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The proportion of explained variance is an important statistic in multiple regression for determining how well the outcome variable is predicted by the predictors. Earlier research on 20 different estimators for the proportion of explained variance, including the exact Olkin–Pratt estimator and the Ezekiel estimator, showed that the exact Olkin–Pratt estimator produced unbiased estimates, and was recommended as a default estimator. In the current study, the same 20 estimators were studied in incomplete data, with missing data being treated using multiple imputation. In earlier research on the proportion of explained variance in multiply imputed data sets, an estimator called R̂SP2 was shown to be the preferred pooled estimator for regular R2. For each of the 20 estimators in the current study, two pooled estimators were proposed: one where the estimator was the average across imputed data sets, and one where R̂SP2 was used as input for the calculation of the specific estimator. Simulations showed that estimates based on R̂SP2 performed best regarding bias and accuracy, and that the Ezekiel estimator was generally the least biased. However, none of the estimators were unbiased at all times, including the exact Olkin–Pratt estimator based on R̂SP2. [ABSTRACT FROM AUTHOR]

We demonstrate that the recently introduced triple generally weighted moving average (GWMA) chart and its counterpart, the double GWMA chart, incorporate sub‐optimal weighting patterns that may assign more weight to certain historical data points at the expense of more recent ones. Moreover, these control charts, when compared to the exponentially weighted moving average (EWMA) chart, exhibit a substantial computational burden. Our findings underscore that a well‐designed EWMA chart offers superior overall performance in comparison to these control charts. [ABSTRACT FROM AUTHOR]

This paper introduces the Monte Carlo simulation (MCS) procedure in combination with an effective finite element method (FEM) based on the refined first-order shear deformation theory (r-FSDT) to examine the random vibration of functionally graded sandwich (FGS) plates with different skin layers subjected to double explosive load (DEL). In the stochastic design methodology, the formulation of the state function for design conditions commonly involves integrating random input parameters, assumed distribution functions, and the stochastic responses derived from problem models. The motion equation of the FGS plate is derived by using Hamilton’s principle. Then, the Newmark-beta method is applied to solve linear second-order ordinary differential equations. Finally, the random vibration of the FGS plate is studied by considering the normal distribution parameters. In general, this research tries to shed light on the effects of geometric parameters and material properties and guide the design of FGS plates subjected to double explosive load with uncertain input parameters. [ABSTRACT FROM AUTHOR]

Asymmetrical probability models are helpful for analyzing skewed data sets since they allow you to describe the form of the distribution and anticipate the chance of extreme events. This article defines a novel approach to continuous moment exponential distribution called the exponentiated generalized moment exponential model. The extension has two additional parameters accounting for the distribution's shape. We extend this distribution probability density, cumulative distribution, hazard rate, and survival functions and establish different key statistical properties. Parameter estimation is obtained using different procedures, notably maximum likelihood estimation, least square, and Bayesian methods. A Monte Carlo simulation experiment is conducted to assess parameter performance and indicator risk measures. This article examines two distinct actual data sets in order to highlight the significance of the proposed model as well as its application in a variety of settings. The new model is compared to a large number of well-known extensions that were developed by other businesses. [ABSTRACT FROM AUTHOR]

This paper introduces the Particle Swarm Optimization (PSO) algorithm to enhance the Latin Hypercube Sampling (LHS) process. The key objective is to mitigate the issues of lengthy computation times and low computational accuracy typically encountered when applying Monte Carlo Simulation (MCS) to LHS for probabilistic trend calculations. The PSO method optimizes sample distribution, enhances global search capabilities, and significantly boosts computational efficiency. To validate its effectiveness, the proposed method was applied to IEEE34 and IEEE-118 node systems containing wind power. The performance was then compared with Latin Hypercubic Important Sampling (LHIS), which integrates significant sampling with the Monte Carlo method. The comparison results indicate that the PSO-enhanced method significantly improves the uniformity and representativeness of the sampling. This enhancement leads to a reduction in data errors and an improvement in both computational accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

Occasional outliers that might be a natural part of a process may distort the properties of a control chart. In this paper, we show that a recently proposed adaptive EWMA (AE) mean chart is highly sensitive to the outliers. The false alarm rate of the AE chart increases when the proportion and/or magnitude of the outliers increase and vice versa. In order to circumvent this demerit of the AE chart, we propose a truncated normal distribution-based AE (TAE) chart for monitoring the mean of a normal process in the presence of outliers. The zero-state and steady-state average run-length profiles of the proposed chart are estimated using Monte Carlo simulations. Based on detailed run-length comparisons, it is found that the TAE chart may outperform the existing EWMA chart (based on a truncated normal distribution) when detecting various mean shift sizes of an outlier-prone normal process. Illustrative examples are also included in this study to demonstrate the implementation of the existing and proposed charts. [ABSTRACT FROM AUTHOR]

