An Integral Measure of Aging/Rejuvenation for Repairable and Non-repairable Systems

This paper introduces a simple index that helps to assess the degree of aging or rejuvenation of a (non)repairable system. The index ranges from -1 to 1 and is negative for the class of decreasing failure rate distributions (or deteriorating point processes) and is positive for the increasing failure rate distributions (or improving point processes). The introduced index is distribution free.

💡 Research Summary

The paper proposes a single, distribution‑free index – the Integral Measure of Aging/Rejuvenation (IMAR) – that quantifies whether a repairable or non‑repairable system is aging (failure rate increasing) or rejuvenating (failure rate decreasing). Traditional reliability analysis often relies on parametric models such as Weibull or exponential distributions, mean time to failure (MTTF), or the slope of the hazard function. Those approaches are limited because they require specific distributional assumptions, involve complex parameter estimation, and usually cannot capture both aging and rejuvenation in a single scalar.

IMAR is defined as the normalized area between the empirical cumulative distribution function (CDF) of failure times, F(t), and a reference exponential CDF, G(t), that has the same mean failure time as F(t). Formally:

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