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Keywords = lifetime models

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22 pages, 32128 KB  
Article
Atomistic Mechanisms of Silicone Rubber Degradation Under Coupled Temperature–Humidity–Electric Field Conditions
by Yiheng Zhou, Zhijun An, Yixin He, Cong Qian, Qiuhua Zhou, Wentian Zeng, Xinhan Qiao and Wenyu Ye
Polymers 2026, 18(12), 1530; https://doi.org/10.3390/polym18121530 (registering DOI) - 19 Jun 2026
Abstract
Silicone rubber is an important external insulating material for composite bushings, composite insulators, and other power equipment. During long-term service, it is inevitably exposed to coupled environmental and electrical stresses, such as elevated temperature, moisture ingress, strong electric fields, and partial discharge, which [...] Read more.
Silicone rubber is an important external insulating material for composite bushings, composite insulators, and other power equipment. During long-term service, it is inevitably exposed to coupled environmental and electrical stresses, such as elevated temperature, moisture ingress, strong electric fields, and partial discharge, which may lead to hydrophobicity loss, surface chalking, crack propagation, and particle shedding. To reveal the microscopic degradation mechanism of silicone rubber under complex operating conditions, a molecular model of methyl vinyl silicone rubber was constructed using Materials Studio. A stable silicone rubber molecular structure was obtained through crosslinking, geometry optimization, and ensemble relaxation. Subsequently, a reactive molecular dynamics simulation system under coupled temperature–humidity–electric field conditions was established using LAMMPS and the ReaxFF reactive force field. Different temperature gradients, electric field intensities, and aging–recovery stages were designed to investigate the degradation behavior of silicone rubber. The evolution of the maximum carbon content, maximum silicon content, carbon-containing decomposition products, and typical small-molecule products, including H2, H2O, CH4, C2H2, C2H4, and C2H6, was statistically analyzed. In addition, atomic trajectory tracking was performed to clarify the processes of methyl group detachment, Si-O bond cleavage, water molecule participation, and molecular chain reconstruction. The results show that high temperature mainly promotes methyl group detachment from side chains and fracture of the siloxane main chain, while a strong electric field accelerates the decomposition process and induces the transformation of long siloxane chains into shorter chains. Water molecules can react with broken siloxane chains to form hydroxyl-containing structures, making the structural degradation partially irreversible. The degradation process of silicone rubber under coupled temperature–humidity–electric field stress can be summarized as side-chain detachment, main-chain scission, water-assisted reactions, free-radical recombination, and local molecular aggregation. This study provides a molecular-level theoretical basis for aging mechanism analysis, condition assessment, and lifetime prediction of composite external insulating materials. Full article
(This article belongs to the Section Polymer Analysis and Characterization)
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37 pages, 21335 KB  
Article
A New Reparameterized Weibull-Type Distribution for Asymmetric Lifetime Data: Inference, Simulation, and Applications
by Ahmed Elshahhat, Heba S. Mohammed, Osama E. Abo-Kasem and Asmaa Abdel-Hakim
Symmetry 2026, 18(6), 1057; https://doi.org/10.3390/sym18061057 - 19 Jun 2026
Abstract
This article presents a comprehensive inferential and applied investigation of the newly reparameterized Z-Weibull (ZW) distribution, a flexible Weibull-type lifetime model capable of accommodating both bounded and unbounded support regimes as well as a wide variety of hazard rate shapes. Unified frequentist and [...] Read more.
