Statistical Papers

, 40:99 | Cite as

Estimation of system reliability

  • David D. Hanagal


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.

Key words and Phrases

Absolutely continuous multivariate exponential model Maximum likelihood estimate S-out-of-K system Stress-Strength model System reliability 


  1. Bhattacharyya, G.K. (1977). Reliability estimation from survivor count data in a stress-strength setting.IAPQR Transactions, 2, 1–15.Google Scholar
  2. 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.MATHCrossRefMathSciNetGoogle Scholar
  3. 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.Google Scholar
  4. 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.Google Scholar
  5. Block, H.W. (1975). Continuous multivariate exponential extensions.Reliability and Fault-tree Analysis, SIAM, 285–306.Google Scholar
  6. Block, H.W. and Basu, A.P. (1974). A continuous bivariate exponential extension.Journal of the American Statistical Association, 69, 1031–37.MATHCrossRefMathSciNetGoogle Scholar
  7. 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.CrossRefMathSciNetGoogle Scholar
  8. Ebrahimi, N. (1982). Estimation of reliability for a series stress-strength system.IEEE Transactions on Reliability, R-31, 202–205.MATHCrossRefGoogle Scholar
  9. Hanagal, D.D. (1993). Some inference results in several symmetric multivariate exponential models.Communications in Statistics, Theory and Methods, 22(9), 2549–66.MATHMathSciNetGoogle Scholar
  10. Johnson, R.A. (1988). Stress-strength models for reliability.Handbook of Statistics, Vol. 7, Quality Control and Reliability, 27–54.Google Scholar
  11. Marshall, A.W. and Olkin, I. (1967). A multivariate exponential distribution.Journal of the American Statistical Association, 62, 30–44.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • David D. Hanagal
    • 1
  1. 1.Departamento de EstadisticaColegio de Postgraduados-MontecilloTexocoMexico

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