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A decomposition for multistate monotone systems

Published online by Cambridge University Press:  14 July 2016

Henry W. Block  and
Thomas H. Savits
Henry W. Block*
Affiliation:
University of Pittsburgh
Thomas H. Savits*
Affiliation:
University of Pittsburgh
*
∗ Research supported by ONR Contract N00014-76-C-0839.
∗∗ Research supported by ONR Contract N00014-76-C-0839 and NSF Grant MCS77-01458.
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Abstract

A decomposition theorem for multistate structure functions is proven. This result is applied to obtain bounds for the system performance function. Another application is made to interpret the multistate structures of Barlow and Wu. Various concepts of multistate importance and coherence are also discussed.

Keywords

MULTISTATE STRUCTURE FUNCTIONBOUNDSSYSTEM PERFORMANCE FUNCTIONCOHERENCERELEVANCEIMPORTANCEASSOCIATED COMPONENTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 391 - 402
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Postal address for both authors: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh PA 15260, U.S.A.

References

Ahmad, A. N., Langberg, N. A., Leon, R. and Proschan, F. (1978) Two concepts of positive dependence with applications in multivariate analysis. Technical Report M486, Department of Statistics, Florida State University.CrossRefGoogle Scholar
Barlow, R. E. and Wu, A. S. (1978) Coherent systems with multistate components. Math. Operat. Res. 3, 275–281.Google Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Block, H. W. and Savits, T. H. (1980) Multivariate IFRA distributions. Ann. Prob. 8, 793–801.Google Scholar
Borges, W. S. and Rodrigues, F. W. (1980) On the axiomatic theory of multistate coherent structures. Unpublished report.Google Scholar
Butler, D. A. (1979) Bounding the reliability of multistate systems. Stanford University, Department of OR, Tech. Report No. 193.Google Scholar
Esary, J. D. and Marshall, A. W. (1979) Multivariate distributions with increasing hazard rate averages. Ann. Prob. 7, 359–370.Google Scholar
El-Neweihi, E., Proschan, F. and Sethuraman, J. (1978) Multistate coherent systems. J. Appl. Prob. 15, 675–688.CrossRefGoogle Scholar
Griffith, W. S. (1980) Multistate reliability models. J. Appl. Prob. 17, 735–744.Google Scholar
Ross, S. (1979) Multi-valued state component reliability systems. Ann. Prob. 7, 379–383.CrossRefGoogle Scholar