Search Results (358)

This paper presents a stochastic analysis of a two-unit cold standby system incorporating imperfect switching mechanisms. Each unit operates in one of three states: normal, partial failure, or total failure. Employing Markov processes, the study evaluates system reliability by examining the mean time to failure (MTTF) and steady-state availability metrics. Failure and repair times are assumed to follow exponential distributions, while the switching mechanism is modeled as either perfect or imperfect. The results highlight the significant influence of switching reliability on both MTTF and system availability. This analysis is crucial for optimizing the performance of complex systems, such as thermal power plants, where continuous and reliable operation is imperative. The study also aligns with recent research trends emphasizing the integration of preventive maintenance and advanced reliability modeling approaches to enhance overall system resilience. Full article

This paper presents the exponentiated power shanker (EPS) distribution, a fresh three-parameter extension of the standard Shanker distribution with the ability to extend a wider class of data behaviors, from right-skewed and heavy-tailed phenomena. The structural properties of the distribution, namely complete and incomplete moments, entropy, and the moment generating function, are derived and examined in a formal manner. Maximum likelihood estimation (MLE) techniques are used for estimation of parameters, as well as a Monte Carlo simulation study to account for estimator performance across varying sample sizes and parameter values. The EPS model is also generalized to a regression paradigm to include covariate data, whose estimation is also conducted via MLE. Practical utility and flexibility of the EPS distribution are demonstrated through two real examples: one for the duration of repairs and another for HIV/AIDS mortality in Germany. Comparisons with some of the existing distributions, i.e., power Zeghdoudi, power Ishita, power Prakaamy, and logistic-Weibull, are made through some of the goodness-of-fit statistics such as log-likelihood, AIC, BIC, and the Kolmogorov–Smirnov statistic. Graphical plots, including PP plots, QQ plots, TTT plots, and empirical CDFs, further confirm the high modeling capacity of the EPS distribution. Results confirm the high goodness-of-fit and flexibility of the EPS model, making it a very good tool for reliability and biomedical modeling. Full article

This paper introduces a novel and flexible class of continuous probability distributions, termed the Alpha Power Survival Ratio-X (APSR-X) family. Unlike many existing transformation-based families, the APSR-X class integrates an alpha power transformation with a survival ratio structure, offering a new mechanism for enhancing shape flexibility while maintaining mathematical tractability. This construction enables fine control over both the tail behavior and the symmetry properties, distinguishing it from traditional alpha power or survival-based extensions. We focus on a key member of this family, the two-parameter Alpha Power Survival Ratio Exponential (APSR-Exp) distribution, deriving essential mathematical properties including moments, quantile functions and hazard rate structures. We estimate the model parameters using eight frequentist methods: the maximum likelihood (MLE), maximum product of spacings (MPSE), least squares (LSE), weighted least squares (WLSE), Anderson–Darling (ADE), right-tailed Anderson–Darling (RADE), Cramér–von Mises (CVME) and percentile (PCE) estimation. Through comprehensive Monte Carlo simulations, we evaluate the estimator performance using bias, mean squared error and mean relative error metrics. The proposed APSR-X framework uniquely enables preservation or controlled modification of the symmetry in probability density and hazard rate functions via its shape parameter. This capability is particularly valuable in reliability and survival analyses, where symmetric patterns represent balanced risk profiles while asymmetric shapes capture skewed failure behaviors. We demonstrate the practical utility of the APSR-Exp model through three real-world applications: economic (tax revenue durations), engineering (mechanical repair times) and medical (infection durations) datasets. In all cases, the proposed model achieves a superior fit over that of the conventional alternatives, supported by goodness-of-fit statistics and visual diagnostics. These findings establish the APSR-X family as a unique, symmetry-aware modeling framework for complex lifetime data. Full article

Unmanned Aerial Vehicles (UAVs) are increasingly used in the new generation of communication systems. They serve as access points, base stations, relays, and gateways to extend network coverage, enhance connectivity, or offer communications services in places lacking telecommunication infrastructure. However, optimizing UAV placement in three-dimensional (3D) environments with diverse user distributions and uneven terrain conditions is a crucial challenge. Therefore, this paper proposes a novel framework to minimize UAV transmission power while ensuring a guaranteed data rate in realistic and complex scenarios. To this end, using the particle swarm optimization evolution (PSO-E) algorithm, this paper analyzes the impact of user-truncated distribution models for suburban, urban and dense urban environments. Extensive simulations demonstrate that dense urban environments demand higher power than suburban and urban environments, with uniform user distributions requiring the most power in all scenarios. Conversely, Gaussian and exponential distributions exhibit lower power requirements, particularly in scenarios with concentrated user hotspots. The proposed model provides insight into achieving efficient network deployment and power optimization, offering practical solutions for future communication networks in complex 3D scenarios. Full article

