Aborting a mission and initiating emergency rescue represent intuitive strategies for mitigating safety risks during mission execution. This study explores the management of emergency risks through adaptive rescue decisions. Our objective is to develop a dynamic decision-making approach for rescue that minimizes the expected costs associated with system malfunctions and mission failures, while also accounting for mission completion rewards. Most existing mission abort models presuppose a brand-new system prior to mission initiation and focus on formulating abort policies tailored to single-mission scenarios. By contrast, our work incorporates the system's initial age before mission execution and multiple sequential missions. To formalize this complex decision-making process, we conceptualize the sequential abort problem using a Markov decision process (MDP). Our findings reveal that optimal abort decisions rely on establishing control limits, which are derived from key parameters including the distributions of system lifetimes, mission durations, and rescue durations. Additionally, we identify specific conditions that dictate binary decisions: either continuing the mission under certain system states or aborting the mission across all possible states. We further provide sufficient conditions regarding the system's initial age prior to mission execution, which facilitate explicit differentiation between two scenarios: whether initiating the mission is optimal, and whether it is more advisable to avoid starting the mission. To demonstrate the practical relevance of our framework, we present detailed case studies focused on railway signal control systems.

This work introduces and examines a new probability distribution from the G-rank-mapped transmuted Fréchet-Weibull (G-RTFW) family, using both quadratic and cubic models. The Quadratic Rank Transmuted Fréchet-Weibull (QRTFW) and Cubic Rank Transmuted Fréchet-Weibull (CRTFW) distributions are specifically investigated, with the current study focused solely on the CRTFW model. We calculated and investigated a wide range of statistical and mathematical aspects of the CRTFW distribution, including its moments, moment generating function, characteristic function, quantile function, mode, random variate generation, hazard rate function, entropy, and order statistics. The suggested model is highly adaptable, capable of simulating both unimodal and bimodal behaviors, as well as tolerating symmetric and asymmetric data structures with variable degrees of kurtosis. The maximum likelihood method was used for parameter estimation, and a full Monte Carlo simulation study was carried out to assess the estimators' performance and efficiency under various circumstances. The simulation results showed that the estimators performed effectively, with bias and mean square error reducing as the sample size increased. To demonstrate the CRTFW distribution's practical application, two real-world sustainability-related datasets were examined. The CRTFW model outperformed numerous well-known lifetime and reliability distributions in terms of flexibility and goodness-of-fit, emphasizing its use for both theoretical and applied data modeling.

The paper introduces a generalized interval entropy measure that provides a comprehensive framework for understanding and quantifying the uncertainty in systems with doubly truncated random variables. By characterizing well-known lifetime distributions (exponential, Pareto, and finite range distributions), deriving a lower bound for the entropy, and exploring stochastic comparisons, the paper demonstrates the usefulness of this measure in reliability modelling, survival analysis and information theory.

The deployment of a technology typically follows an S-shaped curve, characterized by an initial phase of exponential growth, followed by a saturation phase where deployment slows and stabilizes at a maximum level. While existing literature has primarily focused on modeling and theorizing this growth pattern—particularly the early exponential phase—less attention has been paid to the long-term dynamics of sustaining a technological stock after its deployment peak. This gap is critical for incrementally evolving technologies without technical disruption, especially in the context of long-term industrial sustainability. In this study, we propose a model combining an S-curve deployment trajectory with a lifetime distribution of technological equipment, enabling us to simulate both the initial deployment and the subsequent renewal phases. Our key finding is that the characteristics of the deployment phase significantly influence the renewal dynamics. Specifically, when deployment is fast relative to equipment lifespan, production trajectories exhibit overshoot and oscillations—contrary to the smoother dynamics observed with slower deployment. Case studies, such as nuclear reactor deployment, illustrate these phenomena, revealing production overshoots exceeding 200%. We also present case studies on smartphones, passenger cars, consumer goods, photovoltaic panels, and wind turbines. These endogenous production cycles raise concerns about the post-deployment viability of industries, as observed in the nuclear sector. More broadly, our findings highlight the importance of anticipating long-term maintenance challenges for rapidly deployed technologies, a consideration that is particularly relevant in the context of the energy transition. This model provides a foundation for future work on the systemic implications of technology deployment and renewal in low-carbon transitions.

