Al-Mutairi, D. K., Ghitany, M. E. and Kundu, D. \textit{ Inferences on stress-strength reliability from Lindley distributions}, Commun. Statist. Theory Methods 42(8) , 1443-1463, 2013.
Bhattacharyya, G. K. and Johnson, R. A. Estimation of reliability in a multicomponent stress-strength model, J. Amer. Statist. Assoc., 69, 966-970, 1974.
Birnbaum, Z.W. On a use of the Mann-Whitney statistic. In: Proceedings of Third Berkeley Symposium on Mathematical Statistics and Probability, 1, 13-17, University of California Press, Berkeley, CA., 1956
Chen, M.H., Shao, Q.M., Ibrahim and J.G. Monte Carlo methods in Bayesian computation, Springer-Verlag, New York, 2000 .
Eryilmaz, S. Multivariate stress-strength reliability model and its evaluation for coherent structures, J. Multivariate Anal., 99, 1878-1887, 2008.
Gentle, JE. Random number generation and Monte Carlo methods, Springer, New York, 1998.
Ghitany, M. E., Al-Mutairi, D. K. and Aboukhamseen, S. M. Estimation of the reliability of a stress-strength system from power Lindley distributions, Commun. Statist. Simul. Comput., 44 ,118-136, 2015.
Jeffrey, H. Theory of probability, 3rd ed., Oxford University Press, 1961.
Kotz, S., Lumelskii, Y., and Pensky, M. The stress-strength model and its generalization: theory and applications, World Scientific, Singapore, 2003.
Krishnamoorthy, K., Mukherjee, S. and Guo, H. Inference on reliability in two-parameter exponential stress-strength model, Metrika, 6 ,261-273, 2007.
Kundu, D. and Gupta, R. D. Estimation of $P(X <Y)$ for the generalized exponential distribution, Metrika, 61, 291-308, 2005.
Kundu, D. and Gupta, R. D. Estimation of p(Y<X) for Weibull distribution, IEEE Trans. Rel., 55(2), 270-280, 2006.
Kundu, D. and Raqab, M. Z. Estimation of $R = P(Y < X)$ for three-parameter Weibull distribution, Statist.
Probability Lett., 79, 1839-1846, 2009.
Lindley, D. V. Approximation Bayesian methods, Trabajos de Estadistica, 21, 223-237, 1980.
Mudholkar, G.S., Srivastava, D.K. and Freimer, M. The exponentiated Weibull family; a reanalysis of the bus motor failure data, Technometrics, 37, 436 - 445, 1995.
Pakdaman, Z. and Ahmadi, J. Stress- Strength reliability for$P[X_{r:n_{1},k:n_{2}}]$ in exponential case, Journal of the Turkish statistical association, 6(3), 92-102, 2013.
Pandey, M., Uddin, M. B. and Ferdous, J. Reliability estimation of an s-out-of-k system with non-identical component strengths: the Weibull case, Reliab. Eng. Sys. Saf., 36,109-116.
Rao, G. S. a and Kantam,R. R. L. Estimation of reliability in multicomponent stress-strength model: Log-logistic distribution, Electron. J. Appl. Statist. Anal, 3(2), 75-84, 2010.
Rao, G. S. Estimation of reliability in multicomponent stress-strength model based on generalized exponential distribution, Colombian J.Statist., 35(1), 67-76, 2012.
Rao, G. S. and Kantam,R. R. L., Rosaiah, K. and Reddy, J. P. Estimation of reliability in multicomponent stress-strength model based on inverse Rayleigh distribution, J. Statist. Appl. Probability, 3, 261-267, 2013.
Raqab, M. Z. and Kundu, D. Comparison of different estimators of $p(Y<X)$ for a scaled Burr type X distribution, Commun. Statist. Simul. Comput., 34(2), 465 - 483, 2006.
Robert, C.P. and Casella, G. Monte Carlo statistical methods, Second Edition, Springer, NewYork , 2004.
Saracoglu, B., Kinaci, I. and Kundu, D. On estimation of $R = p(Y < X)$ for exponential distribution under progressive type-II censoring, Journal of Statistical Computation and Simulation, 82(5), 729-744, 2012.