As China’s economy grows and travel demand increases, its aviation market has evolved to become the second-largest in the world. This study presents a pioneering analysis of China’s aviation network evolution (1990–2024) by integrating temporal dynamics into a network density matrix theory, addressing critical gaps in prior static network analyses. Unlike conventional studies focusing on isolated topological metrics, we introduce a triangulated methodology: ① a network sequence analysis capturing structural shifts in degree distribution, clustering coefficient, and path length; ② novel redundancy–entropy coupling quantifying complexity evolution beyond traditional efficiency metrics; and ③ economic-network coordination modeling with spatial autocorrelation validation. Key innovations reveal previously unrecognized dynamics: ① Time-embedded density matrices ($\rho$) demonstrate how sparsity balances information propagation efficiency ($\eta$) and response diversity, resolving the paradox of functional yet sparse connectivity. ② Redundancy–entropy synergy exposes adaptive trade-offs. Entropy ($H$) rises 18% (2000–2024), while redundancy ($R$) rebounds post-2010 (0.25→0.33), reflecting the strategic resilience enhancement after early efficiency-focused phases. ③ Economic-network coupling exhibits strong spatial autocorrelation ($Moran’sI>0.16$, $p<0.05$), with eastern China achieving “primary coordination”, while western regions lag due to geographical constraints. The empirical results confirm structural self-organization. Power-law strengthening, route growth exponentially outpacing cities, and clustering ($C$) rising 16% as the path length ($L$) increases, validating the hierarchical hub formation. These findings establish aviation networks as dynamically optimized systems where economic policies and topological laws interactively drive evolution, offering a paradigm shift from descriptive to predictive network management. Full article

For over a century, forgetting research has shown that recall decreases along a power or exponential function over time. It is tempting to assume that empirical forgetting curves are equivalent to the rate at which individual memories are forgotten. This assumption would be erroneous, because forgetting curves are influenced by an often-neglected factor: the distribution of memory strengths relative to a recall threshold. For example, if memories with normally distributed initial strengths were forgotten at a linear rate, percent correct would not be linear, it would decrease rapidly when the peak of the distribution was crossing the recall threshold and slowly when one of the tails was crossing the threshold. We describe a distribution model of memory that explains the divergence between forgetting curves and item forgetting rates. The model predicts that forgetting curves can be approximately linear (or even concave, like the right side of a frown) when percent correct is high. This prediction was supported by previous evidence and an experiment where participants learned word pairs to a criterion. Beyond its theoretical implications, the distribution model also has implications for education: Creating memories that are just above the threshold helps on short-term tests but does not form lasting memories. Full article

The progressive proliferation of sensor deployment in distribution networks (DNs), propelled by the dual drivers of power automation and ubiquitous IoT infrastructure development, has precipitated exponential growth in real-time data generated by multisource heterogeneous (MSH) sensors within multilayer grid architectures. This phenomenon presents dual implications: large-scale datasets offer an enhanced foundation for reliability assessment and dispatch planning in DNs; the dramatic escalation in data volume imposes demands on the computational precision and response speed of traditional evaluation approaches. The identification of critical influencing factors under extreme operating conditions, coupled with dynamic assessment and prediction of DN reliability through MSH data approaches, has emerged as a pressing challenge to address. Through a brief analysis of existing technologies and algorithms, this article reviews the technological development of MSH data analysis in DNs. By integrating the stability advantages of conventional approaches in practice with the computational adaptability of artificial intelligence, this article focuses on discussing key approaches for MSH data processing and assessment. Based on the characteristics of DN data, e.g., diverse sources, heterogeneous structures, and complex correlations, this article proposes several practical future directions. It is expected to provide insights for practitioners in power systems and sensor data processing that offer technical inspirations for intelligent, reliable, and stable next-generation DN construction. Full article

In football, local interactions between players generate long-term game trends at the global scale, and vice versa—the global trends also influence individual decisions and actions. The harmonization of local and global scales often creates self-organizing spatiotemporal patterns in the movements of players and the ball. In this study, we confirmed that, in real football games, the probability distribution of the ball-keeping duration tends to obey negative power-law behavior, exhibiting hierarchical fractal self-similarity at both the local scale (i.e., individual-player level) and at the global scale (i.e., whole-game level). Furthermore, we found that the probability distribution functions transitioned from an exponential distribution to a power-law distribution at a certain characteristic time and that the characteristic time was equal to the upper limit of the time during which the trend of the game was maintained. Full article

