Search Results (358)

In recent years, there has been growing interest in discrete probability distributions due to their ability to model the complex behavior of real-world count data. In this paper, a new discrete mixture distribution based on two Weibull components is introduced, constructed using the general discretization approach. Several important statistical properties of the proposed distribution, including the survival function, hazard rate function, alternative hazard rate function, moments, quantile function, and order statistics are derived. It was concluded from the descriptive measures that the discrete mixture of two Weibull distributions transitions from being positively skewed with heavy tails to a more symmetric and light-tailed form. This demonstrates the high flexibility of the discrete mixture of two Weibull distributions in capturing a wide range of shapes as its parameter values vary. Estimation of the parameters is performed via maximum likelihood under Type II censoring scheme. A simulation study assesses the performance of the maximum likelihood estimators. Furthermore, the applicability of the proposed distribution is demonstrated using two real-life datasets. In summary, this paper constructs the discrete mixture of two Weibull distributions, investigates its statistical characteristics, and estimates its parameters, demonstrating its flexibility and practical applicability. These results highlight its potential as a powerful tool for modeling complex discrete data. Full article

Quantitative analyses in drug-delivery research are frequently distributed across multiple tools, which increases manual handling and the risk of transcription errors. NanoEDW 1.0 is an open source Python application that integrates calibration-curve generation, encapsulation-efficiency (EE%) calculation, and release kinetics modeling in a single, streamlined workflow. This study aims to validate the performance of NanoEDW 1.0 by benchmarking it against spreadsheet/OriginLab^® OriginPro 2025 analyses on experimental datasets from polymeric nanocarrier systems commonly used in drug encapsulation. The software performs linear regression to convert absorbance into concentration, computes EE% from raw experimental values, and fits drug-release profiles to classical models (including zero/first-order, Higuchi, Korsmeyer–Peppas, Weibull, and Modified Gompertz) using non-linear least squares with standard goodness-of-fit metrics (R², RMSE). Results show close agreement with reference workflows for calibration parameters and EE%, as well as statistically comparable release-model fits, while reducing manual steps and analysis time. In conclusion, the validation confirms that NanoEDW 1.0 can streamline routine analyses and enhance reproducibility and accessibility in nanopharmaceutical research; source code and example datasets are provided to foster adoption. Full article

This study presents a methodology for optimizing repair intervals of mining equipment by integrating economic efficiency and reliability criteria. A review of existing maintenance strategies revealed their limitations, and a mathematical model was developed that incorporates both projected financial expenditures and the probability of equipment failures, enabling more accurate prediction of the optimal repair timing. This study introduces a novel integration of the Weibull reliability distribution with a cost-convolution optimization model, explicitly capturing the trade-off between economic efficiency and failure risk. Unlike traditional fixed-schedule approaches, the proposed model provides analytically optimized repair intervals derived from observed degradation trends. Statistical analysis demonstrates that unplanned repairs are, on average, 56% more costly than scheduled ones, highlighting the need to revise current preventive maintenance practices. The cost comparison is based on 34 restoration records collected from publicly available supplier price lists and field maintenance logs, converted into a unified currency. Based on operational data and reliability parameter estimation, the optimal repair interval was determined to be 5129 machine hours, which minimizes both the probability of failure and total maintenance-related financial losses, while reducing unplanned downtime. Unlike traditional fixed-schedule approaches, the proposed model allows adaptive adjustment of maintenance intervals according to the actual degradation characteristics of the equipment. The practical significance of the research lies in its ability to help mining enterprises reduce expenditures on corrective repairs, extend the service life of machinery, and improve overall operational efficiency. The findings contribute to advancing maintenance optimization in the mining industry, supporting more sustainable and cost-effective equipment management. Full article

Particle size distribution (PSD), also referred to as grain-size distribution (GSD), is a fundamental characteristic of granular materials, influencing packing density, porosity, permeability, and mechanical behavior across soils, sediments, and industrial powders. Accurate and reproducible representation of PSD is essential for computational modeling, digital twin development (i.e., virtual replicas of physical systems), and machine learning applications in geosciences and engineering. Despite the widespread use of classical distributions (log-normal, Weibull, Gamma), there remains a lack of systematic frameworks for generating synthetic datasets with controlled statistical properties and reproducibility. This paper introduces a unified computational framework for generating virtual PSDs/GSDs with predefined statistical characteristics and a specified number of grain-size fractions. The approach integrates parametric modeling with two histogram-based allocation strategies: the equal-width method, maintaining uniform bin spacing, and the equal-probability method, distributing grains according to quantiles of the target distribution. Both methods ensure statistical representativeness, reproducibility, and scalability across material classes. The framework is demonstrated on representative cases of soils (Weibull), sedimentary and industrial materials (Gamma), and food powders (log-normal), showing its generality and adaptability. The generated datasets can support sensitivity analyses, experimental validation, and integration with discrete element modeling, computational fluid dynamics, or geostatistical simulations. Full article

