Mixture Representations of the Extropy of Conditional Mixed Systems and Their Information Properties

In this paper, we obtain the mixture representations for the extropy of a mixed used system and the extropy of the inactivity time of a system. These representations demonstrate the extropy of conditional mixed systems as a mixture of a conditional coefficients vector, left (or right) truncated beta distribution, and the baseline distribution of the system components. Based on these representations, the comparisons of the extropy of conditional mixed systems are carried out with respect to the stochastic orders and stochastically ordered conditional coefficients vector between systems. Moreover, some bounds for the extropy of theses systems are derived. The utility of these representations is illustrated in two examples in which the extropy of a mixed used system and the extropy of the inactivity time of a system are computed and compared.