The mean remaining strength of systems ın a stress-strength model

In this paper, we study the mean remaining strength of a component in the stress-strength setup. We present the models for the mean remain- ing strength for systems consisting of n independent components under the k-out-of-n:F , parallel and series configurations. We assume that the strengths of the components are nonidentically distributed random variables and components are designed under the common stress.

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[1] 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.
[2] Asadi, M. and Goliforushani, S. On the mean residual life function of coherent systems, IEEE Trans. Reliab. 57, 574-580, 2008.
[3] 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.
[4] Bhattacharyya, G. K. and Johnson, R. A. Estimation of reliability in a component stress- strength model, J. Amer. Statist. Assn. 69, 966-70, 1974.
[5] 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.
[6] Dewanji, A. and Rao, T. S. On system reliability under stress-strength modeling, Commun. Statist-Theory. Meth. 30 (6), 1185-1196, 2001.
[7] Ebrahimi, N. Estimation of reliability for a series stress-strength system, IEEE Trans. Reliab. 31, 202-205, 1982.
[8] Eryılmaz, S. Consecutive k-Out-of-n: G System in Stress-Strength Setup, Communications in Statistics-Simulation and Computation 37, 579-589, 2008.
[9] Eryılmaz, S. On system reliability in stress-strength setup, Statistics & Probability Letters 80 (9-10), 834-839, 2010.
[10] Greco, L. and Ventura, L. Robust inference for the stress–strength reliability, Statistical Papers 52, 773-788, 2011.
[11] Guess, F. M., Zhang, X., Young, T. M., Le ́n, R. V. Using mean residual life functions o for unique insights into strengths of materials data, International Journal of Reliability and Applications 6 (2), 79-85, 2005.
[12] Guess, F. M., Steele, J. C., Young, T. M., Le ́n, R. V. Applying novel mean residual life confidence intervals, International Journal of Reliability and Applications 7 (2), 177-186, 2006.
[13] Gurler, S. and Bairamov, I. Parallel and k-out-of-n: G systems with nonidentical com- ponents and their mean residual life functions, Appl. Math. Modell. 33 (2), 1116-1125, 2009.
[14] Hanagal, D. D. Estimation of reliability of a component subjected to bivariate exponential stress, Statistical Papers 40, 211-220, 1999.
[15] Hanagal, D. D. Estimation of system reliability, Statistical Papers 40, 99-106, 1999.
[16] Johnson, R. A. Stress-strength Models for Reliability, Handbook of Statistics, Vol 7, Quality Control and Reliability (1988).
[17] Kotz, S., Lumelskii, Y., Pensky, M. The Stress-Strength Model and its Generalizations: Theory and Applications (World Scientific, Singapore, 2003).
[18] Sadegh, M. K. Mean Past and Mean Residual Life Functions of a Parallel System with Nonidentical Components, Communications in Statistics-Theory and Methods 37, 1134- 1145, 2008.
[19] Sadegh, M. K. A note on the mean residual life function of a coherent system with ex- changeable or nonidentical components, Journal of Statistical Planning and Inference 141 (9), 3267-3275, 2011.
[20] 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.
[21] Weibull, W. A statistical distribution function of wide applicability, Journal of Applied Mechanics 18, 293-297, 1951.