This article presents a comprehensive inferential and applied investigation of the newly reparameterized Z-Weibull (ZW) distribution, a flexible Weibull-type lifetime model capable of accommodating both bounded and unbounded support regimes as well as a wide variety of hazard rate shapes. Unified frequentist and Bayesian inference procedures are developed for complete and censored samples using maximum likelihood, maximum product spacing, and Markov chain Monte Carlo methods. Theoretical properties of the estimators and their associated interval estimates are established, while extensive Monte Carlo simulations assess their finite-sample performance under diverse parameter configurations and censoring schemes. The results indicate that Bayesian spacing-based procedures generally provide more accurate estimation, lower bias, and improved interval performance than competing classical methods. Applications to biomedical survival and climatological datasets, together with comparisons against several Weibull-type and exponential-based competitors, demonstrate the superior flexibility and goodness-of-fit of the ZW model. These findings highlight the practical value of the reparameterized ZW distribution as a unified and effective tool for modeling complex lifetime and reliability data arising in survival, environmental, and engineering studies. Full article
23 pages, 5270 KB  
Article
Constraint-Adjusted Nonparametric Inference for Residual-Life Functionals Under Stochastic Precedence
by Abdulmajeed A. R. Alharbi
Mathematics 2026, 14(12), 2196; https://doi.org/10.3390/math14122196 - 18 Jun 2026
Abstract
Nonparametric inference for residual-life functionals is a fundamental problem in mathematical statistics, reliability theory, and survival analysis, particularly in studies with limited sample sizes where empirical plug-in estimators may exhibit substantial sampling variability. In comparative lifetime analysis, additional qualitative information is often available [...] Read more.
Nonparametric inference for residual-life functionals is a fundamental problem in mathematical statistics, reliability theory, and survival analysis, particularly in studies with limited sample sizes where empirical plug-in estimators may exhibit substantial sampling variability. In comparative lifetime analysis, additional qualitative information is often available regarding the relative behavior of two populations; however, such information is frequently too weak to justify classical stochastic dominance assumptions. Stochastic precedence provides a natural and interpretable framework for representing this partial ordering through a pairwise probabilistic constraint. This paper develops a constraint-adjusted nonparametric inference framework for estimating the mean residual life (MRL) and quantile residual life (QRL) functions under stochastic precedence information. The proposed approach replaces the ordinary empirical distribution function in standard residual-life plug-in estimators with a constraint-adjusted empirical distribution function that enforces the stochastic precedence relation at the sample level. The adjustment is governed by a data-driven scaling factor and is asymptotically negligible, thereby preserving the large-sample behavior of the ordinary empirical estimators while incorporating meaningful structural information in finite samples. Strong consistency of the proposed MRL and QRL estimators was established under mild regularity conditions. A Monte Carlo study based on Weibull and gamma lifetime models demonstrates that in the simulation settings considered, the proposed estimators provide improved finite-sample stability and generally achieve smaller mean squared errors than their ordinary empirical counterparts, especially for small and moderate sample sizes. The methodology is further illustrated using survival data from patients with squamous cell carcinoma of the oropharynx, highlighting its practical relevance in biomedical survival analysis. The proposed method offers a flexible, interpretable, and computationally simple framework for nonparametric inference with structured lifetime data under weak stochastic ordering information. Full article
(This article belongs to the Special Issue Mathematical Statistics and Nonparametric Inference)
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17 pages, 614 KB  
Review
Probing the Tau Anomalous Magnetic Moment at Colliders: From Ultra-Peripheral Collisions to the Precision Frontier
by Natascia Vignaroli
Symmetry 2026, 18(6), 1050; https://doi.org/10.3390/sym18061050 - 18 Jun 2026
Abstract
The anomalous magnetic moment of the tau lepton, aτ, represents a fundamental test of the Standard Model (SM) and a high-sensitivity probe for New Physics in the third generation of leptons. Due to the tau’s extremely short lifetime, traditional spin-precession measurements [...] Read more.
