Abstract

This paper introduces a non-parametric test for assessing whether a lifetime distribution belongs to the Used Better than Aged in Convex Ordering (UBAC) class, using Laplace transform ordering. The proposed test addresses a fundamental problem in survival and reliability analysis: distinguishing exponentiality from more general ageing behaviour. Unlike existing approaches, the method accommodates both complete and right-censored data and provides simulated critical values over a wide range of sample sizes.

The asymptotic properties of the test are studied within Pitman’s framework, and its relative efficiency is evaluated against well-known alternatives such as the Weibull, Linear Failure Rate (LFR), and Makeham distributions. Extensive Monte Carlo simulations demonstrate that the proposed procedure maintains good power and stability, even for small samples. The practical relevance of the test is illustrated through applications to several real medical data sets, including leukemia, COVID-19 mortality, liver cancer, and lung cancer survival data. Overall, the proposed method offers a statistically sound and computationally tractable tool for applied researchers in reliability engineering and biomedical survival analysis.

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