In this paper, we adopt the Ishita lifetime distribution to analyze biomedical science and engineering lifetime data under an accelerated life test (ALT) model. This data is exposed concerning the mechanism of a type-I generalized hybrid censoring scheme under a partially step-stress ALT model. The model parameters and the parameters of life (survival and hazard rate function) are estimated using maximum likelihood and Bayesian estimation. Also, the interval estimators are formulated with respect to the normal distribution of the maximum likelihood estimate, two parametric bootstrap confidence techniques, and Bayesian credible intervals. Two real data sets are analyzed to illustrate the proposed methods. Monte Carlo simulation is used to compare various methods.

Abstract Measure of uncertainty in past lifetime distribution plays an important role in the context of information theory, forensic science and other related fields. In the present work, we propose non-parametric kernel type estimator for generalized past entropy function, which was introduced by Gupta and Nanda [9], under $\alpha$ -mixing sample. The resulting estimator is shown to be weak and strong consistent and asymptotically normally distributed under certain regularity conditions. The performance of the estimator is validated through simulation study and a real data set.

We propose a geometry topological framework to analyze storm dynamics by coupling persistent homology with Anti-de Sitter (AdS)-inspired metrics. On radar images of a bow echo event, we compare Euclidean distance with three compressive AdS metrics (α = 0.01, 0.1, 0.3) via time-resolved H1 persistence diagrams for the arc and its internal cells. The moderate curvature setting (α=0.1) offers the best trade-off: it suppresses spurious cycles, preserves salient features, and stabilizes lifetime distributions. Consistently, the arc exhibits longer, more dispersed cycles (large-scale organizer), while cells show shorter, localized patterns (confined convection). Cross-correlations of H1 lifetimes reveal a temporal asymmetry: arc activation precedes cell activation. A differential indicator Δ(t) based on Wasserstein distances quantifies this divergence and aligns with the visual onset in radar, suggesting early warning potential. Results are demonstrated on a rapid Corsica bow echo; broader validation remains future work.

ABSTRACT Many modern products exhibit high reliability under normal operating conditions. Conducting life tests under these conditions may result in very few observed failures, insufficient for accurate inferences. Instead, accelerated life tests (ALTs) must be performed. One of the most popular ALT designs is the step‐stress test, which shortens the product's lifetime by progressively increasing the stress level at which units are subjected at some pre‐specified times. Classical estimation methods based on the maximum likelihood estimator (MLE) enjoy suitable asymptotic properties, but they lack robustness. That is, data contamination can significantly impact the statistical analysis. In this paper, we develop robust inferential methods for highly reliable devices based on the density power divergence (DPD) for estimating and testing under the step‐stress model with intermittent monitoring and Weibull lifetime distributions. We theoretically and empirically examine asymptotic and robustness properties of the minimum DPD estimators and associated Wald‐type test statistics. Moreover, we develop robust estimators and confidence intervals for some important lifetime characteristics. The effect of temperature in solar lights, medium power silicon bipolar transistors, and LED lights using real data arising from a step‐stress ALT is analyzed by applying the robust methods proposed.

