Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-28T17:23:55.219Z Has data issue: false hasContentIssue false

Failure distributions of shock models

Published online by Cambridge University Press:  14 July 2016

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

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1980 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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