# Coherent systems with dependent and identically distributed components: A study of relative ageing based on cumulative hazard and cumulative reversed hazard rate functions

## TL;DR

This paper investigates conditions under which one coherent system with dependent, identically distributed components ages faster than another, using stochastic orders based on cumulative hazard and reversed hazard functions, with applications to k-out-of-n systems.

## Contribution

It provides new sufficient conditions for relative ageing comparisons of coherent systems using cumulative hazard and reversed hazard rates, specifically applied to k-out-of-n systems.

## Key findings

- Sufficient conditions for relative ageing based on hazard functions.
- Application of conditions to k-out-of-n systems.
- Numerical examples illustrating theoretical results.

## Abstract

The relative ageing is an important notion which is useful to measure how a system ages relative to another one. Among all existing stochastic orders, there are two important orders describing the relative ageing of two systems, namely, ageing faster orders in the cumulative hazard and the cumulative reversed hazard rate functions. In this paper, we give some sufficient conditions under which one coherent system ages faster than another one with respect to the aforementioned stochastic orders. Further, we show that the proposed sufficient conditions are satisfied for $k$-out-of-$n$ systems. Moreover, some numerical examples are given to illustrate the developed results.