Sarhan, A. and Kundu, D. Generalized linear failure rate distribution, Commun. Statist. Theory Methods, 38, 642 - 660, 2009.
Shahsanaei, F and Daneshkhah, A. Estimation of stress strength model in generalized linear failure rate distribution, ArXiv Preprint $1312.0401$ v1, 2013.
Xia, Z. P., Yu, J. Y. , Cheng, L. D. , Liu, L. F. and Wang, W. M. Study on the
breaking strength of jute fibers using modified Weibull distribution, Journal of Composites Part A: Applied Science and Manufacturing, 40, 54-59, 2009.
Estimation of reliability in a multicomponent stress- strength model based on generalized linear failure rate distribution
Year 2018,
Volume: 47 Issue: 6, 1634 - 1651, 12.12.2018
In this paper, we consider the problem of estimation reliability in multicomponent stress-strength model, when the system consists of $k$-components have strength are given by independently and identically distributed random variables $X_{1},...,X_{k}$ each component experiencing a random stress governed by a random variable $Y$. The reliability such system is obtained when strength and stress variables are given by a generalized linear failure rate distribution. The system is regarded as alive only if at least $s$ out of $k$ $(s<k)$ strength exceed the stress. The multicomponent reliability of the system is given by $R_{s,k}=P[$ at least $s$ of $X_{1},...,X_{k}$ exceed $Y]$. The maximum likelihood estimator $(MLE)$ and Bayes estimator of $R_{s,k}$ are obtained. A simulation study is performed to compare the different estimators of $R_{s,k}$. Real data is used as a practical application of the proposed procedure.
Al-Mutairi, D. K., Ghitany, M. E. and Kundu, D. \textit{ Inferences on stress-strength reliability from Lindley distributions}, Commun. Statist. Theory Methods 42(8) , 1443-1463, 2013.
Bhattacharyya, G. K. and Johnson, R. A. Estimation of reliability in a multicomponent stress-strength model, J. Amer. Statist. Assoc., 69, 966-970, 1974.
Birnbaum, Z.W. On a use of the Mann-Whitney statistic. In: Proceedings of Third Berkeley Symposium on Mathematical Statistics and Probability, 1, 13-17, University of California Press, Berkeley, CA., 1956
Chen, M.H., Shao, Q.M., Ibrahim and J.G. Monte Carlo methods in Bayesian computation, Springer-Verlag, New York, 2000 .
Eryilmaz, S. Multivariate stress-strength reliability model and its evaluation for coherent structures, J. Multivariate Anal., 99, 1878-1887, 2008.
Gentle, JE. Random number generation and Monte Carlo methods, Springer, New York, 1998.
Ghitany, M. E., Al-Mutairi, D. K. and Aboukhamseen, S. M. Estimation of the reliability of a stress-strength system from power Lindley distributions, Commun. Statist. Simul. Comput., 44 ,118-136, 2015.
Jeffrey, H. Theory of probability, 3rd ed., Oxford University Press, 1961.
Kotz, S., Lumelskii, Y., and Pensky, M. The stress-strength model and its generalization: theory and applications, World Scientific, Singapore, 2003.
Krishnamoorthy, K., Mukherjee, S. and Guo, H. Inference on reliability in two-parameter exponential stress-strength model, Metrika, 6 ,261-273, 2007.
Kundu, D. and Gupta, R. D. Estimation of $P(X <Y)$ for the generalized exponential distribution, Metrika, 61, 291-308, 2005.
Kundu, D. and Gupta, R. D. Estimation of p(Y<X) for Weibull distribution, IEEE Trans. Rel., 55(2), 270-280, 2006.
Kundu, D. and Raqab, M. Z. Estimation of $R = P(Y < X)$ for three-parameter Weibull distribution, Statist.
Probability Lett., 79, 1839-1846, 2009.
Lindley, D. V. Approximation Bayesian methods, Trabajos de Estadistica, 21, 223-237, 1980.
Mudholkar, G.S., Srivastava, D.K. and Freimer, M. The exponentiated Weibull family; a reanalysis of the bus motor failure data, Technometrics, 37, 436 - 445, 1995.
Pakdaman, Z. and Ahmadi, J. Stress- Strength reliability for$P[X_{r:n_{1},k:n_{2}}]$ in exponential case, Journal of the Turkish statistical association, 6(3), 92-102, 2013.
