Journal of Applied Reliability (한국신뢰성학회지:신뢰성응용연구)

The Korean Reliability Society (한국신뢰성학회)
권호 표지

Stress-Strength model with Dependency

종속 관계의 스트레스-강도 모형

  • Kim, Dae-Kyung (Dept. of Statistics, Chonbuk National University) ;
  • Kim, Jin-Woo (Dept. of Finance & Information Statistics, Hallym University) ;
  • Park, Dong-Ho (Dept. of Finance & Information Statistics, Hallym University)
  • 김대경 (전북대학교 통계학과) ;
  • 김진우 (한림대학교 금융정보통계학과) ;
  • 박동호 (한림대학교 금융정보통계학과)
  • Received : 2011.08.14
  • Accepted : 2011.12.02
  • Published : 2011.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

We consider the stress-strength model in which a unit of strength $T_2$ is subjected to environmental stress $T_1$. An important measure considered in stress-strength model is the reliability parameter R=P($T_2$ > $T_1$). The greater the value of R is, the more reliable is the unit to perform its specified task. In this article, we consider the situations in which $T_1$ and $T_2$ are both independent and dependent, and have certain bivariate distributions as their joint distributions. To study the effect of dependency on R, we investigate several bivariate distributions of $T_1$ and $T_2$ and compare the values of R for these distributions. Numerical comparisons are presented depending on the parameter values as well.

Keywords

References

  1. Barlow, R. E. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing, Probability Models, To Begin With, Silver Spring, MD.
  2. Church, J. D. and Harris, B. (1970). The Estimation of Reliability from Stress-Strength Relationships, Technometrics, Vol. 12, pp.49-54. https://doi.org/10.1080/00401706.1970.10488633
  3. Downton, F. (1973). The Estimation of the Pr [Y < X] in the Normal Case, Technometrics, Vol. 15, pp. 551-558.
  4. Fan, J., Prentice, R .L. and Hsu, L. (2000). A Class of Weighted Dependence Measures for Bivariate Failure Time Data, Journal of the Royal Statistical Society, Series B, Vol. 62, pp.181-190. https://doi.org/10.1111/1467-9868.00227
  5. Hougaard, P. (1986). A Class of Multivariate Failure Time Distributions, Biometrika, Vol. 73, No. 3, pp.671-678.
  6. Hougaard, P., Harvald, B. and Holm, N. V. (1992). Measuring the Similarities Between the Lifetimes of Adult Danish Twins Born Between 1881-1930, Journal of the American Statistical Association, Vol. 87, pp. 17-24.
  7. Jeong, H. S. and Kim, J. J.(1995). Nonparametric Estimation of Pr     from Random Censored Data, Journal of the Korean Society for Quality Management, Vol. 23, No. 2, pp. 91-102.
  8. Johnson, R. A. (1988). Stress-Strength Models for Reliability, Handbook of Statistics(Vol. 7), eds. P. R. Krishnaiah and C. R. Rao, Amsterdam; North-Holland.
  9. Kaplan, E. L. and Meier, P. (1958). Nonparametric Estimation from Incomplete Observations, Journal of the American Statistical Association, Vol. 53, pp. 457-481. https://doi.org/10.1080/01621459.1958.10501452
  10. Reiser, B. and Guttman, I. (1986). Statistical Inference for Pr [Y < X], Technometrics, Vol. 28, pp. 253-257.
  11. Weerahandi, S. and Johnson, R. A. (1992). Testing Reliability in a Stress-Strength Model When X and Y are Normally Distributed, Technometrics, Vol. 34, pp. 83-91. https://doi.org/10.2307/1269555
  12. Yum, J. K. and Kim, J. J.(1984). Estimation of Pr [Y < X] in the Censored Case, Journal of the Korean Society for Quality Management, Vol. 12, pp. 9-15.
  13. Yum, J. K. and Kim, J. J.(1985). A Study on the Bayes Estimator of $\theta$ = Pr [Y > X], Journal of the Korean Society for Quality Management, Vol. 13, pp. 8-12.