  Different strategies of reliability theory for the analysis of coherent
systems have been studied by various researchers. Here, the Gini-type index is
utilized as an applicable tool for the study and comparison of the ageing
properties of complex systems. A new stochastic order in terms of Gini-type
index is introduced to compare the speed of ageing of components and systems.
The parallel-series and series-parallel systems with shared components are
studied by their corresponding Gini-type indexes. Also, the generalization of
Gini-type index for the multidimensional case is discussed, and is used to
compare components lifetimes properties in the presence of other dependent
components. It is shown that the ageing properties of a component lifetime can
differ when the other components are working or have already failed. Numerous
illustrative examples are given for better intuition of Gini-type and
generalized Gini-type indexes throughout the paper.
