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Further Properties of Reliability Importance for Continuum Structure Functions

Published online by Cambridge University Press:  27 July 2009

Laurence A. Baxter  and
Seung Min Lee
Laurence A. Baxter
Affiliation:
Department of Applied Mathematics and Statistics State University of New York at Stony Brook Stony Brook, New York 11794
Seung Min Lee
Affiliation:
Department of Applied Mathematics and Statistics State University of New York at Stony Brook Stony Brook, New York 11794
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Abstract

A continuum structure function (CSF) is a nondecreasing mapping from the unit hypercube to the unit interval. The Kim-Baxter definition of the reliability importance of component i in a CSF at system level α, Ri(α), say, is reviewed. Conditions under which Ri(α) is positive, under which Ri(α) is a continuous function of α, and under which Ri(α) ≥ Rj(α) uniformly in α are presented. A simple algorithm for evaluating Ri(α) is described.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 2 , April 1989 , pp. 237 - 246
Copyright
Copyright © Cambridge University Press 1989

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References

REFERENCES

Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinehart and Winston.Google Scholar
Baxter, L.A. (1984). Continuum structures, I. Journal of Applied Probability 21: 802–815.CrossRefGoogle Scholar
Baxter, L.A. (1986). Continuum structures, II. Mathematical Proceedings of the Cambridge Philosophical Society 99: 331–338.CrossRefGoogle Scholar
Baxter, L.A. & Kim, C. (1986). Bounding the stochastic performance of continuum structure functions, I. Journal of Applied Probability 23: 660–669.CrossRefGoogle Scholar
Baxter, L.A. & Kim, C. (1987). Bounding the stochastic performance of continuum structure functions, II. Journal of Applied Probability 24: 609–618.CrossRefGoogle Scholar
Baxter, L.A. & Lee, S.M. (1989). Structure functions with finite minimal vector sets. Journal of Applied Probability 26 (to appear).CrossRefGoogle Scholar
Block, H.W. & Savits, T.H. (1984). Continuous multistate structure functions. Operations Research 23: 703–714.CrossRefGoogle Scholar
Kim, C. & Baxter, L.A. (1987). Reliability importance for continuum structure functions. Journal of Applied Probability 24: 779–785.CrossRefGoogle Scholar
Kim, C. & Baxter, L.A. (1987). Axiomatic characterizations of continuum structure functions. Operations Research Letters 6: 297–300.CrossRefGoogle Scholar
Natvig, B. (1979). A suggestion of a new measure of importance of system components. Stochastic Processes and their Applications 9: 319–330.CrossRefGoogle Scholar