E-Bayesian and hierarchical Bayesian inference of exponentiated lifetime distribution under adaptive progressively censored data with binomial removals

The reliability of ocean-going ship engine fuel systems is crucial for the safety and continuous operation of vessels. Failure of this system can lead to serious operational and economic consequences; therefore, effective diagnostics and failure prediction are essential elements of modern fleet management. This paper presents an analysis of the reliability of fuel systems based on operational data from ten bulk carriers operated by Polska Żegluga Morska in Szczecin. The analysis combined classical statistical methods with artificial intelligence algorithms to develop a hybrid diagnostic and forecasting framework. The Weibull lifetime distribution was applied to estimate time-to-failure parameters, revealing mixed failure mechanisms—random failures (k < 1) and aging-related processes (k > 1). Using the k-means algorithm, ships were automatically classified into two reliability groups: high-failure-rate units and stable operational vessels. Individual linear regression models were then developed for each ship to forecast the time to the next failure, achieving satisfactory predictive performance (R2 > 0.75 for most vessels). Sensitivity analysis quantified model robustness under different disturbance scenarios, yielding mean Relative Prediction Deviation (RPD) values of approximately 65% for Missing Data, 60% for False Failure, and 26% for Data Noise. These results confirm that the proposed hybrid reliability–AI framework is resistant to random noise but sensitive to incomplete or erroneous historical data. The developed approach provides an interpretable and effective tool for predictive maintenance, supporting reliability management and operational decision-making in marine engine systems. The article presents a hybrid model that has been developed to enable the detailed characterization of emergency processes and the identification of the most important factors that influence damage forecasting. For systems with variable failure risk, it was found that both classical probabilistic models and machine learning methods must be considered to interpret damage patterns correctly. Implementing data filtration and validation procedures before using data in artificial intelligence models has been shown to improve forecast stability and increase the usefulness of forecasts for planning repairs.

Major mergers of galaxies are likely to trigger bursty star formation activities. Usually, the accumulation of dense gas and the boost of star formation efficiency (SFE) are considered to be the two main drivers of starbursts. However, it remains unclear how each process operates on the scale of individual star-forming clouds. Here, we present a high-resolution ($2 radiation-hydrodynamic simulation of a gas-rich dwarf galaxy merger using the Realistic ISM modeling in Galaxy Evolution and Lifecycles (RIGEL) model to investigate how mergers affect the properties of the structure of dense star-forming gas and the cloud-scale SFE. With the unprecedented mass and temporal resolution of the simulations, we tracked the evolution of sub-virial dense clouds in the simulation by mapping them across successive snapshots spanning 200,Myr taken at intervals of 0.2,Myr. We find that the merger triggers a $130$ fold increase in the star formation rate (SFR) and shortens the galaxy-wide gas-depletion time by two orders of magnitude compared to those in two matched isolated galaxies. However, the depletion time of individual clouds and their lifetime distribution remained unchanged over the simulation period. The cloud life cycles and cloud-scale SFE are determined by local stellar feedback rather than such environmental factors as tidal fields regardless of the merger process, and the integrated SFE (ε_ of clouds in complex environments remains well-described by an ε_ relation found in idealized isolated-cloud experiments. During the peak of the starburst, the median cloud-scale integrated SFE was lower by only 0.17--0.33,dex compared to the value when the two galaxies were not interacting. The merger boosts the SFR primarily through the accumulation and compression of dense gas fueling star formation. Strong tidal torques assemble ≳10^ clouds, which seed massive stellar clusters. The average separation between star-forming clouds decreases during the merger, which in turn decreases the cloud--cluster spatial de-correlation from ≳1,kpc to ∼0.1,kpc depicted in tuning fork diagrams -- a testable prediction for future observations of interacting low-mass galaxies.