Reliable estimation of low-flow statistics is essential for water quality regulation, ecological protection, and drought management. This study evaluates traditional univariate and two-component Mixture Probability Distributions for modeling 7-day annual minimum flows (7Q) using records from 293 gauging stations across Mexico’s 37 hydrological planning regions, each with at least 20 years of data. Candidate models include Lognormal-3, Gamma-3, Gumbel, Weibull-3, and mixtures (Gumbel–Gumbel, Gumbel–Weibull-3, Weibull-3–Gumbel, Weibull-3–Weibull-3). Parameters are estimated by maximum likelihood, goodness-of-fit is assessed with Kolmogorov–Smirnov and Anderson–Darling tests. Sampling uncertainty is quantified via nonparametric bootstrap, providing 95% confidence intervals for design return levels, including 7Q10. Mixture models are selected as the best fit at 253 of 293 stations (86.3%), with Weibull-3–Weibull-3 dominating (45.1% of all stations) followed by Gumbel–Weibull-3 and Weibull-3–Gumbel; univariate models account for only 13.7% of cases, mainly Lognormal-3, and Gumbel alone is never preferred. Gumbel-only and symmetric G–G mixtures yield negative low-flow return levels at some sites and are therefore considered physically implausible. In contrast, mixtures containing Weibull-3 components ensure non-negative support, provide superior fit to the lower tail, and generally produce narrower bootstrap confidence intervals than the best univariate alternatives, indicating more stable and defensible 7Q10 estimates and providing an additional criterion to distinguish between models with similar goodness-of-fit statistics. These findings have direct implications for Environmental Impact Assessment, effluent permitting, ecological flow setting, drought planning, and regional water policy. The results support integrating Weibull-based mixtures—especially Weibull-3–Weibull-3 and Gumbel–Weibull-3—into Mexico’s national framework for low-flow frequency analysis and regulatory design. Full article

The use of conventional fuel sources from the Earth to generate electrical power leads to several environmental issues such as carbon emissions and ozone depletion. Energy generation from renewable energy sources is one of the most affordable and cleanest techniques. However, the generation of power from non-conventional sources like solar and wind requires the examination of established locations where these resources are plentiful and easily accessible. In this study, an investigation of solar and wind is performed at five different sites in various locations in India. For this examination, data on solar irradiance ($\mathrm{W}/{\mathrm{m}}^2$) and wind speed ($\mathrm{m}/\mathrm{s}$) is taken from the “NASA POWER DAV v.2.5.22” Data Access Viewer created by NASA. The data for solar and wind was taken at hourly intervals. The period of the investigation was ten years, i.e., from January 2014 to December 2023. The solar and wind potential analysis was performed in a probabilistic way to determine the parameters that support the installation of solar–PV panels and wind energy generators at the examined sites for the generation of power from these spontaneously available sources, respectively. To examine the potential of solar and wind sites, the Beta and Weibull probability distribution function (PDF) was used. The parameter estimation of the Beta and Weibull PDF was performed via the Maximum Likelihood method. The chosen method is known for its accuracy and efficiency in handling large datasets. Some key performance prediction indicators were analyzed for the investigated solar and wind locations. The findings provide valuable insights that support renewable energy planning and the optimal design of hybrid power systems. Full article

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. Full article

This paper proposes a novel statistical test for evaluating exponentiality against the recently introduced EBUCL (Exponential Better than Used in Convex Laplace transform order) class of life distributions. The EBUCL class generalizes classical aging concepts and provides a flexible framework for modeling various non-exponential aging behaviors. The test is constructed using Laplace transform ordering and is shown to be effective in distinguishing exponential distributions from EBUCL alternatives. We derive the test statistic, establish its asymptotic properties, and assess its performance using Pitman’s asymptotic efficiency under standard alternatives, including Weibull, Makeham, and linear failure rate distributions. Critical values are obtained through extensive Monte Carlo simulations, and the power of the proposed test is evaluated and compared with existing methods. Furthermore, the test is extended to handle right-censored data, demonstrating its robustness and practical applicability. The effectiveness of the procedure is illustrated through several real-world datasets involving both censored and uncensored observations. The results confirm that the proposed test is a powerful and versatile tool for reliability and survival analysis. Full article

