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Failure distributions of shock models

  • Gary Gottlieb (a1)

Abstract

A single device shock model is studied. The device is subject to some damage process. Under the assumption that as the cumulative damage increases, the probability that any additional damage will cause failure increases, we find sufficient conditions on the shocking process so that the life distribution will be increasing failure rate.

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Postal address: Graduate School of Business Administration, New York University, 100 Trinity Place, New York, NY 10006, U.S.A.

References

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[1] A-Hameed, M. S. and Proschan, F. (1973) Non-stationary shock models. Stoch. Proc. Appl. 1, 383404.
[2] Athreya, K. and Ney, P. (1972) Branching Processes. Springer-Verlag, Berlin.
[3] Barlow, R. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.
[5] Esary, D., Marshall, A. W. and Proschan, F. (1973) Shock models and wear processes. Ann. Prob. 1, 627649.
[5] Gottlieb, G. (1976) Failure distribution of shock models. Technical Report No. 181, Department of Operations Research, Stanford University.
[6] Karlin, S. (1964) Total positivity, absorption probabilities, applications. Trans. Amer. Math. Soc. 111, 33107.
[7] Karlin, S. (1968) Total Positivity , Vol. 1. Stanford University Press.
[8] Morey, R. C. (1965) Stochastic wear processes. Technical Report ORC 65–16, Operations Research Center, University of California, Berkeley.
[9] Morey, R. C. (1966) Some stochastic properties of a compound-renewal damage model. Operat. Res. 14, 902908.

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Failure distributions of shock models

  • Gary Gottlieb (a1)

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