Sequential order statistics can be used to describe the ordered lifetimes of components in a system, where the failure of a component may affect the performance of remaining components. In this paper mixture representations of the residual lifetime and the inactivity time of systems with such failure-dependent components are considered. Stochastic comparisons of differently structured systems are obtained and properties of the weights in the mixture representations are examined. Furthermore, corresponding representations of the residual lifetime and the inactivity time of a system given the additional information about a previous failure time are derived.
M. Burkschat. J. Navarro. "Dynamic signatures of coherent systems based on sequential order statistics." J. Appl. Probab. 50 (1) March 2013. https://doi.org/10.1239/jap/1363784438