# A note on Quantile curves based bivariate reliability concepts

## TL;DR

This paper extends univariate quantile-based reliability concepts to bivariate cases using quantile curves, introducing new hazard rate and mean residual life functions, and analyzing their properties and relationships.

## Contribution

It proposes novel bivariate reliability measures based on quantile curves and explores their properties and relationships, advancing multivariate reliability analysis.

## Key findings

- Defined bivariate hazard rate and mean residual life using quantile curves
- Established relationships between these bivariate reliability functions
- Analyzed uniqueness and reverse time properties of the concepts

## Abstract

We extend the univariate quantile based reliability concepts to the bivariate case using quantile curves. We propose quantile curves based bivariate hazard rate and bivariate mean residual life function and establish a relationship between them. We study the uniqueness properties of these concepts to determine the underlying quantile curve. We also study the quantile curves based reliability concepts in reverse time.