This paper investigates an understudied generalization of the classical exponential, Rayleigh, and Weibull distributions, known as the power generalized Weibull distribution, particularly in the context of censored data. Characterized by one scale parameter and two shape parameters, the proposed model offers enhanced flexibility for modeling diverse lifetime data patterns and hazard rate behaviors. Notably, its hazard rate function can exhibit five distinct shapes, including upside-down bathtub and bathtub shapes. The study focuses on classical and Bayesian estimation frameworks for the model parameters and associated reliability metrics under a unified hybrid censoring scheme. Methodologies include both point estimation (maximum likelihood and posterior mean estimators) and interval estimation (approximate confidence intervals and Bayesian credible intervals). To evaluate the performance of these estimators, a comprehensive simulation study is conducted under varied experimental conditions. Furthermore, two empirical applications on real-world cancer datasets underscore the efficacy of the proposed estimation methods and the practical viability and flexibility of the explored model compared to eleven other existing lifespan models. Full article

Probability models are instrumental in a wide range of applications by being able to accurately model real-world data. Over time, numerous probability models have been developed and applied in practical scenarios. This study introduces the AAP-X family of distributions—a novel, flexible framework for continuous data analysis named after authors Aadil Ajaz and Parvaiz. The proposed family effectively accommodates both symmetric and asymmetric characteristics through its shape-controlling parameter, an essential feature for capturing diverse data patterns. A specific subclass of this family, termed the “AAP Exponential” (AAPEx) model is designed to address the inflexibility of classical exponential distributions by accommodating versatile hazard rate patterns, including increasing, decreasing and bathtub-shaped patterns. Several fundamental mathematical characteristics of the introduced family are derived. The model parameters are estimated using six frequentist estimation approaches, including maximum likelihood, Cramer–von Mises, maximum product of spacing, ordinary least squares, weighted least squares and Anderson–Darling estimation. Monte Carlo simulations demonstrate the finite-sample performance of these estimators, revealing that maximum likelihood estimation and maximum product of spacing estimation exhibit superior accuracy, with bias and mean squared error decreasing systematically as the sample sizes increases. The practical utility and symmetric–asymmetric adaptability of the AAPEx model are validated through five real-world applications, with special emphasis on cancer survival times, COVID-19 mortality rates and reliability data. The findings indicate that the AAPEx model outperforms established competitors based on goodness-of-fit metrics such as the Akaike Information Criteria (AIC), Schwartz Information Criteria (SIC), Akaike Information Criteria Corrected (AICC), Hannan–Quinn Information Criteria (HQIC), Anderson–Darling (A*) test statistic, Cramer–von Mises (W*) test statistic and the Kolmogorov–Smirnov (KS) test statistic and its associated p-value. These results highlight the relevance of symmetry in real-life data modeling and establish the AAPEx family as a powerful tool for analyzing complex data structures in public health, engineering and epidemiology. Full article

The classical exponential model, despite its flexibility, fails to describe data with non-constant failure or between-event dependency. To overcome this limitation, two new bivariate lifetime distributions are introduced in this paper. The Farlie–Gumbel–Morgenstern (FGM)-based and Ali–Mikhail–Haq (AMH)-based modified Fréchet–exponential (MFE) models, by embedding the flexible MEF margin in the FGM and AMH copulas. The resulting distributions accommodate a wide range of positive or negative dependence while retaining analytical traceability. Closed-form expressions for the joint and marginal density, survival, hazard, and reliability functions are derived, together with product moments and moment-generating functions. Unknown parameters are estimated through the maximum likelihood estimation (MLE) and inference functions for margins (IFM) methods, with asymptotic confidence intervals provided for these parameters. An extensive Monte Carlo simulation quantifies the bias, mean squared error, and interval coverage, indicating that IFM retains efficiency while reducing computational complexity for moderate sample sizes. The models are validated using two real datasets, from the medical sector regarding the infection recurrence times of 30 kidney patients undergoing peritoneal dialysis, and from the economic sector regarding the growth of the gross domestic product (GDP). Overall, the proposed copula-linked MFE distributions provide a powerful and economical framework for survival analysis, reliability, and economic studies. Full article

As our society becomes increasingly digitized, the demand for computing power provided by data centers continues to grow; consequently, operating costs are increasing exponentially. Data centers supply virtualized servers to customers, primarily in the form of lightweight containers. Since the number of containers to be allocated is fixed, they should be optimally placed on physical servers to minimize the number of required servers and reduce costs. However, current data center operations do not prioritize reducing the number of physical servers through optimized container placement. Instead, containers are distributed across existing servers primarily to maintain stability. Therefore, costs associated with servers, auxiliary facilities, and electricity consumption have increased. To address this issue, we propose an optimization method that ensures economic efficiency without compromising system stability. Specifically, we utilize deep reinforcement learning (DRL), which has been widely applied in various fields, to optimize container placement. Our approach outperforms traditional heuristic algorithms and offers the additional advantage of handling fixed-size inputs, enabling flexible operation regardless of the number of containers. Using DRL in container placement has further reduced the number of servers and operating costs while enhancing overall system flexibility. Full article

