In this paper, we study the mean remaining strength of a component inthe stress-strength setup. We present the models for the mean remaining strength for systems consisting of n independent components underthe k-out-of-n:F , parallel and series configurations. We assume thatthe strengths of the components are nonidentically distributed randomvariables and components are designed under the common stress.
Asadi, M. and Bairamov, I. The Mean Residual Life Function of a k-out-of-n Structure at the System Level, IEEE Trans. Reliab. 55(2), 314-318, 2006.
Asadi, M. and Goliforushani, S. On the mean residual life function of coherent systems, IEEE Trans. Reliab. 57, 574-580, 2008.
Bairamov, I., Ahsanullah, M., Akhundov, I. A residual life function of a system having parallel or series structures, J. Statist. Theor. Appl. 1 (2), 119-132, 2002.
Bhattacharyya, G. K. and Johnson, R. A. Estimation of reliability in a component stressstrength model, J. Amer. Statist. Assn. 69, 966-70, 1974.
Bhattacharyya, G. K. and Johnson, R. A. Stress-strength models for system reliability, Proceedings of the symposium on Reliability and Fault Tree Analysis SIAM 509-532, 1975. Dewanji, A. and Rao, T. S. On system reliability under stress-strength modeling, Commun. Statist-Theory. Meth. 30 (6), 1185-1196, 2001.
Ebrahimi, N. Estimation of reliability for a series stress-strength system, IEEE Trans. Reliab. 31, 202-205, 1982.
Eryılmaz, S. Consecutive k-Out-of-n: G System in Stress-Strength Setup, Communications in Statistics-Simulation and Computation 37, 579-589, 2008.
Eryılmaz, S. On system reliability in stress-strength setup, Statistics & Probability Letters 80 (9-10), 834-839, 2010.
Greco, L. and Ventura, L. Robust inference for the stress–strength reliability, Statistical Papers 52, 773-788, 2011.
Guess, F. M., Zhang, X., Young, T. M., Le´ on, R. V. Using mean residual life functions for unique insights into strengths of materials data, International Journal of Reliability and Applications 6 (2), 79-85, 2005.
Guess, F. M., Steele, J. C., Young, T. M., Le´ on, R. V. Applying novel mean residual life confidence intervals, International Journal of Reliability and Applications 7 (2), 177-186,
Gurler, S. and Bairamov, I. Parallel and k-out-of-n: G systems with nonidentical components and their mean residual life functions, Appl. Math. Modell. 33 (2), 1116-1125, 200
Hanagal, D. D. Estimation of reliability of a component subjected to bivariate exponential stress, Statistical Papers 40, 211-220, 1999.
Hanagal, D. D. Estimation of system reliability, Statistical Papers 40, 99-106, 1999.
Johnson, R. A. Stress-strength Models for Reliability, Handbook of Statistics, Vol 7, Quality Control and Reliability (1988).
Kotz, S., Lumelskii, Y., Pensky, M. The Stress-Strength Model and its Generalizations: Theory and Applications (World Scientific, Singapore, 2003).
Sadegh, M. K. Mean Past and Mean Residual Life Functions of a Parallel System with Nonidentical Components, Communications in Statistics-Theory and Methods 37, 11341145, 2008.
Sadegh, M. K. A note on the mean residual life function of a coherent system with exchangeable or nonidentical components, Journal of Statistical Planning and Inference 141 (9), 3267-3275, 2011.
Shen, Y., Xie, M., and Tang, L.C. On the change point of the mean residual life of series and parallel systems, Australian and New Zealand Journal of Statistics 52, 109-121, 2010.
Weibull, W. A statistical distribution function of wide applicability, Journal of Applied Mechanics 18, 293-297, 1951.
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The Mean Remaining Strength Of Systems In A Stress-Strength Model
Year 2013,
Volume: 42 Issue: 2, 181 - 187, 01.02.2013
Asadi, M. and Bairamov, I. The Mean Residual Life Function of a k-out-of-n Structure at the System Level, IEEE Trans. Reliab. 55(2), 314-318, 2006.
Asadi, M. and Goliforushani, S. On the mean residual life function of coherent systems, IEEE Trans. Reliab. 57, 574-580, 2008.
Bairamov, I., Ahsanullah, M., Akhundov, I. A residual life function of a system having parallel or series structures, J. Statist. Theor. Appl. 1 (2), 119-132, 2002.