This paper introduces a novel three-parameter probability model, the unit-Gompertz–Makeham (UGM) distribution, designed for modeling bounded data on the unit interval (0,1). By transforming the classical Gompertz–Makeham distribution, we derive a unit-support distribution that flexibly accommodates a wide range of shapes in both the density and hazard rate functions, including increasing, decreasing, bathtub, and inverted-bathtub forms. The UGM density exhibits rich patterns such as symmetric, unimodal, U-shaped, J-shaped, and uniform-like forms, enhancing its ability to fit real-world bounded data more effectively than many existing models. We provide a thorough mathematical treatment of the UGM distribution, deriving explicit expressions for its quantile function, mode, central and non-central moments, mean residual life, moment-generating function, and order statistics. To facilitate parameter estimation, eight classical techniques, including maximum likelihood, least squares, and Cramér–von Mises methods, are developed and compared via a detailed simulation study assessing their accuracy and robustness under varying sample sizes and parameter settings. The practical relevance and superior performance of the UGM distribution are demonstrated using two real-world engineering datasets, where it outperforms existing bounded models, such as beta, Kumaraswamy, unit-Weibull, unit-gamma, and unit-Birnbaum–Saunders. These results highlight the UGM distribution’s potential as a versatile and powerful tool for modeling bounded data in reliability engineering, quality control, and related fields. Full article

This study investigates date palm fiber (DPF) and sheep wool hybrid polyester composites with fiber loadings of 0%, 10%, 20%, and 30% by weight, fabricated by compression molding, to develop a sustainable and reliable material system. Experimental data from prior work were modeled using Weibull analysis for reliability evaluation and response surface methodology (RSM) for multi-objective optimization. Weibull statistics fitted a two-parameter distribution to tensile strength and fracture toughness, extracting shape (η) and scale ($\beta$) parameters to quantify variability and failure probability. The analysis showed that 20% hybrid content achieved the highest scale values ($\beta$ = 28.85 MPa for tensile strength and $\beta$ = 15.03 $\mathrm{M}\mathrm{P}\mathrm{a}\sqrt{\mathrm{m}}$ for fracture toughness) and comparatively low scatter (η = 10.39 and 9.2, respectively), indicating superior reliability. RSM quadratic models were developed for tensile strength, fracture toughness, thermal conductivity, acoustic attenuation, and water absorption, and were combined using desirability functions. The RSM optimization was found at 18.97% fiber content with a desirability index of 0.673, predicting 25.89 MPa tensile strength, 14.23 $\mathrm{M}\mathrm{P}\mathrm{a}\sqrt{\mathrm{m}}$ fracture toughness, 0.08 W/m·K thermal conductivity, 20.49 dB acoustic attenuation, and 5.11% water absorption. Overlaying Weibull cumulative distribution functions with RSM desirability surfaces linked probabilistic reliability zones (90–95% survival) to the deterministic optimization peak. This integration establishes a unified framework for designing natural fiber composites by embedding reliability into multi-property optimization. Full article

Increasing the amount of data with complex dynamics requires the constant updating of statistical distributions. This study aimed to introduce a new three-parameter distribution, named the new exponentiated Weibull (NEW) distribution, by applying the logarithmic transformation to the exponentiated Weibull distribution. The exponentiated Weibull distribution is a powerful generalization of the Weibull distribution that includes several classical distributions as special cases—Weibull, exponential, Rayleigh, and exponentiated exponential—which make it capable of capturing diverse forms of hazard functions. By combining the advantages of the logarithmic transformation and exponentiated Weibull, the new distribution offers great flexibility in modeling different forms of hazard functions, including increasing, J-shaped, reverse-J-shaped, and bathtub-shaped functions. Some mathematical properties of the NEW distribution were studied. Moreover, four different methods of estimation—the maximum likelihood (ML), least squares (LS), Cramer–Von Mises (CVM), and percentile (PE) methods—were employed to estimate the distribution parameters. To assess the performance of the estimates, three simulation studies were conducted, showing the benefit of the ML method, followed by the PE method, in estimating the model parameters. Additionally, five datasets were used to evaluate the effectiveness of the new distribution in fitting real data. Compared with some Weibull-type extensions, the results demonstrate the superiority of the new distribution in modeling various forms of real data and provide evidence for the applicability of the new distribution. Full article