Load frequency control (LFC) is essential for maintaining the stability of power systems subjected to load variations and renewable energy disturbances. This paper presents two advanced Proportional–Integral–Derivative–Acceleration (PIDA) controllers optimized using hybrid techniques: Teaching–Learning-Based Optimization combined with transit search (PIDA-TLBO-TS) and with Exponential Distribution Optimization (PIDA-TLBO-EDO). The proposed hybrid optimization approaches integrate global exploration and local exploitation capabilities to achieve near-global optimal solutions with superior convergence performance. Three test scenarios are studied to assess controller performance: a load disturbance in area 1, a disturbance in area 2, and a disturbance introduced by stochastic wave energy input. In each case, the proposed hybrid controllers are benchmarked against the conventional TLBO-based PIDA controller available in the literature. Simulation results confirm that the hybrid PIDA-TLBO-EDO controller consistently outperforms the alternatives in terms of peak-to-peak oscillation, root mean square (RMS) error, settling time, and overshoot. Specifically, it achieves a 0.49% to 15% reduction in peak-to-peak oscillations and a 2.5% to 18% improvement in RMS error, along with a 10.27% improvement in tie-line power deviation and a 15.38% reduction in frequency oscillations under wave energy disturbances. Moreover, the PIDA structure, enhanced by its acceleration term, contributes to better dynamic response compared to traditional controller designs. The results highlight the effectiveness and robustness of the proposed hybrid controllers in damping oscillations and maintaining system stability, particularly in modern power systems with high levels of renewable energy integration. This study emphasizes the potential of combining complementary optimization techniques to enhance LFC system performance under diverse and challenging conditions. Full article

With the increasing demand for power supply reliability, efficient load restoration in large-scale distribution networks post-outage scenarios has become a critical challenge. However, traditional methods become computationally prohibitive as network expansion leads to exponential growth of decision variables. This study proposes a multi-agent reinforcement learning (MARL) framework enhanced by distribution network partitioning to address this challenge. Firstly, an improved Girvan–Newman algorithm is employed to achieve balanced partitioning of the network, defining the state space of each agent and action boundaries within the multi-agent system (MAS). Subsequently, a counterfactual reasoning framework solved by the QTRAN-alt algorithm is incorporated to refine action selection during training, thereby accelerating convergence and enhancing decision-making efficiency during execution. Experimental validation using a 27-bus system and a 70-bus system demonstrates that the proposed QTRAN-alt with the Girvan–Newman method achieves fast convergence and high returns compared to typical MARL approaches. Furthermore, the proposed methodology significantly improves the success rate of full system restoration without violating constraints. Full article

Quantifying changes in soil properties greatly benefits our understanding of soil management and sustainable land use, especially in the context of strong anthropogenic activities and climate change. This study investigated the effects of long-term reclamation on soil properties in an artificial oasis region with a cultivation history of more than 50 years. Critical soil properties were measured at 77 sites, and a total of 462 soil samples were collected down to a depth of 1 m, which captures both surface and subsurface processes that are critical for long-term cultivation effects. Thirteen critical soil properties were analyzed, among which four properties—soil organic carbon (SOC), total phosphorus (TP), pH, and ammonium nitrogen (NH₄⁺)—were selected for detailed analysis due to their ecological significance and low intercorrelation. By comparing cultivated soils with nearby desert soils, this study found that semicentennial cultivation led to significant improvements in soil properties, including increased concentrations of SOC, NH₄⁺, and TP, as well as reduced pH throughout the soil profile, indicating improved fertility and reduced alkalinity. Further analysis suggested that environmental factors—including temperature, clay content, evaporation differences between surface and subsurface layers, sparse vegetation cover, cotton root distribution, as well as prolonged irrigation and fertilization—collectively contributed to the enhancement of SOC decomposition and the reduction of soil alkalinity. Furthermore, three-dimensional digital soil mapping was performed to investigate the effects of long-term cultivation on the distributions of soil properties at unvisited sites. The soil depth functions were separately fitted to model the vertical variation in the soil properties, including the exponential function, power function, logarithmic function, and cubic polynomial function, and the parameters were extrapolated to unvisited sites via the quantile regression forest (QRF), boosted regression tree, and multiple linear regression techniques. The QRF technique yielded the best performance for SOC (R² = 0.78 and RMSE = 0.62), TP (R² = 0.79 and RMSE = 0.12), pH (R² = 0.78 and RMSE = 0.10), and NH₄⁺ (R² = 0.71 and RMSE = 0.38). The results showed that depth function coupled with machine learning methods can predict the spatial distribution of soil properties in arid areas efficiently and accurately. These research conclusions will lead to more effective targeted measures and guarantees for local agricultural development and food security. Full article