The mean remaining strength of parallel systems in a stress-strength model based on exponential distribution

Yıl 2019, Cilt: 68 Sayı: 2, 1435 - 1451, 01.08.2019

Fatih Kızılaslan

https://doi.org/10.31801/cfsuasmas.539171

Cited By: 5

Öz

The mean remaining strength of any coherent system is one of the important characteristics in stress-strength reliability. It shows that the system on the average how long can be safe under the stress. In this paper, we consider the mean remaining strength of the parallel systems in the stress-strength model. We assume that the strength and stress components constitute parallel systems separately. The mean remaining strength and its estimations are obtained when the all components follow the exponential distribution. The likelihood ratio order between the remaining strength of the parallel systems is presented for two-component case. The simulation study is performed to compare the derived estimates and their results are presented.

Anahtar Kelimeler

Mean remaining strength, exponential and generalized exponential distributions, stress-strength model

Kaynakça

• Birnbaum, Z. W., On a use of Mann-Whitney statistics, in Proc. 3rd Berkeley Symposium on Mathematical Statistics and Probability 1, (1956), 13-17.
• Birnbaum, Z. W. and McCarty, B. C., A distribution-free upper confidence bounds for Pr(Y<X) based on independent samples of X and Y, The Annals of Mathematical Statistic 29(2), (1958), 558-562.
• Kotz, S., Lumelskii, Y., Pensky, M., The Stress-Strength Model and its Generalizations: Theory and Applications, World Scientific, Singapore, 2003.
• Kundu, D., Gupta, R. D., Estimation of P(Y<X) for generalized exponential distribution, Metrika 61, (2005), 291-308.
• Basirat, M., Baratpour, S. and Ahmadi, J., Statistical inferences for stress--strength in the proportional hazard models based on progressive Type-II censored samples, Journal of Statistical Computation and Simulation 85(3), (2015), 431-449.
• Basirat, M., Baratpour, S. and Ahmadi, J., On estimation of stress-strength parameter using record values from proportional hazard rate models, Communications in Statistics - Theory and Methods 45(19), (2016), 5787-5801.
• Asgharzadeh, A., Kazemi, M. and Kundu, D., Estimation of P(X>Y) for Weibull distribution based on hybrid censored samples, International Journal of System Assurance Engineering and Management 8(1), (2017), 489-498.
• Bhattacharyya, G. K. and Johnson, R. A. Estimation of reliability in multicomponent stress-strength model, Journal of American Statistical Association 69, (1974), 966-970.
• Bhattacharyya, G. K. and Johnson, R. A. Stress--strength models for system reliability, Proceedings of the Symposium on Reliability and Fault Tree Analysis SIAM, (1975), 509-532.
• Eryilmaz, S., Consecutive k-Out-of-n : G System in Stress-Strength Setup, Communications in Statistics - Simulation and Computation, 37(3), (2008), 579-589.
• Eryilmaz, S., On system reliability in stress-strength setup, Statistics & Probability Letters 80, (2010), 834-839.
• Pakdaman, Z. and Ahmadi, J., Stress-strength reliability for P(X_{r:n₁}<Y_{k:n₂}) in the exponential case, Istatistik: Journal of The Turkish Statistical Association 6(3), (2013), 92-102.
• Pakdaman, Z. and Ahmadi, J., Point estimation of the stress-strength reliability parameter for parallel system with independent and non-identical components, Communications in Statistics-Simulation and Computation, 47(4), (2018), 1193-1203.
• Hassan, M. K. H., Estimation a stress-strength model for P(Y_{r:n₁}<X_{k:n₂}) using the Lindley distribution, Revista Colombiana de Estadística 40(1), (2017), 105-121.
• Kızılaslan, F., Classical and Bayesian estimation of reliability in a multicomponent stress--strength model based on the proportional reversed hazard rate mode, Mathematics and Computers in Simulation 136, (2017), 36-62.
• Gürler, S., The mean remaining strength of systems in a stress-strength model, Hacettepe Journal of Mathematics and Statistics 42(2), (2013), 181-187.
• Bairamov (Bayramoglu), I., Gurler, S. and Ucer, B., On the mean remaining strength of the k-out-of-n:F system with exchangeable components, Communications in Statistics-Simulation and Computation 44(1), (2015), 1-13.
• Gurler, S., Ucer, B. H. and Bairamov, I., On the mean remaining strength at the system level for some bivariate survival models based on exponential distribution, Journal of Computational and Applied Mathematics 290, (2015), 535-542.
• Gupta, R. D. and Kundu, D., Generalized exponential distributions, Australian & New Zealand Journal of Statistics 41, (1999), 173-188.
• Dewan, I. and Khaledi, B., On stochastic comparisons of residual life time at random time, Statistics and Probability Letters 88, (2014), 73-79.
• Misra, N. and Naqvi, S., Stochastic comparison of residual lifetime mixture models, Operations Research Letters 46, (2018), 122-127.
• Misra, N. and Naqvi, S., Some unified results on stochastic properties of residual lifetime at random times, Brazilian Journal of Probability and Statistics 32(2), (2018), 422-436
• Shakedand, M. and Shanthikumar, J. G., Stochastic Orders, Springer Series in Statistics, 2007.
• Ghitany, M. E., Al-Jarallah, R. A. and Balakrishnan, N., On the existence and uniqueness of the MLEs of the parameters of a general class of exponentiated distributions, Statistics 47(3), (2013), 605-612.
• Gradshteyn, I. S and Ryzhik, I. M., Table of Integrals, Series and Products, 5th ed. Boston, USA: Academic Press, 2007.
• Rao, C. R., Linear Statistical Inference and Its Applications. New York: Wiley; 1965.
• Lindley, D. V., Approximate Bayes method, Trabajos de Estadistica 3, (1980), 281-288.
• Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B., Bayesian Data Analysis. Chapman Hall, London, 2003.
• Chen, M. H. and Shao, Q. M., Monte Carlo estimation of Bayesian credible and HPD intervals, Journal of Computational and Graphical Statistics 8(1), (1999), 69-92.