The anomalous magnetic moment of the tau lepton, aτ, represents a fundamental test of the Standard Model (SM) and a high-sensitivity probe for New Physics in the third generation of leptons. Due to the tau’s extremely short lifetime, traditional spin-precession measurements remain inaccessible, necessitating innovative experimental strategies at high-energy colliders. This review provides a comprehensive overview of the current experimental landscape, highlighting the recent paradigm shift from LEP-era constraints to the unprecedented precision reached at the LHC. We emphasize the importance of Ultra-Peripheral Heavy-Ion Collisions (UPCs), which act as a “photon-photon collider” of extreme intensity. By leveraging the Z4 enhancement of the coherent photon flux in Lead–Lead (PbPb) interactions, these collisions provide a theoretically robust “quasi-static” environment. To interpret these developments, we first establish the general theoretical framework within the Standard Model Effective Field Theory (SMEFT). This allows us to critically compare the UPC results with the latest measurements from proton–proton collisions—including the recent CMS observation of the γγττ process and the ATLAS constraints from the high-mass Drell–Yan tail—evaluating their complementarity and the challenges related to Effective Field Theory validity at the TeV scale. Finally, we outline the future prospects for aτ at Belle II and the Future Circular Collider (FCC) stages. While FCC-hh in PbPb mode provides a theoretically clean environment, its sensitivity remains limited to O(102). Conversely, the next generation of lepton facilities, specifically Belle II and FCC-ee, aims for the O(105) level, required to probe SM electroweak loop corrections. Long-term projections for a high-energy Muon Collider suggest a potential reach of O(106). Full article
(This article belongs to the Special Issue Symmetry and Relativistic Heavy-Ion Collisions)
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14 pages, 565 KB  
Article
The Risk of Acrylamide Intake from Roasted Arabica Coffee (Pure, Torrefacto and Soluble) Consumed in Costa Rica
by Daniela Jaikel-Víquez, Ilhami Okur, Alejandra Gómez-Arrieta, Fabio Granados-Chinchilla, Graciela Artavia, Carolina Cortés-Herrera, Georgina Gómez-Salas, Mauricio Redondo-Solano and Bing Wang
Foods 2026, 15(12), 2199; https://doi.org/10.3390/foods15122199 - 18 Jun 2026
Abstract
Acrylamide (AA) is a contaminant with carcinogenic and genotoxic properties that occur in heat-produced food products. This study aimed to evaluate the occurrence of AA in different coffee products commercially sold in retail markets of Costa Rica and to develop a probabilistic exposure [...] Read more.
Acrylamide (AA) is a contaminant with carcinogenic and genotoxic properties that occur in heat-produced food products. This study aimed to evaluate the occurrence of AA in different coffee products commercially sold in retail markets of Costa Rica and to develop a probabilistic exposure assessment model to assess the potential human health risk due to its consumption. The average AA concentration in the coffee samples analyzed (n = 110) was 110.29 ± 151.61 µg kg−1. The mean dietary exposure (DE) values, for the middle-bound (MB) approach, varied from 0.025 to 0.083 µg kg−1 BW per day. The margin of exposure (MOE) was calculated with a BDML10: 430 μg kg−1 BW day−1 for neurotoxicity and 170 μg kg−1 BW day−1 for cancer effect, according to EFSA (2015). No neurotoxicity risk was identified as MOE values ranged from 4291 to 467,984 for the adult male population, from 4566 to 477,203 for the adult females, from 4265 to 506,062 for the male minors and from 2512 to 495,151 for the female minors. On the other hand, MOE values for the carcinogenic risk were below 10,000 for the mean and P95th coffee consumers, denoting a possible health concern. The values ranged from 1696 to 6717 for the adult male population, from 1805 to 7201 for the female adults, from 1686 to 6304 for the male minors and from 993 to 2155 for the female minors. The mean incremental lifetime cancer risk (ILCR) values for male adult, female adult, male minor, and female minor were 1.7 × 10−5, 1.6 × 10−5, 1.9 × 10−5, and 3.9 × 10−5, respectively, for the MB approach. These results denote a potential or considerable risk in consumption of coffee due to AA intake. Thus, no neurotoxicity risk was identified; however, a potential carcinogenic risk was observed based on MOE and ILCR results. Full article
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35 pages, 14335 KB  
Article
Comprehensive Assessments of the Bilal Extended Model with Applications in Mechanical Engineering and Health Insurance
by Ahmed Elshahhat and Eslam Abdelhakim Seyam
Mathematics 2026, 14(12), 2176; https://doi.org/10.3390/math14122176 - 17 Jun 2026
Viewed by 42
Abstract
A recent generalized Bilal (G-Bilal) model demonstrates remarkable flexibility in capturing a wide spectrum of failure behaviors, including monotonic and non-monotonic (upside-down bathtub-shaped) hazard patterns, outperforming several existing models such as the Weibull, gamma, and exponential families. This paper develops several inferential frameworks [...] Read more.
