Skip to main content
SpringerLink
Log in

Estimation of system reliability

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

Abstract

In this paper, we estimate the reliability of a system with k components. The system functions when at least s (1≤s≤k) components survive a common random stress. We assume that the strengths of these k components are subjected to a common stress which is independent of the strengths of these k components. If (X 1,X 2,…,X k ) are strengths of k components subjected to a common stress (Y), then the reliability of the system or system reliability is given byR=P[Y<X (k−s+1)] whereX (k−s+1) is (k−s+1)-th order statistic of (X 1,…,X k ). We estimate R when (X 1,…,X k ) follow an absolutely continuous multivariate exponential (ACMVE) distribution of Hanagal (1993) which is the submodel of Block (1975) and Y follows an independent exponential distribution. We also obtain the asymptotic normal (AN) distribution of the proposed estimator.

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

Bibliography

  • Bhattacharyya, G.K. (1977). Reliability estimation from survivor count data in a stress-strength setting.IAPQR Transactions, 2, 1–15.

    Google Scholar 

  • Bhattacharyya, G.K. and Johnson, R.A. (1974). Estimation of reliability in a multicomponent stress-strength model.Journal of the American Statistical Association, 69, 966–70.

    Article  MATH  MathSciNet  Google Scholar 

  • Bhattacharyya, G.K. and Johnson, R.A. (1975). Stress-strength models for system reliability.Proceedings of the Symposium on Reliability and Fault-tree Analysis, SIAM, 509–32.

  • Bhattacharyya, G.K. and Johnson, R.A. (1977). Estimation of system reliability by nonparametric techniques.Bulletin of Mathematical Society of Greece. (Memorial Volume), 94–105.

  • Block, H.W. (1975). Continuous multivariate exponential extensions.Reliability and Fault-tree Analysis, SIAM, 285–306.

  • 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 

  • Ebrahimi, N. (1982). Estimation of reliability for a series stress-strength system.IEEE Transactions on Reliability, R-31, 202–205.

    Article  MATH  Google Scholar 

  • Hanagal, D.D. (1993). Some inference results in several symmetric multivariate exponential models.Communications in Statistics, Theory and Methods, 22(9), 2549–66.

    MATH  MathSciNet  Google Scholar 

  • Johnson, R.A. (1988). Stress-strength models for reliability.Handbook of Statistics, Vol. 7, Quality Control and Reliability, 27–54.

  • 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 

Download references

Author information

Authors and Affiliations

  1. Departamento de Estadistica, Colegio de Postgraduados-Montecillo, CP 56230, Texoco, Mexico

    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 system reliability. Statistical Papers 40, 99–106 (1999). https://doi.org/10.1007/BF02927113

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02927113

Key words and Phrases

Search

Navigation