Skip to main content
Log in

Reliability properties of systems with exchangeable components and exponential conditional distributions

  • Published:
Test Aims and scope Submit manuscript

Abstract

We study basic properties for bivariate systems with exchangeable components and exponential conditional distributions which represent bi-component biological or engineering systems with structural dependency. This is equivalent to suppose that we have similar components with the bivariate exponential conditional joint distribution defined by Arnold and Strauss (1988). Specifically, we study the reliability functions, the moments, some aging measures, ordering and classification properties for series and parallel systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Arnold, B. C., Castillo, E., andSarabia, J. M. (1999).Conditional Specification of Statistical Models. Springer-Verlag, New York.

    MATH  Google Scholar 

  • Arnold, B. C. andStrauss, D. J. (1988). Bivariate distributions with exponential conditionals.Journal of the American Statistical Association, 83:522–527.

    Article  MATH  MathSciNet  Google Scholar 

  • Baggs, G. E. andNagaraja, H. N. (1996). Reliability properties of order statistics from bivariate exponential distributions.Communications in Statistics-Stochastic Models, 12(4):611–631.

    MATH  MathSciNet  Google Scholar 

  • Balakrishnan, N. andAkhundov, I. S. (2003). A characterization by linearity of the regression function based on order statistics.Statistics & Probability Letters, 63:435–440.

    Article  MATH  MathSciNet  Google Scholar 

  • Barlow, R. E. andProschan, F. (1975).Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.

    MATH  Google Scholar 

  • Belzunce, F., Franco, M., Ruiz, J. M., andRuiz, M. C. (2001). On partial orderings between coherent systems with different structures.Probability in the Engineering and Informational Sciences, 15:273–293.

    Article  MATH  MathSciNet  Google Scholar 

  • Block, H. W. andJoe, H. (1997). Tail behavior of the failure rate functions of mixtures.Lifetime and Data Analysis, 3:269–288.

    Article  MATH  Google Scholar 

  • Cox, D. R. andOakes, D. (1984).Analysis of Survival Data, Chapman & Hall/CRC, London.

    Google Scholar 

  • Glaser, R. E. (1980). Bathtub and related failure rate characteirzations.Journal of the American Statistical Association, 75:667–672.

    Article  MATH  MathSciNet  Google Scholar 

  • Gupta, P. L. andGupta, R. C. (2001). Failure rate of the minimum and maximum of a multivariate normal distribution.Metrika, 53:39–49.

    Article  MATH  MathSciNet  Google Scholar 

  • Gupta, R. C. (2001). Reliability studies of bivariate distributions with pareto conditionals.Journal of Multivariate Analysis, 76:214–225.

    Article  MATH  MathSciNet  Google Scholar 

  • Kanjo, A. I. andAbouammoh, A. M. (1995). Closure of mean remaining life classes under formation of parallel systems.Pakistan Journal of Statistics, 11:153–158.

    MATH  MathSciNet  Google Scholar 

  • Roy, D. (2001). Some properties of a classification system for multivariate life distributions.IEEE Transactions on Reliability, 50:214–220.

    Article  Google Scholar 

  • Rychlik, T. (2001a). Mean-variance bounds for order statistics from dependent dfr, ifr, dfra and ifra samples.Journal of Statistical Planning and Inference, 92:21–38.

    Article  MATH  MathSciNet  Google Scholar 

  • Rychlik, T. (2001b). Stability of order statistics under dependence.Annals of the Institute of Statistical Mathematics, 53:877–894.

    Article  MATH  MathSciNet  Google Scholar 

  • Shaked, M. andShanthikumar, J. G. (1994).Stochastic Orders and Their Applications, Academic Press, San Diego.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to José M. Ruiz.

Additional information

Supported by Ministerio de Ciencia y Tecnología under grant BFM2003-02947

Rights and permissions

Reprints and permissions

About this article

Cite this article

Navarro, J., Ruiz, J.M. & Sandoval, C.J. Reliability properties of systems with exchangeable components and exponential conditional distributions. Test 15, 471–484 (2006). https://doi.org/10.1007/BF02607062

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02607062

Key Words

AMS subject classification

Navigation