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Another look at the moment bounds on reliability

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Debasis Sengupta
Debasis Sengupta*
Affiliation:
Indian Statistical Institute, Calcutta
*
∗ Postal address: Applied Statistics, Surveys and Computing Division, Indian Statistical Institute, 203 Barrackpore Trunk Road, Calcutta 700 035, India.
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Abstract

In this paper a unified derivation of the upper and lower bounds (in terms of the mean) of an IFR, DFR, IFRA, DFRA, NBU or NWU reliability function is presented. The method of proof provides a simpler alternative to the various proofs known in the literature. Moreover, this method can be used to generalize the existing results in two ways, as demonstrated here. First, the bounds for the reliability function are obtained in terms of any finite moment in all these cases. Subsequently we provide a moment bound on a reliability function which ages faster or slower than a known one in some sense. The existing literature does not offer any of these generalizations, except for a few results which are available in an unnecessarily complicated form.

Keywords

CONVEXITYSTAR-SHAPEDNESSSUPERADDITIVITYRELIABILITY BOUNDSHAZARD FUNCTIONIFRDFRIFRADFRANBUNWU

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 777 - 787
Copyright
Copyright © Applied Probability Trust 1994 

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References

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