This paper discusses whether the principal response features of composites subjected to fatigue loadings, including residual strength and lifetime statistics under variable amplitude (VA) loadings, can be resolved based on constant amplitude (CA) fatigue life data. The approach is based on the strength-residual strength-life equal-rank assumption (SRSLERA), providing a statistical correspondence between the static strength, residual strength, and fatigue life distribution functions under CA loadings. Under VA loadings, the strength degradation progression and then the fatigue lifetime are calculated by dividing the loading spectrum into a sequence of CA block loadings of given extents (including one cycle), and assuming that the strength at the end of a generic block loading equals the strength at the start of the consecutive one, namely the equivalent residual strength assumption (ERSA). The consequences of SRSLERA and ERSA are first discussed by re-elaborating a series of uniaxial, statistically sound CA residual strength and fatigue life data obtained under different loading ratios, R, ranging from pure tension to mixed tension–compression to pure compression. It is shown that the static strength Weibull’s shape and scale parameters, as well as the fatigue formulation parameters recovered under pure compression or tension loadings, represent the fingerprint of composite materials subjected to fatigue and characterize their uniqueness. The residual strength statistics, fatigue probability density functions (PDFs), and constant life diagram (CLD) construction are theoretically reported. Then, based on ERSA, the statistical lifetimes under VA loadings and the cycle-by-cycle damage progressions of block repeated loadings are analyzed, and a residual strength-based damage rule is compared to Miner’s rule. Full article

The exponential distribution is one of the most popular models for fitting lifetime data. This study proposes a novel generalization of the exponential distribution, referred to as the exponentiated generalized Weibull exponential, for the modeling of lifetime data. This new distribution is a member of a family that combines two well-known distribution families: the exponentiated generalized family and the T-X family. It has five parameters, allowing it to fit data that exhibit increasing, decreasing, bathtub, upside-down bathtub, S-shaped, J-shaped and reversed-J hazard rates. Some mathematical and statistical properties of the newly suggested distribution are derived and the estimation of its parameters is studied using the method of maximum likelihood. Different simulation studies have been applied to evaluate the parameter estimation. Four lifetime datasets are analyzed to investigate the superiority of the proposed exponentiated generalized Weibull exponential distribution. A regression model based on the proposed distribution is then developed for both complete and censored samples, and its performance is assessed on two real datasets. The new distribution and its associated regression model are empirically demonstrated to be practically useful. Full article

This study evaluates GPM-IMERG (Global Precipitation Measurement-Integrated Multi-satellite Retrievals) and CHIRPS (Climate Hazards Group InfraRed Precipitation with Stations) satellite precipitation data in Türkiye’s Akçay Sub-Basin by comparing them with rain gauge observations from the Finike and Elmali meteorological stations. Statistical metrics including Pearson’s correlation coefficient, Nash-Sutcliffe Efficiency (NSE), and Root Mean Square Error (RMSE) were used to assess performance. The study also examines distributional fit via the Kolmogorov–Smirnov (K-S) test and evaluates extreme rainfall detection accuracy using metrics like Probability of Detection (POD), False Alarm Ratio (FAR), and Critical Success Index (CSI). Results indicate that GPM-IMERG agrees well with rain gauge observations at the monthly scale (Pearson = 0.943; RMSE = 50.81 mm), but shows reduced accuracy at the daily scale (Pearson = 0.592; RMSE = 12.45 mm). The K-S test showed that the Beta distribution best fits monthly rainfall (threshold = 253.39 mm), while the Weibull distribution suits daily rainfall (threshold = 5.34 mm). GPM-IMERG achieved a POD of 0.778 and FAR of 0.222 for monthly extremes, while daily performance was lower (POD = 0.478; FAR = 0.388). These findings highlight the value of comparing satellite and ground-based data to improve flood risk assessment and enhance climate resilience in data-scarce basins. Full article

Life distribution comparison is important in reliability and survival analysis to model system aging and longevity. The article develops a non-parametric hypothesis test procedure for testing exponentiality against the Used Better than Aged in Laplace transform (UBAL) family of life distributions. The test in this case is developed based on moment inequalities in the Laplace transform, which yields a computationally straightforward and theoretically sound methodology. We establish the asymptotic behavior of the test statistic and evaluate its performance through Monte Carlo simulations, showing acceptable power against common alternatives such as the Weibull, linear failure rate, and Makeham distributions. Critical values are also provided for practical use under complete and right-censored data. The usefulness of the procedure is also illustrated on real medical data sets, including leukemia, liver cancer, and lung cancer patient survival times, and COVID-19 deaths data. The results indicate the applicability and success of the proposed method in detecting deviations from exponentiality. Overall, this research contributes a handy statistical method for reliability, risk analysis, and medical survival analysis, where system aging is of the utmost importance. Full article