A recent generalized Bilal (G-Bilal) model demonstrates remarkable flexibility in capturing a wide spectrum of failure behaviors, including monotonic and non-monotonic (upside-down bathtub-shaped) hazard patterns, outperforming several existing models such as the Weibull, gamma, and exponential families. This paper develops several inferential frameworks for different G-Bilal parameters of life using samples gathered by improved Type-II adaptive progressive censoring. This enhanced design ensures optimal control of test duration while maintaining high inferential precision. Expressions for the model parameters, reliability, and hazard rate functions are derived, followed by the development of maximum likelihood (ML) and maximum product of spacing (MPS) estimators with their asymptotic confidence intervals using the observed Fisher information with the delta approach. Furthermore, Bayesian estimators and two associated credible intervals are proposed under independent gamma priors and computed through Markov iterations, with both ML and MPS posteriors considered. Extensive Monte Carlo experiments confirm the consistency, robustness, and precision of the proposed estimators, with Bayesian spacing-based methods exhibiting superior accuracy and coverage. The model’s practical potential is further verified through two real applications: one involving mechanical system lifetimes and another analyzing health insurance premium data, representing physical and actuarial domains, respectively. Using the introduced censoring, the proposed G-Bilal model outperforms all competing models in terms of goodness-of-fit and reliability estimates in both cases. The results underscore the G-Bilal model’s adaptability, computational stability, and empirical superiority, establishing it as a powerful tool for modern reliability and actuarial risk assessments. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods for Mechanics and Engineering)
21 pages, 2502 KB  
Article
Research on Early Warning Models for Swine Feeding Dynamic Signatures Based on Electronic Automated Feeding Data
by Yima Wang, Yuancheng Xie, Jianlan Wang, Yuhan Zhang, Wei Wei, Jie Chen, Jinbi Zhang and Zengxiang Pan
Animals 2026, 16(12), 1880; https://doi.org/10.3390/ani16121880 - 17 Jun 2026
Viewed by 51
Abstract
One of the keys to improving feed conversion rates in Precision Livestock Farming (PLF) is the early identification of growth impediments. However, the swine farming data collected by Electronic Feeding Station (EFS) are often disorganized and lack effective labeling. Data from healthy pigs [...] Read more.
One of the keys to improving feed conversion rates in Precision Livestock Farming (PLF) is the early identification of growth impediments. However, the swine farming data collected by Electronic Feeding Station (EFS) are often disorganized and lack effective labeling. Data from healthy pigs are frequently intermixed with that from sick pigs, leading to label leakage and survivor bias in models, particularly when age is included as a feature. To address these known issues, this study breaks away from traditional modeling methods. First, we clean and classify the time-series data from electronic feeding stations, using age-cohort baselines as one of the criteria for determining high and low productivity, thereby avoiding problems such as label leakage. Next, we construct a high-dimensional feature matrix that captures dynamic derivatives such as feeding acceleration and weight gain acceleration, which together serve as behavioral feature fingerprints. To test the system, we optimized the mixed-model algorithm and evaluated the model based on behavioral deviations among individual pigs after removing all absolute age labels. Our results indicate that the full-feature model achieved an ROC-AUC of 0.778 and an F1-score of 0.4137 at the optimal threshold. Interestingly, SHAP attribution analysis revealed that “intake peer deviation,” “Cumulative Intake and Lifetime Avg Intake,” and “feeding acceleration” served as precursors to low productivity and growth retardation in this dataset, with these factors proving more significant than absolute feed intake or age. Our ablation experiments confirmed that a model based solely on behavioral features (excluding age labels) maintained an ROC-AUC of 0.773, successfully decoupling pig growth performance from growth stage. Our model can detect changes in feeding dynamic signatures at an average of 12.3 days, thereby providing insights for pig growth assessment, health monitoring, or more informed culling decisions. Full article
(This article belongs to the Section Pigs)
16 pages, 706 KB  
Article
Quantile Reparameterized Regression Model and Machine Learning with Long-Term Survivors
by Edwin M. M. Ortega, Gabriela M. Rodrigues, Valdemiro P. Vigas, Gauss M. Cordeiro, Vicente G. Cancho and Michael W. Kattan
Axioms 2026, 15(6), 451; https://doi.org/10.3390/axioms15060451 - 17 Jun 2026
Viewed by 31
Abstract
We propose a quantile-based survival model that accounts for a cure fraction. By modeling unobserved event causes with a negative binomial distribution and time-to-event with the generalized log-logistic Weibull distribution, we estimate parameters using a frequentist framework. We validated our model and applied [...] Read more.
