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On estimating a stress-strength type reliability

Year 2018, Volume: 47 Issue: 1, 243 - 253, 01.02.2018

Abstract

This article deals with estimating an extension of the well-known stress-strength reliability in nonparametric setup. By means of Monte Carlo simulations, the proposed estimator is compared with its parametric analogs in the case of exponential distribution. The results show that the estimator could be highly effcient in many situations considered.

References

  • Bohn, L.L. A review of nonparametric ranked set sampling methodology. Communications in Statistics: Theory and Methods 25, 2675-2685, 1996.
  • Chen, Z., Bai, Z., and Sinha, B.K. Ranked set sampling: Theory and Applications. Springer, New York, 2004.
  • Dong, X., Zhang, L., and Li, F. Estimation of reliability for exponential distributions using ranked set sampling with unequal samples. Quality Technology & Quantitative Management 10, 319-328, 2013.
  • Kotz, S., Lumelskii, Y., and Pensky, M. The stress-strength model and its generalizations. Theory and applications. World Scientic, Singapore, 2003.
  • Kvam, P.H., and Samaniego, F.J. Nonparametric maximum likelihood estimation based on ranked set samples. Journal of the American Statistical Association 89, 526-537, 1994.
  • McIntyre, G.A. A method for unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research 3, 385-390, 1952.
  • Pakdaman, Z., and Ahmadi, J. Stress-strength reliability for P(Xr:n1 < Yk:n2 ) in the exponential case. STATSTK 6, 92-102, 2013.
  • Samawi, H., Abu-Dayyeh, W., and Ahmed, S. Extreme ranked set sampling. Biometrical Journal 30, 577-586, 1996.
  • Sengupta, S., and Mukhuti, S. Unbiased estimation of P(X > Y ) for exponential populations using order statistics with application in ranked set sampling. Communications in Statistics: Theory and Methods 37, 898-916, 2008.
Year 2018, Volume: 47 Issue: 1, 243 - 253, 01.02.2018

Abstract

References

  • Bohn, L.L. A review of nonparametric ranked set sampling methodology. Communications in Statistics: Theory and Methods 25, 2675-2685, 1996.
  • Chen, Z., Bai, Z., and Sinha, B.K. Ranked set sampling: Theory and Applications. Springer, New York, 2004.
  • Dong, X., Zhang, L., and Li, F. Estimation of reliability for exponential distributions using ranked set sampling with unequal samples. Quality Technology & Quantitative Management 10, 319-328, 2013.
  • Kotz, S., Lumelskii, Y., and Pensky, M. The stress-strength model and its generalizations. Theory and applications. World Scientic, Singapore, 2003.
  • Kvam, P.H., and Samaniego, F.J. Nonparametric maximum likelihood estimation based on ranked set samples. Journal of the American Statistical Association 89, 526-537, 1994.
  • McIntyre, G.A. A method for unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research 3, 385-390, 1952.
  • Pakdaman, Z., and Ahmadi, J. Stress-strength reliability for P(Xr:n1 < Yk:n2 ) in the exponential case. STATSTK 6, 92-102, 2013.
  • Samawi, H., Abu-Dayyeh, W., and Ahmed, S. Extreme ranked set sampling. Biometrical Journal 30, 577-586, 1996.
  • Sengupta, S., and Mukhuti, S. Unbiased estimation of P(X > Y ) for exponential populations using order statistics with application in ranked set sampling. Communications in Statistics: Theory and Methods 37, 898-916, 2008.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Statistics
Authors

M. Mahdizadeh

Publication Date February 1, 2018
Published in Issue Year 2018 Volume: 47 Issue: 1

Cite

APA Mahdizadeh, M. (2018). On estimating a stress-strength type reliability. Hacettepe Journal of Mathematics and Statistics, 47(1), 243-253.
AMA Mahdizadeh M. On estimating a stress-strength type reliability. Hacettepe Journal of Mathematics and Statistics. February 2018;47(1):243-253.
Chicago Mahdizadeh, M. “On Estimating a Stress-Strength Type Reliability”. Hacettepe Journal of Mathematics and Statistics 47, no. 1 (February 2018): 243-53.
EndNote Mahdizadeh M (February 1, 2018) On estimating a stress-strength type reliability. Hacettepe Journal of Mathematics and Statistics 47 1 243–253.
IEEE M. Mahdizadeh, “On estimating a stress-strength type reliability”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 1, pp. 243–253, 2018.
ISNAD Mahdizadeh, M. “On Estimating a Stress-Strength Type Reliability”. Hacettepe Journal of Mathematics and Statistics 47/1 (February 2018), 243-253.
JAMA Mahdizadeh M. On estimating a stress-strength type reliability. Hacettepe Journal of Mathematics and Statistics. 2018;47:243–253.
MLA Mahdizadeh, M. “On Estimating a Stress-Strength Type Reliability”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 1, 2018, pp. 243-5.
Vancouver Mahdizadeh M. On estimating a stress-strength type reliability. Hacettepe Journal of Mathematics and Statistics. 2018;47(1):243-5.