Exact and entropy-based nonparametric tests for exponentiality against increasing failure rate alternatives

Testing exponentiality against increasing failure rate (IFR) alternatives is a central problem in reliability theory with direct implications for aging characterization and maintenance optimization. In this paper, I introduce a novel entropy-based nonparametric test family constructed from fractional generalized cumulative residual entropy (FGCRE). The proposed statistics were formulated as scale-invariant L-functionals indexed by a tuning parameter, enabling adaptive sensitivity to diverse forms and magnitudes of IFR departures. A principal contribution of this work is the derivation of the exact finite-sample null distribution under exponentiality through a normalized spacing representation, thereby permitting fully exact, distribution-free inference without reliance on asymptotic approximations. Extensive Monte Carlo simulations demonstrated that the proposed test exhibits consistently strong and stable power, exceeding 0.85 in moderate sample sizes under Weibull alternatives and outperforming several established procedures, particularly in challenging discrimination regimes. Applications to real datasets from reliability engineering and environmental studies further confirmed the practical effectiveness of the proposed methodology in detecting positive aging behavior. Overall, the proposed framework offers a theoretically rigorous, flexible, and computationally efficient tool for exact and asymptotic testing of exponentiality against IFR alternatives.