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Paper   IPM / M / 16003
School of Mathematics
  Title:   Stochastic comparisons on conditional residual lifetime and inactivity time of coherent systems with exchangeable components
  Author(s):  Mahdi Tavangar (Joint with E. Salehi)
  Status:   Published
  Journal: Statist. Probab. Lett.
  Vol.:  145
  Year:  2019
  Pages:   327-337
  Supported by:  IPM
The paper describes and develops two concepts of conditional residual lifetime of the system, given that at a fixed time a certain number of components have failed but still there are some functioning components, and conditional inactivity time of the failed components in the system, given that at that time a certain number of components have failed but the system is still alive. We consider the m-out-of-n and the coherent systems consisting of n components whose lifetimes are assumed to have an exchangeable joint distribution function. Some stochastic ordering results on the conditional residual lifetime and the conditional inactivity time are provided. Several illustrative examples are also given.

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