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Importance of Components for a System

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  • Nader Ebrahimi
  • Nima Y. Jalali
  • Ehsan S. Soofi
  • Refik Soyer

Abstract

Which component is most important for a system's survival? We answer this question by ranking the information relationship between a system and its components. The mutual information (M) measures dependence between the operational states of the system and a component for a mission time as well as between their life lengths. This measure ranks each component in terms of its expected utility for predicting the system's survival. We explore some relationships between the ordering of importance of components by M and by Zellner's Maximal Data Information (MDIP) criterion. For many systems the bivariate distribution of the component and system lifetimes does not have a density with respect to the two-dimensional Lebesgue measure. For these systems, M is not defined, so we use a modification of a mutual information index to cover such situations. Our results for ordering dependence are general in terms of binary structures, sum of random variables, and order statistics.

Suggested Citation

  • Nader Ebrahimi & Nima Y. Jalali & Ehsan S. Soofi & Refik Soyer, 2014. "Importance of Components for a System," Econometric Reviews, Taylor & Francis Journals, vol. 33(1-4), pages 395-420, June.
    • Handle: RePEc:taf:emetrv:v:33:y:2014:i:1-4:p:395-420
    DOI: 10.1080/07474938.2013.807652
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    1. Arnold Zellner, 1997. "Bayesian Analysis in Econometrics and Statistics," Books, Edward Elgar Publishing, number 825.
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    1. Ebrahimi, Nader & Jalali, Nima Y. & Soofi, Ehsan S., 2014. "Comparison, utility, and partition of dependence under absolutely continuous and singular distributions," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 32-50.

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