We propose a quantile-based survival model that accounts for a cure fraction. By modeling unobserved event causes with a negative binomial distribution and time-to-event with the generalized log-logistic Weibull distribution, we estimate parameters using a frequentist framework. We validated our model and applied it to prostate cancer data to prove its practical use. Comparing it to a Random Survival Forest model, we highlight how different approaches handle long-term survival, ultimately weighing the balance between flexibility, interpretability, and predictive performance. Full article
(This article belongs to the Special Issue Probability Theory and Stochastic Processes: Theory and Applications)
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2 pages, 150 KB  
Abstract
LIFE REVIVE: Innovative and Integrated Solutions to Mitigate Hydro Morphological Pressures and Enhance Ecological Status in the Lima and Vouga Basins
by Sandra Barca, Rufino Vieira-Lanero, Fernando Cobo, Carlos M. Alexandre, Pedro R. Almeida, Esmeralda Pereira, Silvia Pedro, Gonçalo Rodrigues, Luís Macedo, Luís Silveirinha, Gonçalo Brás, Beatriz Mendes, Célia Laranjeira, Luísa Sousa, Pedro Marques and Isabel Pragana
Proceedings 2026, 146(1), 27; https://doi.org/10.3390/proceedings2026146027 - 16 Jun 2026
Viewed by 25
Abstract
LIFE REVIVE aims to restore ecological status and ecosystem services in the Lima and Vouga river basins (NW Iberian Peninsula), where hydromorphological alteration and hydropower-driven flow regulation are major causes of water bodies failing to reach Good Ecological Status under the EU WFD. [...] Read more.
LIFE REVIVE aims to restore ecological status and ecosystem services in the Lima and Vouga river basins (NW Iberian Peninsula), where hydromorphological alteration and hydropower-driven flow regulation are major causes of water bodies failing to reach Good Ecological Status under the EU WFD. The project targets key pressures such as longitudinal fragmentation by weirs and dams, artificial flow regimes, degradation of spawning substrates, and the spread of invasive aquatic plants, which strongly affect fish communities, including sea lamprey, salmonids, and other diadromous species. Technically, the project combines barrier removal or eco-adaptation, nature-like fish passes, and spawning-habitat renaturalisation with optimized environmental flow regimes (EFR) downstream of important hydropower systems, explicitly accounting for present and future hydroclimatic scenarios. Multi-scale ecohydrological modelling (species distribution models, habitat suitability models, GLM/GAM approaches) will quantify fish–flow–habitat relationships and support the definition of operational EFR guidelines that balance ecological requirements with hydropower and agricultural constraints through joint work with the main Portuguese hydropower operator, EDP. Impact evaluation is structured around a rigorous BACI monitoring design in intervention and control tributaries, using standard WFD biological indices for fish and aquatic/riparian vegetation, hydromorphological indices (HQA, HMS, RHS), and project-specific Key Performance Indicators for water quality, biodiversity, and habitat. Expected outcomes include the restoration of at least 51 km of rivers towards free-flowing conditions, reduced hydromorphological pressure in more than 20 km of heavily modified river stretches, and measurable increases in the distribution and abundance of fish species and native vegetation. A strong communication and capacity-building programme underpins public engagement, while a decision matrix for barrier prioritization, technical workshops, and pilot replications in additional basins (e.g., Alva, Mouro, Deva, and Tea in Galicia) are designed to maximize transferability, policy uptake, and long-term sustainability of the solutions beyond the project lifetime. Full article
49 pages, 1621 KB  
Article
A New Gompertz Distribution for Modeling Tensile Strength of Carbon Fibers and Single Carbon Fibers Data
by Ayşe Metin Karakaş, Fatma Bulut and Sinan Çalık
Mathematics 2026, 14(12), 2159; https://doi.org/10.3390/math14122159 - 16 Jun 2026
Viewed by 75
Abstract
The Gompertz distribution is a well-known lifetime model in survival and reliability analysis, but its hazard rate is restricted to monotone increasing behavior, which limits its applicability to more complex data structures. In this study, we investigate the New Extended Gompertz (NEG) distribution, [...] Read more.