Bhattacharyya, G. K. and Johnson, R. A. Estimation of reliability in a component stressstrength model, J. Amer. Statist. Assn. 69, 966-70, 1974.
Bhattacharyya, G. K. and Johnson, R. A. Stress-strength models for system reliability, Proceedings of the symposium on Reliability and Fault Tree Analysis SIAM 509-532, 1975. Dewanji, A. and Rao, T. S. On system reliability under stress-strength modeling, Commun. Statist-Theory. Meth. 30 (6), 1185-1196, 2001.
Ebrahimi, N. Estimation of reliability for a series stress-strength system, IEEE Trans. Reliab. 31, 202-205, 1982.
Eryılmaz, S. Consecutive k-Out-of-n: G System in Stress-Strength Setup, Communications in Statistics-Simulation and Computation 37, 579-589, 2008.
Eryılmaz, S. On system reliability in stress-strength setup, Statistics & Probability Letters 80 (9-10), 834-839, 2010.
Greco, L. and Ventura, L. Robust inference for the stress–strength reliability, Statistical Papers 52, 773-788, 2011.
Guess, F. M., Zhang, X., Young, T. M., Le´ on, R. V. Using mean residual life functions for unique insights into strengths of materials data, International Journal of Reliability and Applications 6 (2), 79-85, 2005.
Guess, F. M., Steele, J. C., Young, T. M., Le´ on, R. V. Applying novel mean residual life confidence intervals, International Journal of Reliability and Applications 7 (2), 177-186,
Gurler, S. and Bairamov, I. Parallel and k-out-of-n: G systems with nonidentical components and their mean residual life functions, Appl. Math. Modell. 33 (2), 1116-1125, 200
Hanagal, D. D. Estimation of reliability of a component subjected to bivariate exponential stress, Statistical Papers 40, 211-220, 1999.
Hanagal, D. D. Estimation of system reliability, Statistical Papers 40, 99-106, 1999.
Johnson, R. A. Stress-strength Models for Reliability, Handbook of Statistics, Vol 7, Quality Control and Reliability (1988).
Kotz, S., Lumelskii, Y., Pensky, M. The Stress-Strength Model and its Generalizations: Theory and Applications (World Scientific, Singapore, 2003).
Sadegh, M. K. Mean Past and Mean Residual Life Functions of a Parallel System with Nonidentical Components, Communications in Statistics-Theory and Methods 37, 11341145, 2008.
Sadegh, M. K. A note on the mean residual life function of a coherent system with exchangeable or nonidentical components, Journal of Statistical Planning and Inference 141 (9), 3267-3275, 2011.
Shen, Y., Xie, M., and Tang, L.C. On the change point of the mean residual life of series and parallel systems, Australian and New Zealand Journal of Statistics 52, 109-121, 2010.
Weibull, W. A statistical distribution function of wide applicability, Journal of Applied Mechanics 18, 293-297, 1951.
Gürler, S. (2013). The Mean Remaining Strength Of Systems In A Stress-Strength Model. Hacettepe Journal of Mathematics and Statistics, 42(2), 181-187.
AMA
Gürler S. The Mean Remaining Strength Of Systems In A Stress-Strength Model. Hacettepe Journal of Mathematics and Statistics. February 2013;42(2):181-187.
Chicago
Gürler, Selma. “The Mean Remaining Strength Of Systems In A Stress-Strength Model”. Hacettepe Journal of Mathematics and Statistics 42, no. 2 (February 2013): 181-87.
EndNote
Gürler S (February 1, 2013) The Mean Remaining Strength Of Systems In A Stress-Strength Model. Hacettepe Journal of Mathematics and Statistics 42 2 181–187.
IEEE
S. Gürler, “The Mean Remaining Strength Of Systems In A Stress-Strength Model”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 2, pp. 181–187, 2013.
ISNAD
Gürler, Selma. “The Mean Remaining Strength Of Systems In A Stress-Strength Model”. Hacettepe Journal of Mathematics and Statistics 42/2 (February2013), 181-187.
JAMA
Gürler S. The Mean Remaining Strength Of Systems In A Stress-Strength Model. Hacettepe Journal of Mathematics and Statistics. 2013;42:181–187.
MLA
Gürler, Selma. “The Mean Remaining Strength Of Systems In A Stress-Strength Model”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 2, 2013, pp. 181-7.
Vancouver
Gürler S. The Mean Remaining Strength Of Systems In A Stress-Strength Model. Hacettepe Journal of Mathematics and Statistics. 2013;42(2):181-7.