Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Influences of Dependence Degrees of a Component for the Mean Time to Failure of a System

  • Kim, Dae-Kyung (Department of Statistics, Chonbuk National University) ;
  • Oh, Ji-Eun (Department of Statistics, Chonbuk National University)
  • Received : 2011.11.15
  • Accepted : 2012.01.10
  • Published : 2012.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

This article considers the mean time to failure(MTTF) of a dependent parallel system. We study how the degree of dependency components influences the increase in the mean lifetime for this system. The results are illustrated by tables and figures.

Keywords

References

  1. Balakrishnan, N. and Lai, C. D. (2009). Continuous Bivariate Distributions, Springer.
  2. Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika, 65, 141-151. https://doi.org/10.1093/biomet/65.1.141
  3. Esary, F. D. and Proschan, F. (1970). A reliability bound for systems of maintained interdependent components, Journal of the American Statistical Association, 65, 329-338. https://doi.org/10.1080/01621459.1970.10481083
  4. Freund, J. E. (1961). A bivariate extension of the exponential distribution, Journal of the American Statistical Association, 56, 971-977. https://doi.org/10.1080/01621459.1961.10482138
  5. Gumbel, E. J. (1960). Bivariate exponential distributions, Journal of the American Statistical Association, 56, 698-707.
  6. Hanagal, D. D. (1996). A multivariate Weibull distribution, Econ Qual Control, 11, 193-200.
  7. Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distribution - 1, Houghton Mifflin Company, Boston.
  8. Lehmann, E, L. (1966). Some concepts of dependence, Annals of Mathematical Statistics, 37, 1137-1153. https://doi.org/10.1214/aoms/1177699260
  9. Lu, J. C. (1989). Weibull extension of the Freund and Marshall-Olkin bivariate exponential models, IEEE Transaction on Reliability, 38, 615-619. https://doi.org/10.1109/24.46492
  10. Lu, J. C. and Bhattachrayya, G. K. (1990). Some new constructions of bivariate Weibull models, Annals of Institute of Statistical Mathematics, 42, 543-559. https://doi.org/10.1007/BF00049307
  11. Marshall, A. W. and Olkin, I. A. (1967). A multivariate exponential distribution, Journal of the American Statistical Association, 62, 30-44. https://doi.org/10.1080/01621459.1967.10482885
  12. Mino, T., Yoshikawa, N., Suzuki, K., Horikawa, Y. and Abe, Y. (2003). The mean of lifespan under dependent competing risks with application to mice data, Journal of Health and Sports Science, Juntendo University, 7, 68-74.
  13. Moeschberger, M. L. (1974). Life tests under dependent competing causes of failure, Technometrics, 16, 39-47. https://doi.org/10.1080/00401706.1974.10489147
  14. Murthy, D. N. P. and Nguyen, D. G. (1985). Study of two component system with Failure interaction, Naval Research Logistics Quarterly, 32, 239-247. https://doi.org/10.1002/nav.3800320205
  15. Rachev, S. T., Wu, C. and Yakovlev, A. Y. (1995). A bivariate limiting distribution of tumor latency time, Mathematical Biosciences, 127, 127-147. https://doi.org/10.1016/0025-5564(94)00043-Y