent Stress-Strength Based on Two parameter Exponentiated Weibull distribution, Communication in Statistics Theory and Methods, 66 , 7495-7502.
[10] Parameshwar V Pandit*, Shubhashree Joshi, (2018) ." Reliability Estimation in Multicomponent Stress-strength Model based on Generalized Pareto Distribution", American Journal of Applied Mathematics and Statistics, 6(5), 210-217.
[11] Pandit P. V. and Joshi, S., (2018), "Reliability Estimation in Multicomponent Stress – Strength Model based on Generalized Pareto Distribution", American Journal of Applied Mathematics and Statistics, 6(5), 210-217.
[12] Abdulateef, E. A. and Salman, A. N.(2019), "On Shrinkage Estimation of R(s,k) in Case of Exponentiated Pareto distribution", Ibn Al – Haitham Journal for Pure & Applications, 32(1),147-156.