Water contamination is a major environmental issue, especially in rapidly growing industrialized areas like Singrauli. This study addresses research gaps regarding the hydrochemical characterization, health risk assessment, and source identification of contaminants. Hydrochemistry shows the concentrations of Na+, Ca2+, F−, Mn, As, Mo, Sr, and Ni were above the permissible limit for drinking usage. Water quality index (WQI), heavy metal pollution (HMPI), and evaluation indices (HMEI) revealed As, Mn, Cd, Mo, Co, and Ni were the key heavy elements contributing towards aqueous media pollution in the Singrauli area. Additionally, F was also considered one of the major contaminants. In health risk assessment, the higher values of hazard quotient (HQ) for non-carcinogens were associated with Mn, As, Mo, and F; and hazard index (HI) values > 1 were found in 70% and 55% of samples for children and adults, respectively. Carcinogenic risk (CR) for human health was associated with As. CR values in 56.7% (for adults) and 61.7% (for children) of the total samples exceeded 1 × 10–4. Monte Carlo simulation was applied and highlighted the significant risk factors responsible for both carcinogenic and non-carcinogenic health impacts. 19.2%, 7.3%, and 6.9% of the simulated HQ values for adults and 30.1%, 16.9%, and 10.6% for children were above the safe limit for F, As, and Mn, respectively. Additionally, only 43.8% and 24.8% of the simulated HI for adults and children were within the safe limit. Irrespective of age groups, all the simulated values of As in CR were above 1 × 10–6; and 60% (for adults) and 77.1% (for children) of the values were above 1 × 10–4. This outcome emphasizes the urgency of pollution control measures, especially for As, F, and Mn, to safeguard public health. Moreover, a multivariate statistical approach revealed that both geogenic and anthropogenic sources were responsible for contamination. Therefore, regular monitoring, filtration, and purification are mandatory to ensure safe drinking water for human consumption. [ABSTRACT FROM AUTHOR]

The current study aims to introduce a new polymeric composite consisting of epoxy resin as the matrix and gadolinium oxide (Gd2O3) as the neutron adsorption ingredient. The shielding performance of the composite was assessed by neutron attenuation experiments with an Am-Be source and polyethylene moderator. The results of these experiments showed an appreciable agreement with the Monte Carlo simulations. Other characteristics of the composite, including mechanical strength, thermal stability, microtexture, and its chemical compositions, were examined using standard tensile test, thermogravimetric analysis, X-ray diffraction, scanning electron microscopy, static light scattering analyses, and Fourier-transform infrared spectroscopy (FTIR). The results indicated that the new composites offer appreciable neutron absorption properties so that samples with 0.5%, 2%, 5%, and 10% Gd2O3 content could reduce the neutron beam intensity by 54%, 63%, 66%, and 70% at a thickness of 4 cm. [ABSTRACT FROM AUTHOR]

Diseased conditions of articular cartilage such as osteoarthritis (OA) are accompanied by a change in the water concentration, together with a decrease in cartilage thickness. These parameters are important indicators of the normal joint functioning. Light scattering in a heterogeneous joint tissue is a complex process and it is important to supplement its study with understanding gained from modelling. In this work we employed Monte Carlo for analysis of the relationship between changes in cartilage parameters and calculated diffuse reflectance spectra. It has been shown that water absorption peak at 980 nm is determined by both water content and cartilage thickness, while changes in diffuse reflectance spectra at 1450 nm are mostly driven only by water content. Since independent assessment of these parameters is clinically relevant, several approaches for their determination were developed. A heuristic algorithm for cartilage thickness determination and its quality metrics (R 2 = 0.96) were obtained. Several regression models were developed using the amplitudes of diffuse reflectance spectra at different wavelengths and it was shown that the use of a wide range of wavelengths (850–1700 nm) allows to determine the cartilage water concentration and its thickness with the accuracy R 2 0.96 and 0.99 while measuring at different probe-detector distances. [ABSTRACT FROM AUTHOR]

AbstractThe utilization of dynamic probability control limits (DPCLs) can prove advantageous in the development of control charts, particularly in scenarios where sample sizes, areas of opportunity, or any other covariate values exhibit temporal fluctuations. In this study, we design the DPCLs-based two adaptive EWMA (AE) and adaptive CUSUM (AC) charts for monitoring the mean of a normally distributed process. We use Monte Carlo simulations to estimate the conditional false alarm rates, zero-state and steady-state (SS) average run-length profiles of the adaptive charts. It is found that the proposed AE and AC charts outperform the existing AE chart in terms of relative mean index. An example is given to demonstrate the implementation of the proposed charts. [ABSTRACT FROM AUTHOR]