Abstract BACKGROUND Glioblastoma is one of the most aggressive brain cancers, marked by rapid progression and resistance to treatment. Its cellular heterogeneity and invasive nature make it particularly hard to manage. New tools are needed to better understand its biology and improve diagnostics and therapies. NADH Fluorescence Lifetime Imaging Microscopy (NADH-FLIM) is a promising technique that reveals metabolic states by measuring NADH fluorescence lifetime: shorter lifetimes indicate glycolysis, while longer lifetimes are linked to oxidative phosphorylation (OXPHOS). This enables the identification of metabolic heterogeneity in tumor tissues. MATERIAL AND METHODS We applied NADH-FLIM to formalin-fixed paraffin-embedded (FFPE) glioblastoma sections to assess NADH lifetime distribution in key tumor structures recognized by pathologists: (1) palisading cells near necrosis, (2) microvascular proliferation, and (3) neuronal and perivascular satellitosis. Additionally, we analyzed tumor cells overexpressing FGFR3 or carrying the IDH1 mutation to study their specific metabolic profiles. RESULTS Each tumor structure showed a distinct NADH lifetime signature, reflecting different metabolic states. For example, microvascular proliferation displayed lifetimes consistent with OXPHOS, while the surrounding tumoral astrocytic areas showed profiles more consistent with glycolysis. FLIM also identified isolated tumor cells in regions appearing histologically normal, including areas of early invasion. In FGFR3-overexpressing and IDH1-mutant cells, FLIM highlighted unique metabolic behaviors associated with these genetic changes. CONCLUSION NADH-FLIM enables precise mapping of metabolic heterogeneity in glioblastoma, offering insights beyond conventional histology. It can detect metabolically distinct tumor subpopulations, aiding in diagnosis and potentially guiding personalized therapies. This technique represents a significant step forward in understanding glioblastoma biology.

Alpha-synuclein (αsyn) misfolding and aggregation underlie several neurodegenerative disorders, including Parkinson's disease. Early oligomeric intermediates are particularly toxic yet remain challenging to detect and characterize within cellular systems. Here, we employed the luminescent conjugated oligothiophene h-FTAA to investigate early aggregation events of human wildtype (huWT) and A53T-mutated αsyn (huA53T) both in vitro and in HEK293 cells stably expressing native human-αsyn. Comparative fibrillation assays revealed that h-FTAA detected αsyn aggregation with higher sensitivity and earlier onset than Thioflavin T, with the A53T variant displaying accelerated fibrillation. HEK293 cells stably expressing huWT- or huA53T-αsyn were exposed to respective pre-formed fibrils (PFFs), assessed via immunocytochemistry, h-FTAA staining, spectral emission profiling, and fluorescence lifetime imaging microscopy (FLIM). Notably, huA53T PFFs promoted earlier aggregation patterns and yielded narrower fluorescence lifetime distributions compared with huWT PFFs. Spectral imaging showed h-FTAA emission maxima (~550-580 nm) red-shifted and broadened in cells along with variable lifetimes (0.68-0.87 ns), indicating heterogeneous aggregate conformations influenced by cellular milieu. These findings demonstrate that h-FTAA is useful for distinguishing early αsyn conformers in living systems and, together with stable αsyn-expressing HEK293 cells, offers a platform for probing early αsyn morphotypes. Taken together, this opens for further discovery of biomarkers and drugs that can interfere with αsyn aggregation.

