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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 Linear Two-Dimensional Consecutive K-Type Systems in Multi-State Case(Elsevier Ltd, 2026) Yi, H.; Balakrishnan, N.; Li, X.In the context of consecutive k -type systems, multi-state system models are only considered in the one-dimensional case and not in the two-dimensional case due to the complexity involved. In this paper, we consider several linear two-dimensional consecutive k -type systems in the multi-state case for the first time, as generalization of consecutive k -out-of- n systems and l -consecutive- k -out-of- n systems without/with overlapping. These systems include multi-state linear connected-(k , r)-out-of-(m, n): G systems, multi-state linear connected-(k , r)-or-(r , k)-out-of-(m, n): G systems, multi-state linear l -connected-(k , r)-out-of-(m, n): G systems without/with overlapping, and multi-state linear l -connected-(k , r)-or-(r , k)-out-of-(m, n): G systems without/with overlapping. We then derive their reliability functions by using the finite Markov chain imbedding approach (FMCIA) in a new way. We also present several examples to illustrate all the results developed here. © 2026 Elsevier Ltd.Article Distance-Based Estimation Under Progressive Type-I Interval Censoring(Taylor & Francis Ltd, 2026) Balakrishnan, N.; Castilla, E.Monte Carlo simulation is used to demonstrate improved estimation performance of proposed distance-type estimators for lifetime models under progressive Type-I interval censoring. We propose novel distance-based estimators for lifetime models under progressive Type-I interval censoring. These estimators minimize the discrepancy between observed and model-based conditional failure probabilities using either quadratic or Mahalanobis distances, providing natural alternatives to maximum likelihood estimators (MLEs). Through extensive Monte Carlo simulations, we demonstrate that the Mahalanobis estimator outperforms MLE, particularly under heavy censoring or sparse data. The quadratic estimator also yields competitive results, especially under model misspecification. Two real data examples illustrate the practical advantages of the proposed approach.