The Gompertz distribution is a well-known lifetime model in survival and reliability analysis, but its hazard rate is restricted to monotone increasing behavior, which limits its applicability to more complex data structures. In this study, we investigate the New Extended Gompertz (NEG) distribution, which is obtained by applying the existing NE-X generator framework to the classical Gompertz baseline distribution. Thus, the NEG model is a special case within an already established generator family rather than an entirely new family of distributions. The main contribution of this paper is not the introduction of a new generator, but rather a comprehensive and systematic investigation of this particular Gompertz-based extension, including its statistical properties, estimation procedures, and practical applications. The proposed model introduces an additional shape parameter that provides increased flexibility in modeling skewness, tail behavior, and hazard-rate structures, allowing for increasing, decreasing, bathtub-shaped, and unimodal hazard patterns under different parameter configurations. Several mathematical properties of the NEG distribution are derived, including explicit expressions for the density, distribution, survival, and hazard-rate functions, as well as moments, entropy measures, and series representations. Parameter estimation is performed using both maximum likelihood and Bayesian approaches, with numerical optimization and Metropolis–Hastings MCMC procedures employed due to the absence of closed-form estimators. The finite-sample behavior of the estimators is investigated through extensive Monte Carlo simulation studies under three different parameter settings. The practical usefulness of the NEG distribution is illustrated using two real datasets on carbon-fiber tensile strength. Comparative results with several competing Gompertz-type models indicate that the NEG distribution provides competitive performance. However, all comparisons should be interpreted within the context of the considered datasets and parameter settings, rather than as claims of universal superiority. The findings suggest that the NEG distribution offers a flexible and practical extension of the Gompertz model for lifetime data analysis. Full article
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20 pages, 13953 KB  
Article
A Lifetime Consumption Model for Combined Creep and Fatigue Loading of Aluminum Bonding Wires
by Holm Altenbach, Cassandra Moers and Christian Dresbach
Appl. Sci. 2026, 16(12), 6058; https://doi.org/10.3390/app16126058 - 15 Jun 2026
Viewed by 83
Abstract
(1) Aluminum bonding wires are mostly used for electrical contact and transmission of electrical signals in power electronic modules. Combined cyclical mechanical and thermal loads acting on the wires can lead to premature failure of the whole module. For this purpose, based on [...] Read more.
(1) Aluminum bonding wires are mostly used for electrical contact and transmission of electrical signals in power electronic modules. Combined cyclical mechanical and thermal loads acting on the wires can lead to premature failure of the whole module. For this purpose, based on extensive fatigue tests on a 300 µm Al-Pure wire, the authors developed, calibrated and applied a fatigue life model for a cycle range of R=0.1 to R=0.7 to other comparable aluminum wires in two previous publications. (2) Since the model is supposed to be used in an FEM post-processor for predicting the lifetime of wire bridges, the existing model was expanded in the following work. (3) Temperature dependence is included in the fatigue model, and it is made more robust in the whole possible R-range to be able to cope with the highly variable load cases in real components. In addition, a creep rupture model was developed and combined with the fatigue model by linear damage accumulation. (4) The applicability of the lifetime consumption model is demonstrated for several combined load cases. It is shown that it is necessary to consider both fatigue and creep in a combined model for a reliable lifetime prediction. Otherwise, the lifetime could be underestimated by several orders of magnitude, depending on the load case. Full article
(This article belongs to the Special Issue Fatigue and Fracture Behavior of Engineering Materials)
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23 pages, 1243 KB  
Article
A Sensor-Aware Multi-Agent Reinforcement Learning Framework for Joint Data Offloading and Power Control in Edge-Assisted Wireless Sensor Networks
by Peiying Zhang, Ruixin Wang, Yuekai Sun and Yujie Yuan
Sensors 2026, 26(12), 3802; https://doi.org/10.3390/s26123802 - 15 Jun 2026
Viewed by 259
Abstract
Wireless sensor networks supported by mobile edge computing are increasingly required to process heterogeneous sensing data under stringent latency, reliability, and energy constraints. However, most existing task-offloading studies are still formulated for generic user equipment and primarily focus on uplink transmission, which is [...] Read more.