Abstract. Meteorological processes such as gust fronts, roll structures, internal boundary-layer development and smaller-scale turbulence complicate the physical interpretation of measured aerosol particle properties, fluxes, and transport in the marine atmospheric boundary layer (MABL). To better decipher maritime aerosol measurements by aircraft, ships, and towers we describe an ensemble of particle trajectories using high-resolution large eddy simulations (LES) of surface-emitted aerosol particle within a Lagrangian framework. We identified two clusters of particle trajectory types from which we created probabilistic distributions of particle histories: (a) short-lived particles that do not exit the surface layer and are subsequently deposited back to the ocean; and (b) much older particles that are able to exit the surface layer into the mixed layer and subsequently oscillate up and down through convective roll structures. After emission in a neutral atmosphere, particles slowly disperse through the MABL requiring, on average, up to 100 min to mix to the ∼ 570 m deep mixed-layer inversion. However, for even slightly unstable conditions, particles are rapidly transported to the top of the MABL in roll structure updrafts, where they then more slowly diffuse downwards, with some similarities to a looping plume rise to the stable inversion followed by fumigation. Consequently, particles can exhibit a bimodal lifetime distribution that results in different particle ages by altitude. Further, based on wind speed and stability, the initial looping behavior following an emission event spans 15 to 30 min and may result in sampling “blind spots” up to 15 km downwind. Overall, our findings suggest that there should be a consideration of the representativeness of particle ages, even in what is often assumed to be a well-mixed MABL. This representativeness is related to how long particles have been suspended and whether they were sourced locally, which is critical for situations such as for measuring wind-generated emissions or ship track plumes. Further, the Lagrangian technique for treating the particle transport captures the inherently random motion of the MABL turbulence and does not exhibit artificial numerical diffusion. As such, it produces differences when compared to a traditional, column-based eddy-diffusivity approach used in mesoscale to global scale models. We used the LES to drive a one-dimensional (1D) column model to approximate single grid point physics. The results were starkly different near the surface, with the 1D column model missing the looping behavior and showing a slow upward dispersion. This difference in the 1D and LES frameworks is an excellent example of subgrid problems and may explain some of the differences between observations and global and mesoscale model simulations of marine particle vertical distribution and dry scavenging.

Inward-rectifier potassium (Kir) channels are essential for regulating various physiological processes and are implicated in several life-threatening diseases, making them key drug targets. KirBac1.1, a well-characterized prokaryotic homolog of Kir channels, is known to undergo anionic lipid-dependent gating. Although the slide helix is an important structural component in the gating mechanism of KirBac1.1, its structural dynamics associated with the anionic lipid-driven activation is not well understood. Here, we have reconstituted KirBac1.1 in zwitterionic 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and anionic POPC/ 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-(1′-rac-glycerol) (sodium salt) (POPG) membranes to stabilize the inactive and active conformations of the channel, respectively. Our liposome K+ flux assay results show that all the slide helix single-cysteine mutants display PG-driven gating, and increasing the PG from 25 to 40 mol% does not have any linear dependency on both the activation and K+ flux rates. Site-directed 7-nitrobenz-2-oxa-1,3,-diazol-4-yl (NBD) fluorescence results suggest that the structural dynamics of the slide helix is significantly altered upon PG-induced activation. For instance, we observe significant changes in hydration dynamics and rotational mobility of slide helix residues between functional states. Maximum entropy method-based lifetime distribution analysis suggests that the conformational heterogeneity of the slide helix is functional-state dependent. Importantly, membrane penetration depth measurements reveal that the slide helix in the active KirBac1.1 is located ~3 Å deeper within the membrane interface, well supported by increased fluorescence lifetimes. Notably, the non-linear relationship between structural dynamics and PG content highlights the critical role of lipid-protein interactions and membrane surface charge in PG-mediated KirBac1.1 activation. These findings provide valuable insights into Kir channel gating mechanisms and lipid-dependent gating of other channels.

Quantifying uncertainty in complex systems is a central problem in reliability analysis and engineering applications. In this work, we develop an information-theoretic framework for analyzing linear consecutive k-out-of-n:G systems using the cumulative residual Tsallis entropy (CRTE). A general analytical expression for CRTE is derived, and its behavior is investigated under various stochastic ordering relations, providing insight into the reliability of systems governed by continuous lifetime distributions. To address challenges in large-scale settings or with nonstandard lifetimes, we establish analytical bounds that serve as practical tools for uncertainty quantification and reliability assessment. Beyond theoretical contributions, we propose a nonparametric CRTE-based test for dispersive ordering, establish its asymptotic distribution, and confirm its statistical properties through extensive Monte Carlo simulations. The methodology is further illustrated with real lifetime data, highlighting the interpretability and effectiveness of CRTE as a probabilistic entropy measure for reliability modeling. The results demonstrate that CRTE provides a versatile and computationally feasible approach for bounding analysis, characterization, and inference in systems where uncertainty plays a critical role, aligning with current advances in entropy-based uncertainty quantification.

