Analysis of reliability systems via Gini-type index

TL;DR

This paper introduces a Gini-type index to analyze and compare the aging properties of complex reliability systems, including new stochastic orders and multidimensional generalizations.

Contribution

It presents a novel Gini-type index and stochastic order for assessing aging in complex systems, including shared components and multidimensional cases.

Findings

Gini-type index effectively compares aging properties of systems.

New stochastic order based on Gini-type index introduced.

Illustrative examples demonstrate practical applications.

Abstract

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.