Testing for aging behavior is a fundamental problem in reliability analysis. We study tests of exponentiality against new better than used in expectation (NBUE) alternatives. Many Hollander–Proschan type procedures can be interpreted as weighted functionals of a common mean residual life gap, but are often presented in isolated forms, making it difficult to understand how weighting affects sensitivity to different alternatives. We develop a unified weighted-functional framework in which several classical procedures arise as special or limiting cases. Within this framework, we construct a centered and studentized statistic with an asymptotic normal null distribution and an explicit centering term. Pitman efficiency analysis and Monte Carlo experiments illustrate how weighting influences sensitivity and finite-sample performance, while real-data applications demonstrate practical interpretability.

Group testing is an efficient screening method that reduces the number of tests by pooling multiple samples, making it especially effective in low-prevalence settings. This strategy gained significant attention during the COVID-19 pandemic, and has since been applied to detect various infectious diseases, including HIV, chlamydia, gonorrhea, influenza, and Zika virus. In this paper, we introduce a semi-parametric logistic single-index model for analyzing high-dimensional group testing data, which is particularly flexible in capturing complex nonlinear relationships. The proposed method achieves variable selection by parameter regularization, which proves especially beneficial for extracting relevant information from high-dimensional data. The performance of the model is evaluated through simulations across four group testing strategies: master pool testing, Dorfman testing, halving testing, and array testing. Further validation is provided using real-world data. The results demonstrate that our approach offers a flexible and robust tool for analyzing high-dimensional group testing data, with important applications in epidemiology and public health.