In this paper, we conduct statistical inferences on the process capability index $S_{pmk}^{\prime }$ for a lifetime distribution called the generalized KM exponential distribution. Some statistical properties of the distribution are reported, accompanied by figures that illustrate its shape characteristics based on the probability density function and the hazard rate function. The process capability index $S_{pmk}^{\prime }$ is used to evaluate processes that deviate from a non-normal distribution. The maximum likelihood estimate for $S_{pmk}^{\prime}$ is obtained using the invariance property of the maximum likelihood estimator. Furthermore, point estimates for $S_{pmk}^{^{\prime}}$ are derived based on least squares, weighted least squares, Anderson-Darling, and Cramér-von Mises estimators. Furthermore, two real data analyses are performed to assess the applicability of the $S_{pmk}^{^{\prime}}$ process capability index to the generalized KM exponential distribution.

This study explores the application of Tsallis entropy in evaluating uncertainty within the framework of consecutive k-out-of-n good systems, which are widely utilized in various reliability and engineering contexts. We derive new analytical expressions and meaningful bounds for the Tsallis entropy under various lifetime distributions, offering fresh insight into the structural behavior of system-level uncertainty. The approach establishes theoretical connections with classical entropy measures, such as Shannon and Rényi entropies, and provides a foundation for comparing systems under different stochastic orders. A nonparametric estimator is proposed to estimate the Tsallis entropy in this setting, and its performance is evaluated through Monte Carlo simulations. In addition, we develop a new entropy-based test for exponentiality, building on the distinctive properties of system lifetimes. So, Tsallis entropy serves as a flexible tool in both reliability characterization and statistical inference.

This study introduces the generalized multiple dependent state repetitive sampling plan, which integrates repetitive and generalized multiple dependent state sampling plans. The proposed plan is studied for the accelerated life test, which calculates the mean lifetime using the right-truncated Shanker distribution and considers economic design to reduce inspection costs. The acceleration factors of temperature and voltage are defined based on the Arrhenius model and the inverse power law model. The nonlinear optimization technique determines the optimal plan parameters of the proposed plan to satisfy consumer and producer risks simultaneously. A sensitivity analysis is performed to assess the impact of the model parameters on the proposed plan solution using an orthogonal experimental design with multiple linear regression. This study found that the proposed plan is more efficient in terms of the operating characteristic function, average sample number, and probability of taking additional samples. In addition, two real datasets are considered for the Shanker distribution and the right-truncated Shanker distribution, finding that two real datasets fit with the right-truncated Shanker distribution better than the Shanker distribution. The proposed plan was more flexible, efficient, and economical than the existing sampling plans for accelerated life tests following the right-truncated Shanker distribution.

Effective sample design has a major role in the quality of parameter estimation in statistical parameter estimation issues. The ranking set sampling (RSS) strategy is effective and a less costly option than simple random sampling (SRS). A novel mixture continuous lifetime distribution that has been proposed recently is the power Chris-Jerry distribution (PC-JD). It is useful for modeling a number of real data sets. This paper investigates the RSS approach for estimating the PC-JD’s parameters. There are roughly sixteen different techniques of estimation that are used, such as the maximum likelihood method, the percentiles method, some methods based on minimum distance, the Kolmogorov method, and some methods based on minimum and maximum spacing distances. In comparison to a SRS, the simulation research assesses the performance of the suggested RSS-based estimates in terms of some measures of accuracy. To identify the optimal estimating strategy, the partial and overall ranks of many estimates are shown. According to numerical results, the maximum likelihood approach seems to be quite beneficial in evaluating the estimated quality of RSS and SRS. RSS is a more effective sampling approach than SRS owing to its better efficiency. Additionally, the different estimation techniques with survival data for both sampling techniques are examined.