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Article Robust Divergence-Based Tests of Hypotheses for Simple Step-Stress Accelerated Life-Testing Under Gamma Lifetime Distributions(Elsevier B.V., 2026) Balakrishnan, N.; Jaenada, M.; Pardo, L.Many modern devices are highly reliable, with long lifetimes before their failure. Conducting reliability tests under actual use conditions may require therefore impractically long experimental times to gather sufficient data for developing accurate inference. To address this, Accelerated Life Tests (ALTs) are often used in industrial experiments to induce product degradation and eventual failure more quickly by increasing certain environmental stress factors. Data collected under such increased stress conditions are analyzed, and results are then extrapolated to normal operating conditions. These tests typically involve a small number of devices and so pose significant challenges, such as interval-censoring. As a result, the outcomes are particularly sensitive to outliers in the data. Additionally, a comprehensive analysis requires more than just point estimation; inferential methods such as confidence intervals and hypothesis testing are essential to fully assess the reliability behaviour of the product. This paper presents robust statistical methods based on minimum divergence estimators for analyzing ALT data of highly reliable devices under step-stress conditions and Gamma lifetime distributions. Robust test statistics generalizing the Rao test and divergence-based tests for testing linear null hypothesis are then developed. These hypotheses include in particular tests for the significance of the identified stress factors and for the validity of the assumption of exponential lifetimes. © 2026Article Fröbenius Expansions for Second-Order Random Differential Equations: Stochastic Analysis and Applications to Lindley-Type Damping Models(Elsevier B.V., 2026) Halim, H.; Kerker, M.A.; Boduroğlu, E.This paper develops a Frobenius series framework for the stochastic analysis of second–order random differential equations of the form Y¨(t)+A(t)Y˙(t)=0,where the damping coefficient A(t) is a positive stochastic process and the initial conditions are square–integrable random variables. Assuming mean–square analyticity of A(t) in a neighborhood of the initial time, we establish existence and uniqueness of the solution in L2(Ω) and derive exponentially convergent truncation error bounds for the associated Frobenius expansion. The resulting series representation enables the numerical approximation of the probability density function of Y(t) via Monte Carlo simulation. To improve computational efficiency, a control variates strategy is incorporated for variance reduction. A comprehensive numerical study is conducted for a broad family of positive, right–skewed damping distributions, including the Lindley, XLindley, New XLindley (NXLD), Gamma–Lindley, Inverse–Lindley, Truncated–Lindley, Log–Lindley, and a newly proposed Mixed Lindley–Uniform model. The simulations illustrate how different tail behaviors and boundedness properties of the damping coefficient influence the stochastic dynamics and the accuracy of density estimation. Finally, stylized applications to option pricing and Value–at–Risk estimation are presented to illustrate how the Frobenius–based framework and control variates methodology can be embedded within standard uncertainty quantification workflows. Overall, the proposed approach provides a flexible and computationally efficient tool for the analysis of randomly damped dynamical systems. © 2026 Elsevier B.V.
