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Original Articles

Interval Estimation of the Stress-Strength Reliability with Independent Normal Random Variables

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Pages 1210-1221 | Received 19 Sep 2011, Accepted 17 Dec 2012, Published online: 17 Mar 2015

References

  • Azuma, J., Maegdefessel, L., Kitagawa, T., Dalman, R., McConnell, M.V. (2011). Assessment of elastase-induced murine abdominal aortic aneurysms: comparison of ultrasound imaging with in situ video microscopy. J. Biomed. Biotechnol doi: Article ID 252141, 10.1155/2011/252141.
  • Barndorff-Nielsen, O.E. (1986). Inference on full and partial parameters based on the standardized signed log-likelihood ratio. Biometrika 73: 307322.
  • Barndorff-Nielsen, O.E. (1991). Modified signed log-likelihood ratio. Biometrika 78: 557563.
  • Basu, A.P. (1981). The estimation of P(X < Y) for distributions useful in life testing. Naval Res. Logistics Quart. 28: 383392.
  • Church, J.D., Harris, B. (1970). The estimation of reliability from stress-strength relationships. Technometrics 12: 4954.
  • Downton, F. (1973). The estimation of Pr(Y < X) in the normal case. Technometrics 15: 551558.
  • Enis, P., Geisser, S. (1971). Estimation of the probability that X < Y. J. Amer. Statist. Assoc. 66: 162168.
  • Fraser, D., Reid, N. (1995). Ancillaries and third order significance. Utilitas Mathematica 47: 3353.
  • Fraser, D., Reid, N., Li, R., Wong, A. (2003). P-value formulas from likelihood asymptotics: bridging the singularities. J. Statist. Rese. 37: 115.
  • Guo, H., Krishnamoorthy, K. (2004). New approximate inferential methods for the reliability parameter in a stress-strength model: the normal case. Commun. Statist. Theor. Meth. 33: 17151731.
  • Hall, I.J. (1984). Approximate one-sided tolerance limits for the difference or sum of two independent normal variates. J. Qual. Technol. 16: 1519.
  • Harris, B., Soms, A.P. (1983). A note on a difficulty inherent in estimating reliability from stress- strength relationships. Naval Rese. Logistics Quart. 30: 659663.
  • Kotz, S., Lumelskii, Y., M. Pensky, (2003). The Stress-Strength Model and Its Generalizations: Theory and Applications. Singapore: World Scientific.
  • Mazumdar, M. (1970). Some estimates of reliability using inference theory. Naval Res. Logistics Quart. 17: 159165.
  • Neal, D.M., Matthews, W. T. Wangel, M. G., (1991). Model Sensitivity in Stress-Strength Reliability Computations. US Army Materials Technology Laboratory, Watertown MA, TR 91-3.
  • Reid, N. (1996). Likelihood and higher-order approximations to tail areas: a review and annotated bibliography. Can. J. Statist. 24: 141166.
  • Reiser, B., Guttman, I. (1986). Statistical inference for Pr(Y < X): the normal case. Technometrics 28: 253257.
  • Schwartz, L., Wearden, S. (1959). A distribution-free asymptotic method of estimating, testing and setting confidence limits for heritability. Biometrics 15: 227235.
  • Severeni, T. (2000). Likelihood Methods in Statistics. New York: Oxford University Press.
  • Simonoff, J.S., Hochberg, Y., Reiser, B. (1986). Alternative estimation procedures for Pr(X < Y) in categorized data. Biometrics 42: 895907.
  • Weerahandi, S., Johnson, R.A. (1992). Testing reliability in a stress-strength model when X and Y are normally distributed. Technometrics 34: 8391.

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