An exact and interpretable test for detecting aging behavior in reliability and survival data

Abstract

The identification of aging behavior in reliability and survival data is a central problem with important implications for risk assessment, system reliability, and decision-making in applied fields. The exponential model serves as the standard benchmark corresponding to the absence of aging, making the detection of departures from this model a key statistical task. This paper develops an exact nonparametric test for detecting increasing failure rate in average (IFRA) type aging in complete lifetime data. The test is constructed through a deviation functional derived from the defining properties of the IFRA class, providing a structurally meaningful and practically interpretable measure of departure from exponentiality. A main contribution is the derivation of an exact finite-sample representation of the test statistic under the exponential model using a normalized spacings framework, allowing accurate inference without reliance on asymptotic approximations. An asymptotic normal characterization is also established to support efficient large-sample implementation. To enhance practical applicability, a scale-invariant formulation is developed to remove dependence on unknown parameters. The performance of the proposed method is evaluated through extensive Monte Carlo simulations under a range of alternative models, including linear failure rate, Makeham, Gamma, and Weibull distributions. The results demonstrate consistently strong empirical power and competitive performance relative to existing procedures across different sample sizes. The practical utility of the method is further illustrated through applications to real-world datasets, where it provides coherent and interpretable assessments of aging behavior. Overall, the proposed approach offers a statistically rigorous and practically relevant tool for detecting aging patterns in reliability and survival data, combining exact finite-sample validity, asymptotic tractability, and strong empirical performance. In practical terms, the test helps determine whether a system or population shows signs of aging (increasing average risk over time) or behaves as if failures occur randomly at a constant rate.