Skip to main content
SpringerLink
Log in

Estimation of reliability of a component subjected to bivariate exponential stress

  • Notes
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

In this paper, we estimate the reliability of a component subjected to two different stresses which are independent of the strength of a component. We assume that the distribution of stresses follow a bivariate exponential (BVE) distribution. If X is the strength of a component subjected to two stresses (Y 1,Y 2), then the reliability of a component is given by R=P[Y 1+Y 2<X]. We estimate R when (Y 1,Y 2) follow different BVE models proposed by Marshall-Olkin (1967), Block-Basu-(1974), Freund (1961) and Proschan-Sullo (1974). The distribution of X is assumed to be exponential. The asymptotic normal (AN) distributions of these estimates of R are obtained.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Block, H.W. and Basu, A.P. (1974). A continuous bivariate exponential extension.Journal of the American Statistical Association, 69, 1031–37.

    Article  MATH  MathSciNet  Google Scholar 

  • Chandra, S. and Owen, D.B. (1975). On estimating the reliability of a component subjected to several different stresses (strengths)Naval Research Logistics Quarterly, 22, 31–39.

    Article  MathSciNet  Google Scholar 

  • Freund, J.E. (1961). A bivariate extension of the exponential distribution.Journal of the American Statistical Association, 56, 971–77.

    Article  MATH  MathSciNet  Google Scholar 

  • Hanagal, D.D. (1992). Some inference results in modified Freund's bivariate exponential distribution.Biometrical Journal, 34(6), 745–56.

    Article  MATH  Google Scholar 

  • Hanagal, D.D. and Kale, B.K. (1991a). Large sample tests of independence for absolutely continuous bivariate exponential distribution.Communications in Statistics, Theory and Methods, 20(4), 1301–13.

    Article  MathSciNet  Google Scholar 

  • Hanagal, D.D. and Kale, B.K. (1991b). Large sample tests of λ3 in the bivariate exponential distribution.Statistics and Probability Letters, 12(4), 311–13.

    Article  MathSciNet  Google Scholar 

  • Hanagal, D.D. and Kale, B.K. (1992). Large sample tests for testing symmetry and independence in some bivariate exponential models.Communications in Statistics, Theory and Mehods, 21(9), 2625–43.

    Article  MATH  MathSciNet  Google Scholar 

  • Marshall, A.W. and Olkin, I. (1967). A multivariate exponential distribution.Journal of the American Statistical Association, 62, 30–44.

    Article  MATH  MathSciNet  Google Scholar 

  • Proschan, F. and Sullo, P. (1974). Estimating the parameters of bivariate exponential distributions in several sampling situations.Reliability and Biometry, SIAM, 423–40.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Pune, 411007, Pune, India

    David D. Hanagal

Authors
  1. David D. Hanagal
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hanagal, D.D. Estimation of reliability of a component subjected to bivariate exponential stress. Statistical Papers 40, 211–220 (1999). https://doi.org/10.1007/BF02925519

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02925519

Keywords

Search

Navigation