Analysis of reliability systems via Gini-type index

- A Gini-type index was proposed to assess the degree of ageing in reliability systems.
- We discuss properties of such index, and define a related stochastic order.
- Reliability systems with shared components are studied by means of Gini-type indexes.
- Generalization to the multidimensional case with dependent components is discussed.

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.