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Multicomponent lifetime distributions in the presence of ageing

Part of: Special processes Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Juanjuan Fan ,
S. G. Ghurye  and
Richard A. Levine
Juanjuan Fan*
Affiliation:
University of California
S. G. Ghurye*
Affiliation:
University of Alberta
Richard A. Levine*
Affiliation:
University of California
*
∗Postal address: Division of Statistics, University of California, Davis, CA 95616, USA
∗∗Postal address: University of Alberta, Edmonton, Canada
∗Postal address: Division of Statistics, University of California, Davis, CA 95616, USA
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Abstract

Lifetime distributions for multicomponent systems are developed through the interplay of ageing and stress shocks to the system. The ageing process is explicitly modeled by an exponential function with rate affected by the magnitude of stresses from a compound Poisson process shock model. Applications of these life distributions and associated failure rates towards the study of multicomponent system survival are discussed. In particular, we illustrate the behavior of these survival functions in relevant subsets of the parameter space.

Keywords

Poisson shock processageing processsurvival functionfailure rate

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 521 - 533
Copyright
Copyright © by the Applied Probability Trust 2000 

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References

Balakrishnan, N., and Basu, A. P. (1995). The Exponential Distribution: Theory, Methods, and Applications. Gordon and Breach, Australia.Google Scholar
Duffy, D. L., Martin, N. G., and Mathews, J. D. (1990). Appendectomy in Australian twins. Amer. J. Human Genet. 47, 590–592.Google ScholarPubMed
Esary, J. D., Marshall, A. W., and Proschan, F. (1973). Shock models and wear processes. Ann. Prob. 1, 627–649.CrossRefGoogle Scholar
Fagiuoli, E., and Pellerey, F. (1994). Preservation of certain classes of life distributions under Poisson shock models. J. Appl. Prob. 31, 458–465.CrossRefGoogle Scholar
Ghurye, S. G. (1987). Some multivariate lifetime distributions. Adv. Appl. Prob. 19, 138–155.Google Scholar
Ghurye, S. G., and Marshall, A. W. (1984). Shock processes with aftereffects and multivariate lack of memory. J. Appl. Prob. 21, 786–801.Google Scholar
Horiuchi, S., and Wilmoth, J. R. (1997). Age patterns of the life table ageing rate for major causes of death in Japan, 1951–1990. J. Gerontol. Ser. A, Biol. Sci. Med. Sci. 52, 67–77.Google Scholar
Marshall, A. W., and Olkin, I. (1967). A multivariate exponential distribution. J. Amer. Statist. Assoc. 62, 30–44.CrossRefGoogle Scholar
Sheu, S. H., and Griffith, W. S. (1996). Optimal number of minimal repairs before replacement of a system subject to shocks. Naval Res. Logist. 43, 319–333.3.0.CO;2-C>CrossRefGoogle Scholar