**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31819

##### Comparing Interval Estimators for Reliability in a Dependent Set-up

**Authors:**
Alessandro Barbiero

**Abstract:**

In this paper some procedures for building confidence intervals for the reliability in stress-strength models are discussed and empirically compared. The particular case of a bivariate normal setup is considered. The confidence intervals suggested are obtained employing approximations or asymptotic properties of maximum likelihood estimators. The coverage and the precision of these intervals are empirically checked through a simulation study. An application to real paired data is also provided.

**Keywords:**
Approximate estimators,
asymptotic theory,
confidence interval,
Monte Carlo simulations,
stress-strength,
variance estimation.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1074427

**References:**

[1] Z.W. Birnbaum, "On a use of the Mann-Whitney statistic", Proceedings of the Third Berkley Symposium on Mathematical Statistics and Probability, vol. 1, Univ. of Calif. Press, pp. 13-17, 1976.

[2] Z.W. Birnbaum and R.C. McCarty, "A distribution-free upper confidence bound for P(Y < X) based on independent samples of X and Y", Annals of Mathematical Statistics, vol. 29, pp. 558-562, 1958.

[3] J.D. Church and B. Harris, "The Estimation of Reliability from Stress- Strength Relationships", Technometrics, vol. 12(1), pp.49-54, 1970.

[4] J.L. Devore, Probability and Statistics for Engineering and the Sciences, Duxbury Press, 2003

[5] Z. Govindarazulu, "Two-Sided Confidence Limits for P(X

[8] S. Kotz, Y. Lumelskii, and M. Pensky, The stress-strength model and its generalizations - Theory and Applications, World Scientific Publishing, 2003

[9] R.C. Gupta and S. Subramanian, "Estimation of reliability in a bivariate normal distribution with equal coefficients of variation", Communications in Statistics - Simulation and Computation, vol. 27(3), pp. 675-698, 1998.

[10] S.P. Mukherjee and L.K. Sharan, "Estimation of failure probability from a bivariate normal stress-strength distribution", Microelectronics Reliability, vol. 25, pp. 699-702, 1985.

[11] S. Nadarajah and S. Kotz, "Reliability for some bivariate exponential distributions", Mathematical problems in engineering, Article ID 41652, pp. 1-14, 2006.

[12] S. Nadarajah and S. Kotz, "Reliability for some bivariate beta distributions", Mathematical problems in engineering, vol. 1, pp. 101-112, 2006.

[13] S. Nadarajah and S. Kotz, "Reliability For A Bivariate Gamma Distribution", Economic Quality Control, vol. 20(1), pp. 111-119, 2005.

[14] S. B. Nandi and A. B. Aich, "A Note on Confidence Bounds for P(X >Y) in Bivariate Normal Samples", Sankhya: The Indian Journal of Statistics, vol. 56B(2), pp. 129-136, 1994.

[15] D.B. Owen, K.T. Craswell, and D.L. Hanson, "Nonparametric upper confidence bounds for Pr {Y