Variance Residual Life Ageing Intensity Function

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.