Mean Residual Life Ageing Intensity Function

TL;DR

This paper introduces the mean residual life ageing intensity (MRLAI) function to analyze component ageing, explores its properties under reliability operations, and defines a new order for system ageing behavior.

Contribution

It proposes the MRLAI function, studies its closure properties, and introduces a new ageing order for systems, advancing the analysis of ageing patterns in reliability theory.

Findings

MRLAI function effectively characterizes component ageing.

Closure properties of MRLAI under reliability operations are established.

A new mean residual life ageing intensity order is defined and analyzed.

Abstract

The ageing intensity function is a powerful analytical tool that provides valuable insights into the ageing process across diverse domains such as reliability engineering, actuarial science, and healthcare. Its applications continue to expand as researchers delve deeper into understanding the complex dynamics of ageing and its implications for society. One common approach to defining the ageing intensity function is through the hazard rate or failure rate function, extensively explored in scholarly literature. Equally significant to the hazard rate function is the mean residual life function, which plays a crucial role in analyzing the ageing patterns exhibited by units or components. This article introduces the mean residual life ageing intensity (MRLAI) function to delve into component ageing behaviours across various distributions. Additionally, we scrutinize the closure properties of the MRLAI function across different reliability operations. Furthermore, a new order termed the mean residual life ageing intensity order is defined to analyze the ageing behaviour of a system, and the closure property of this order under various reliability operations is discussed.