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On the reduction in remaining system lifetime due to the failure of a specific component

Published online by Cambridge University Press:  14 July 2016

Bent Natvig
Bent Natvig*
Affiliation:
University of California, Berkeley
*
∗Permanent address: Matematisk Institutt, Universitetet i Oslo, Blindern, Oslo 3, Norway.
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Abstract

In a previous paper, Natvig [4], we suggested a new measure of the importance of a component in a coherent system and derived some of its properties. The measure is for the case of components not undergoing repair proportional to the expected reduction in remaining system lifetime due to the failure of the component. In the present paper, we arrive at the whole distribution of this reduction in remaining system lifetime. Furthermore, for the case where components have proportional hazards, and are not repaired, a speculation of another measure is given. This measure is proportional to the derivative of the expected total lifetime of a new system with respect to the inverse of the component's proportional hazard rate.

Keywords

COHERENT STRUCTURECOMPONENT IMPORTANCELIFETIME REDUCTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 642 - 652
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

This research was supported by the Royal Norwegian Council for Scientific and Industrial Research and the Johan and Mimi Wesmann Foundation.

References

[1] Barlow, R. E. and Proschan, F. (1975) Importance of system components and fault tree events. Stoch. Proc. Appl. 3, 153–173.CrossRefGoogle Scholar
[2] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
[3] Fussel, J. B. (1975) How to hand-calculate system reliability and safety characteristics. IEEE Trans. Reliability 24, 169–174.Google Scholar
[4] Natvig, B. (1979) A suggestion of a new measure of importance of system components. Stoch. Proc. Appl. 9, 319–330.Google Scholar
[5] Vesely, W. E. Reactor safety research. United States Energy Commission, Washington D.C. Private communication to H. E. Lambert.Google Scholar