Mixture Representations of Residual Lifetimes of Used Systems

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Mixture Representations for the Joint Distribution of Lifetimes of two Coherent Systems with Shared Components (2013, background): “Other representations under different conditions (such as Xj :n ≤ x or Xj :n > x) have been obtained in [2], [3], [6], [16], [18], [19], [22], [25], [32], [34], and [35].”
The Joint Signature of Coherent Systems with Shared Components (2010, background): “Similar representations for the residual lifetime (T − t | T > t) of T can be seen in [4] and [9].”
Comparisons of coherent systems using stochastic precedence (2010, methodology): “This procedure is illustrated in the next section (see Example 4). Finally, we would like to note that our results can also be applied to compare the residual lifetimes of two coherent systems using the representations given in Li and Zhang (2008), Navarro et al. (2008a) and Samaniego et al. (2009”