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Reliability importance for continuum structure functions

Published online by Cambridge University Press:  14 July 2016

Chul Kim  and
Laurence A. Baxter
Chul Kim*
Affiliation:
State University of New York at Stony Brook
Laurence A. Baxter*
Affiliation:
State University of New York at Stony Brook
*
∗Present address: Agency for Defense Development, P.O. Box 35, Daejeon, Korea.
∗∗Postal address: Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794, USA.
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Abstract

A continuum structure function is a non-decreasing mapping from the unit hypercube to the unit interval. A definition of the reliability importance, ℛi(α) say, of component i at system level α(0 < α ≦ 1) is proposed. Some properties of this function are deduced, in particular conditions under which and conditions under which ℛi(α) is positive (0 < α < 1).

Keywords

KEY VECTOR

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 779 - 785
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research supported by the Air Force Office of Scientific Research, AFSC, USAF, under grant AFOSR-84–0243. The US Government is authorised to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.

References

Barlow, R. E. and Proschan, F. (1975a) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Barlow, R. E. and Proschan, F. (1975b) Importance of system components and fault tree events. Stoch. Proc. Appl. 3, 153–173.Google Scholar
Barlow, R. E. and Wu, A. S. (1978) Coherent systems with multi-state components. Math. Operat. Res. 3, 275–281.Google Scholar
Baxter, L. A. (1984) Continuum structures I. J. Appl. Prob. 21, 802–815.Google Scholar
Baxter, L. A. (1986) Continuum structures II. Math. Proc. Camb. Phil. Soc. 99, 331–338.Google Scholar
Baxter, L. A. and Kim, C. (1987) Bounding the stochastic performance of continuum structure functions II. J. Appl. Prob. 24, 609–618.Google Scholar
Billingsley, P. (1979) Probability and Measure. Wiley, New York.Google Scholar
Birnbaum, Z. W. (1969) On the importance of different components in a multicomponent system. In Multivariate Analysis II, ed. Krishnaiah, P. R., Academic Press, New York, 581–592.Google Scholar
Block, H. W. and Savits, T. H. (1982) A decomposition for multistate monotone systems. J. Appl. Prob. 19, 391–402.CrossRefGoogle Scholar
Block, H. W. and Savits, T. H. (1984) Continuous multistate structure functions. Operat. Res. 32, 703–714.Google Scholar
Griffith, W. S. (1980) Multistate reliability models. J. Appl. Prob. 17, 735–744.Google Scholar
Natvig, B. (1979) A suggestion of a new measure of importance of system components. Stoch. Proc. Appl. 9, 319–330.Google Scholar
Natvig, B. (1982) Two suggestions of how to define a multistate coherent system. Adv. Appl. Prob. 14, 434–455.Google Scholar
Natvig, B. (1985a) New light on measures of importance of system components. Scand. J. Statist. 12, 43–54.Google Scholar
Natvig, B. (1985b) Recent developments in multistate reliability theory. In Probabilistic Methods in the Mechanics of Solids and Structures, ed. Eggwertz, S. and Lind, N. C., Springer-Verlag, Berlin, 385–393.Google Scholar