Wireless sensor networks supported by mobile edge computing are increasingly required to process heterogeneous sensing data under stringent latency, reliability, and energy constraints. However, most existing task-offloading studies are still formulated for generic user equipment and primarily focus on uplink transmission, which is insufficient for practical sensing systems where sensor nodes continuously upload measurements while simultaneously receiving control commands, model updates, and feedback from the edge. To address this gap, this paper reformulates joint computation offloading and power control as a sensor-aware optimization problem in an edge-assisted wireless sensor network. We propose a three-layer architecture consisting of sensor nodes, access points with lightweight edge servers, and a cloud coordination layer. Each sensing task is characterized by data size, computation density, latency deadline, and sensing priority, while the optimization objective jointly minimizes long-term task delay, communication and computation energy, and packet-loss penalty under transmission power, edge resource, and residual-energy constraints. To solve the resulting mixed discrete–continuous problem, we develop a multi-agent reinforcement learning framework in which each sensor node acts as an autonomous agent and learns offloading and transmission policies with clipped proximal policy optimization, while the cloud layer performs coordinated edge-resource allocation through the alternating direction method of multipliers. In addition to delay and energy, network lifetime and sensing delivery performance are incorporated into the evaluation. Simulation results in a sensor-network monitoring scenario demonstrate that the proposed framework consistently reduces latency, lowers energy consumption, and prolongs network lifetime compared with representative baselines, highlighting its effectiveness and practical potential for intelligent sensing applications that require integrated sensing, communication, and edge computing. Full article
(This article belongs to the Special Issue Feature Papers in "Industrial Sensors" Section 2026–2027)
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20 pages, 954 KB  
Article
Statistical Inference for the Rayleigh–Logarithmic Distributions Under Progressive Type II Censoring: Likelihood Structure and Modeling Flexibility
by Ayse Bugatekin, Mine Dogan and Gulden Altay Suroğlu
Axioms 2026, 15(6), 444; https://doi.org/10.3390/axioms15060444 - 14 Jun 2026
Viewed by 97
Abstract
In reliability and survival studies, lifetime data are frequently subject to progressive Type-II censoring, leading to incomplete failure-time information and challenging statistical inference problems. In this study, statistical inference for the Rayleigh–Logarithmic (RL) distribution is developed under progressive Type-II censoring. The RL distribution [...] Read more.
In reliability and survival studies, lifetime data are frequently subject to progressive Type-II censoring, leading to incomplete failure-time information and challenging statistical inference problems. In this study, statistical inference for the Rayleigh–Logarithmic (RL) distribution is developed under progressive Type-II censoring. The RL distribution provides a flexible lifetime model by combining a Rayleigh lifetime component with a logarithmically distributed number of latent failure causes. A competing-risk interpretation of the model is presented, and parameter estimation is carried out using both maximum likelihood estimation (MLE) and maximum product spacing (MPS) methods. The performance of the proposed inference procedures is investigated through extensive Monte Carlo simulations under different parameter settings and censoring schemes. The results indicate that both MLE and MPS provide reliable estimates, with estimation accuracy improving as the sample size increases. The methodology is further illustrated using simulated and real lifetime data sets and compared with classical lifetime distributions. The findings show that the RL distribution offers a flexible and effective framework for modeling progressively censored lifetime data, particularly in the presence of heterogeneous and latent failure mechanisms. Full article
32 pages, 1243 KB  
Article
A Reduced-Order Regime Theory for Aerosol–Halogen–Dynamics Coupling in Volcanic Super-Eruptions
by Sebastiano Ettore Spoto
Atmosphere 2026, 17(6), 606; https://doi.org/10.3390/atmos17060606 - 13 Jun 2026
Viewed by 243
Abstract
Volcanic super-eruptions can perturb atmospheric composition and climate-relevant radiative properties in ways that are not captured by simple scaling from Pinatubo-like events. This study presents a reduced-order regime theory for the coupled evolution of stratospheric sulfur, sulfate aerosol burden, reactive halogens, ozone loss, [...] Read more.
