  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.
