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A stress–strength system

Published online by Cambridge University Press:  14 July 2016

Nader Ebrahimi
Nader Ebrahimi*
Affiliation:
Northern Illinois University
*
∗Postal address: Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115–2888, USA.
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Abstract

Suppose Y is the strength of a system subjected to a sequence of stresses X1, X2, X3, · ··. Let N(t) be the number of stresses occurring by time t and let T be the lifetime of the system. Then the survival distribution of is given by where and . In this note we aim at determining from the above model various non-parametric classes of life distributions which are of interest in reliability theory.

Keywords

SHOCK MODELSSTRESS AND STRENGTH MODELSPOISSON PROCESSESNON-HOMOGENEOUS POISSON PROCESSESASSOCIATED RANDOM VARIABLESDFRDFRANWUIMRLNWUETOTAL POSITIVITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 467 - 472
Copyright
Copyright © Applied Probability Trust 1985 

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References

A-Hameed, M. S. and Proschan, F. (1973) Non stationary shock models. Stoch. Proc. Appl. 1, 383–404.CrossRefGoogle Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Bryson, M. C. and Siddiqui, M. M. (1969) Some criteria for aging. J. Amer. Statist. Assoc. 64, 1472–1483.CrossRefGoogle Scholar
Esary, J. D., Proschan, F. and Walkup, D. W. (1967) Association of random variables, with application. Ann. Math. Statist. 39, 433–441.Google Scholar
Esary, J. D., Marshall, A. W. and Proschan, F. (1973) Shock models and wear processes. Ann. Prob. 1, 627–649.CrossRefGoogle Scholar
Ghosh, M. and Ebrahimi, N. (1982) Shock models leading to IFR and DMRL. J. Appl. Prob. 19, 158–166.CrossRefGoogle Scholar
Haines, A. (1973) Some Contributions to the Theory of Restricted Classes of Distributions with Applications to Reliability. Ph.D. Dissertation. The George Washington University.Google Scholar
Proschan, F. and Hollander, M. (1982) Nonparametric concepts and methods in reliability. Technical report No. 77, Stanford University.Google Scholar