Geometric and Harmonic Aging Intensity function and a Reliability Perspective

TL;DR

This paper introduces new aging notions based on geometric and harmonic means of failure rates, explores their properties, and applies them to reliability analysis with case studies and simulated data.

Contribution

It proposes generalized aging functions using geometric and harmonic hazard rates, providing new characterization results and probabilistic orderings in reliability theory.

Findings

Well-known distributions exhibit monotonic aging classes.

New probabilistic orders based on geometric and harmonic hazard rates.

Applications demonstrated through case studies and simulated data.

Abstract

In this paper, we introduce some new notions of aging based on geometric, harmonic means of failure rate and aging intensity function. We define a generalized version of aging functions called specific interval-average geometric hazard rate, specific interval-average harmonic hazard rate. We focus on some characterization results and their inter-relationships among the resulting non-parametric classes of distributions. Monotonic nature of so defined aging classes are exhibited by some well known probability distributions. Probabilistic orders based on these functions are taken up for further study. The work is illustrated through case studies and a simulated data having applications in reliability/survival analysis.