Pandey, M., Uddin, M. B. and Ferdous, J. Reliability estimation of an s-out-of-k system with non-identical component strengths: the Weibull case, Reliab. Eng. Sys. Saf., 36,109-116.
Rao, G. S. a and Kantam,R. R. L. Estimation of reliability in multicomponent stress-strength model: Log-logistic distribution, Electron. J. Appl. Statist. Anal, 3(2), 75-84, 2010.
Rao, G. S. Estimation of reliability in multicomponent stress-strength model based on generalized exponential distribution, Colombian J.Statist., 35(1), 67-76, 2012.
Rao, G. S. and Kantam,R. R. L., Rosaiah, K. and Reddy, J. P. Estimation of reliability in multicomponent stress-strength model based on inverse Rayleigh distribution, J. Statist. Appl. Probability, 3, 261-267, 2013.
Raqab, M. Z. and Kundu, D. Comparison of different estimators of $p(Y<X)$ for a scaled Burr type X distribution, Commun. Statist. Simul. Comput., 34(2), 465 - 483, 2006.
Robert, C.P. and Casella, G. Monte Carlo statistical methods, Second Edition, Springer, NewYork , 2004.
Saracoglu, B., Kinaci, I. and Kundu, D. On estimation of $R = p(Y < X)$ for exponential distribution under progressive type-II censoring, Journal of Statistical Computation and Simulation, 82(5), 729-744, 2012.
Sarhan, A. and Kundu, D. Generalized linear failure rate distribution, Commun. Statist. Theory Methods, 38, 642 - 660, 2009.
Shahsanaei, F and Daneshkhah, A. Estimation of stress strength model in generalized linear failure rate distribution, ArXiv Preprint $1312.0401$ v1, 2013.
Xia, Z. P., Yu, J. Y. , Cheng, L. D. , Liu, L. F. and Wang, W. M. Study on the
breaking strength of jute fibers using modified Weibull distribution, Journal of Composites Part A: Applied Science and Manufacturing, 40, 54-59, 2009.
Hassan, M. K., & Alohali, M. İ. (2018). Estimation of reliability in a multicomponent stress- strength model based on generalized linear failure rate distribution. Hacettepe Journal of Mathematics and Statistics, 47(6), 1634-1651.
AMA
Hassan MK, Alohali Mİ. Estimation of reliability in a multicomponent stress- strength model based on generalized linear failure rate distribution. Hacettepe Journal of Mathematics and Statistics. December 2018;47(6):1634-1651.
Chicago
Hassan, M. Kh., and M. İ. Alohali. “Estimation of Reliability in a Multicomponent Stress- Strength Model Based on Generalized Linear Failure Rate Distribution”. Hacettepe Journal of Mathematics and Statistics 47, no. 6 (December 2018): 1634-51.
EndNote
Hassan MK, Alohali Mİ (December 1, 2018) Estimation of reliability in a multicomponent stress- strength model based on generalized linear failure rate distribution. Hacettepe Journal of Mathematics and Statistics 47 6 1634–1651.
IEEE
M. K. Hassan and M. İ. Alohali, “Estimation of reliability in a multicomponent stress- strength model based on generalized linear failure rate distribution”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, pp. 1634–1651, 2018.
ISNAD
Hassan, M. Kh. - Alohali, M. İ. “Estimation of Reliability in a Multicomponent Stress- Strength Model Based on Generalized Linear Failure Rate Distribution”. Hacettepe Journal of Mathematics and Statistics 47/6 (December 2018), 1634-1651.
JAMA
Hassan MK, Alohali Mİ. Estimation of reliability in a multicomponent stress- strength model based on generalized linear failure rate distribution. Hacettepe Journal of Mathematics and Statistics. 2018;47:1634–1651.
MLA
Hassan, M. Kh. and M. İ. Alohali. “Estimation of Reliability in a Multicomponent Stress- Strength Model Based on Generalized Linear Failure Rate Distribution”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, 2018, pp. 1634-51.
Vancouver
Hassan MK, Alohali Mİ. Estimation of reliability in a multicomponent stress- strength model based on generalized linear failure rate distribution. Hacettepe Journal of Mathematics and Statistics. 2018;47(6):1634-51.