Variance Residual Life Ageing Intensity Function

TL;DR

This paper introduces the Variance Residual Life Ageing Intensity (VRLAI) function, a new metric for quantifying ageing in systems, and explores its properties, ordering, and implications for reliability analysis.

Contribution

The paper proposes the VRLAI function as a novel measure of ageing and characterizes its properties, including closure and ordering, across different distributions and systems.

Findings

VRLAI function effectively measures ageing characteristics.

VRLAI ordering provides a new way to compare system ageing.

Closure properties of VRLAI order are established for coherent systems.

Abstract

Quantitative measurement of ageing across systems and components is crucial for accurately assessing reliability and predicting failure probabilities. This measurement supports effective maintenance scheduling, performance optimisation, and cost management. Examining the ageing characteristics of a system that operates beyond a specified time $t > 0$ yields valuable insights. This paper introduces a novel metric for ageing, termed the Variance Residual Life Ageing Intensity (VRLAI) function, and explores its properties across various probability distributions. Additionally, we characterise the closure properties of the two ageing classes defined by the VRLAI function. We propose a new ordering, called the Variance Residual Life Ageing Intensity (VRLAI) ordering, and discuss its various properties. Furthermore, we examine the closure of the VRLAI order under coherent systems.