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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

Abstract

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.

References

  • 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.

The Mean Remaining Strength Of Systems In A Stress-Strength Model

Year 2013, Volume: 42 Issue: 2, 181 - 187, 01.02.2013

Abstract

-

References

  • 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.
There are 20 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

Selma Gürler This is me

Publication Date February 1, 2013
Published in Issue Year 2013 Volume: 42 Issue: 2

Cite

APA 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 (February 2013), 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.