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  • The Joint Signature of Coherent Systems with Shared Components

  • Part of
  • Jorge Navarro, Francisco J. Samaniego, N. Balakrishnan
  • Journal:
    Journal of Applied Probability / Volume 47 / Issue 1 / March 2010
    Published online by Cambridge University Press:
    14 July 2016, pp. 235-253
    Print publication:
    March 2010
    • Article
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  • System signatures are useful tools in the study and comparison of coherent systems. In this paper, we define and study a similar concept, called the joint signature, for two coherent systems which share some components. Under an independent and identically distributed assumption on component lifetimes, a pseudo-mixture representation based on this joint signature is obtained for the joint distribution of the lifetimes of both systems. Sufficient conditions are given based on the respective joint signatures of two pairs of systems, each with shared components, to ensure various forms of bivariate stochastic orderings between the joint lifetimes of the two pairs of systems.