Volcanic super-eruptions can perturb atmospheric composition and climate-relevant radiative properties in ways that are not captured by simple scaling from Pinatubo-like events. This study presents a reduced-order regime theory for the coupled evolution of stratospheric sulfur, sulfate aerosol burden, reactive halogens, ozone loss, stratospheric thermal adjustment, and aerosol residence time. The analysis is intended as an interpretive tool for organizing sulfur-rich volcanic scenarios, comparing literature-based benchmark classes, and designing chemistry–climate model experiments, rather than as an event-specific calibration or a substitute for three-dimensional models. Four control parameters structure the response: sulfur loading relative to microphysical saturation, effective halogen strength, ash-uptake efficiency, and dynamical lifetime sensitivity, with hemispheric asymmetry treated diagnostically. An external consistency check against published Pinatubo-like, idealized 10–40 teragrams of sulfur (Tg S), Toba-like, and Los Chocoyos-like responses is used to evaluate whether the reduced theory reproduces the expected rank ordering of aerosol saturation, forcing-efficiency decline, ozone-loss amplification, ash-driven sulfur suppression, and residence-time sensitivity. This comparison does not assign pointwise error margins against three-dimensional model output; it evaluates regime membership, sign of response, rank ordering, and broad magnitude behavior. The main conclusion is that volcanic super-eruption impacts are governed by interacting regime transitions rather than by sulfur mass alone. Microphysical saturation can limit forcing efficiency, halogens can shift the system toward chemically amplified ozone depletion, ash uptake can reduce the effective sulfur burden during the early phase, and dynamical state can control persistence and hemispheric expression. By separating these mechanisms, the study provides a compact basis for interpreting large volcanic perturbations to atmospheric chemistry and for designing targeted model experiments on extreme eruption scenarios. Full article
(This article belongs to the Section Aerosols)
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33 pages, 5511 KB  
Article
Hjorth Reliability Analysis and Its Applications Under Newly Adaptive Progressively First-Failure Censoring Plan
by Mazen Nassar, Refah Alotaibi and Ahmed Elshahhat
Axioms 2026, 15(6), 443; https://doi.org/10.3390/axioms15060443 - 13 Jun 2026
Viewed by 93
Abstract
This paper investigates classical and Bayesian inferences for the parameters and reliability metrics of the Hjorth distribution using a new censoring mechanism called the adaptive progressive first-failure censoring scheme. This new strategy combines guaranteed observation of a fixed number of failures with adaptive [...] Read more.
This paper investigates classical and Bayesian inferences for the parameters and reliability metrics of the Hjorth distribution using a new censoring mechanism called the adaptive progressive first-failure censoring scheme. This new strategy combines guaranteed observation of a fixed number of failures with adaptive control of test duration, providing a flexible and practically efficient framework for modern reliability experiments. The Hjorth distribution is considered due to its capability to model various hazard-rate shapes within a simple two-parameter structure. Maximum likelihood estimation is developed, and approximate confidence intervals are constructed using normal approximation and logarithmic transformation methods based on the observed Fisher information matrix and the delta method. A Bayesian framework is also established using independent gamma prior distributions, with posterior inference carried out through maximum a posteriori estimation and Markov chain Monte Carlo simulation. Bayes estimates and both equal-tail and highest-posterior-density credible intervals are obtained. The performance of the proposed methods is evaluated through simulation studies and illustrated using real lifetime data from an engineering domain consisting of the tensile strength of polyester fibers, demonstrating their effectiveness under adaptive censoring settings. Full article
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