# On Relative Ageing of Coherent Systems with Dependent Identically Distributed Components

## TL;DR

This paper investigates how coherent systems age relative to each other using hazard and reversed hazard rates, providing conditions for dominance and comparing redundancy strategies and used systems.

## Contribution

It introduces new sufficient conditions for comparing systems' relative ageing and examines the effectiveness of redundancy placement and used components.

## Key findings

- Active redundancy at component level can be more effective than at system level.
- Conditions established for one system to dominate another in ageing faster orders.
- Comparison of used systems and systems with used components regarding relative ageing.

## Abstract

Relative ageing describes how a system ages with respect to another one. The ageing faster orders are the ones which compare the relative ageings of two systems. Here, we study ageing faster orders in the hazard and the reversed hazard rates. We provide some sufficient conditions for proving that one coherent system dominates another system with respect to ageing faster orders. Further, we investigate whether the active redundancy at the component level is more effective than that at the system level with respect to ageing faster orders, for a coherent system. Furthermore, a used coherent system and a coherent system made out of used components are compared with respect to ageing faster orders.