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Component Importance for Continuum Structure Functions with Underlying Binary Structures

  • Published : 2007.12.31

Abstract

A continuum structure function (CSF) is a non-decreasing mapping from the unit hypercube to the unit interval. A B-type CSF, defined in the text, is a CSF whose behaviour is modeled by its underlying binary structures. As the measure of importance of a system component for a B-type CSF, the structural and reliability importance of a component at a system level ${\alpha}$(0 < ${\alpha}$ < 1) are defined and their properties are deduced.

Keywords

References

  1. Barlow, R. E. and Wu, A. S. (1978). Coherent systems with multi-state components. Mathematics of Operations Research, 3, 275-281 https://doi.org/10.1287/moor.3.4.275
  2. Baxter, L. A. (1984). Continuum structures I. Journal of Applied Probability, 21, 802-815 https://doi.org/10.2307/3213697
  3. Baxter, L. A. (1986). Continuum structures II. Mathematical Proceedings of the Cambridge Philosophical Society, 99, 331-338
  4. Baxter, L. A. and Lee, S. M. (1989a). Structure functions with finite minimal vector sets. Journal of Applied Probability, 26, 196-201 https://doi.org/10.2307/3214331
  5. Baxter, L. A. and Lee, S. M. (1989b). Further properties of reliability importance for continuum structure functions. Probability in the Engineering and Informational Sciences, 3, 237-246 https://doi.org/10.1017/S026996480000111X
  6. Birnbaum, Z. W. (1969). On the Importance of Different Components in a Multicomponent System in Multivariate Analysis-II (P. R. Krishnaiah, ed.). 581-592, Academic Press, New York
  7. Birnbaum, Z. W., Esary, J. D. and Saunders, S. C. (1961). Multicomponent systems and structures, and their reliability. Technometrics, 3, 55-77 https://doi.org/10.2307/1266477
  8. Block, H. W. and Savits T. H. (1982). A decomposition for multistate monotone systems. Journal of Applied Probability, 19, 391-402 https://doi.org/10.2307/3213490
  9. Borges, W. de S. and Rodrigues, F. W. (1983). Axiomatic characterization of continuum structure functions. Mathematics of Operations Research, 8, 435-438 https://doi.org/10.1287/moor.8.3.435
  10. Griffith, W. S. (1980). Multistate reliability models. Journal of Applied Probability, 17, 735-744 https://doi.org/10.2307/3212967
  11. Griffith, W. S. (1997). A note on the characterization of the Barlow and Wu continuum structure functions. Operations Research Letters, 21, 65-67 https://doi.org/10.1016/S0167-6377(97)00021-7
  12. Kim, C. and Baxter, L. A. (1987). Axiomatic characterizations of continuum structure functions. Operations Research Letters, 6, 297-300 https://doi.org/10.1016/0167-6377(87)90047-2
  13. Lee, S. M. (2003). On the characterization of continuum structure functions. Operations Research Letters, 31, 268-272 https://doi.org/10.1016/S0167-6377(02)00240-7
  14. Natvig, B. (1982). Two suggestions of how to define a multistate coherent system. Advances in Applied Probability, 14, 434-455 https://doi.org/10.2307/1426529