This review spotlights the role of atomic‐level modeling in research on metal‐organic frameworks (MOFs), especially the key methodologies of density functional theory (DFT), Monte Carlo (MC) simulations, and molecular dynamics (MD) simulations. The discussion focuses on how periodic and cluster‐based DFT calculations can provide novel insights into MOF properties, with a focus on predicting structural transformations, understanding thermodynamic properties and catalysis, and providing information or properties that are fed into classical simulations such as force field parameters or partial charges. Classical simulation methods, highlighting force field selection, databases of MOFs for high‐throughput screening, and the synergistic nature of MC and MD simulations, are described. By predicting equilibrium thermodynamic and dynamic properties, these methods offer a wide perspective on MOF behavior and mechanisms. Additionally, the incorporation of machine learning (ML) techniques into quantum and classical simulations is discussed. These methods can enhance accuracy, expedite simulation setup, reduce computational costs, as well as predict key parameters, optimize geometries, and estimate MOF stability. By charting the growth and promise of computational research in the MOF field, the aim is to provide insights and recommendations to facilitate the incorporation of computational modeling more broadly into MOF research. [ABSTRACT FROM AUTHOR]

PurposeMaterials and methodsResultsDiscussionConclusionEvaluating students’ attitudes toward research is essential for instructors of any research methods class, as students’ general attitudes toward research may impact if and how they integrate research into practice decision making. However, few psychometrically sound, multidimensional instruments that can be used with Master of Social Work (MSW) students exist.This work used confirmatory factor analysis to evaluate the psychometric properties of the Revised Attitudes Toward Research Scale with a diverse sample of 396 master’s level social work students. Multiple indicators, multiple causes models and a series of Monte Carlo simulations were then used to assess the relationship between various dimensions of students’ attitudes toward research, their prior research exposure/training, and their sociodemographic characteristics.Results indicate that the overall performance of the measure with this sample of MSW students was strong, and the factor structure was consistent with that found when evaluated with different samples in previous research. Moreover, various sociodemographic characteristics predicted scores on the research usefulness, research anxiety, and positive research predisposition subscales.The use of this tool allows instructors to identify students with high levels of research-related anxiety and those who may not intuitively comprehend the need to understand empirical research findings and integrate them into practice decision making.The authors offer suggestions for integrating this validated tool into social work research methods classes to assist in developing students’ ability to engage in all steps of the evidence-based practice process once in the field. [ABSTRACT FROM AUTHOR]

AbstractStratified sampling is one of the powerful variance reduction methods for analyzing system performance, such as reliability, with stochastic simulation. It divides the input space into disjoint subsets, called strata, to draw samples from each stratum. Partitioning the input space properly and allocating greater computational effort to crucial strata can help accurately estimate system performance with a limited computational budget. How to create strata, however, has yet to be thoroughly examined. Strata design faces the curse of dimensionality and data scarcity as the input dimension increases. We analytically derive the optimal stratification structure that minimizes the estimation variance for univariate problems. Further, reconciling the optimal stratification into decision trees, we devise a robust algorithm for multi-dimensional problems. Numerical experiments and a wind turbine case study demonstrate the superiority of the proposed method in terms of variance reduction, leading to computational efficiency and scalability. [ABSTRACT FROM AUTHOR]

The long-debated question in analytical chemistry of which of the area ratio or the intensity ratio is the more precise has yielded no definitive analytical conclusion. To address this issue theoretically, we derived analytical solutions for the lower limits of estimation precision for spectral parameters, including the intensity ratio and area ratio, based on the Cramér–Rao lower bound (CRLB) framework for a Gaussian spectrum. The precisions of spectral parameter estimations from the analytical solutions were consistent with results obtained from Monte Carlo simulations. Our theoretical and simulation results revealed that the precision of estimating the area ratio surpassed that of the intensity ratio by a factor of 2 . Additionally, our experimental results aligned well with both theoretical predictions and simulation outcomes, further validating our approach. This increased precision of the area ratio is due to negative covariance between intensity and bandwidth, rather than the area containing more intensity information, as often misinterpreted. Consequently, and quite counter intuitively, prior bandwidth and intensity related information does not improve the area ratio precision: it worsens it. The analytical solution we derived represents the fundamental limits of spectral parameter measurement precision. Thus, it can be used as an alternative method for estimating the minimum error when experimental measurement uncertainty cannot be determined. [ABSTRACT FROM AUTHOR]

It is an established and already accomplished fact that probability-based methodologies (or probability/statistical distributions) play the roles of imperative tools in illustrating and describing applied phenomena. Paying attention to these previous facts, this paper considers the evolution of a new probability distribution. Thus, the main achievement of this paper leads to a new probability distribution as a result of combining the exponentiated exponential model with a tangent-based stratagem. The new model is called the tangent exponentiated exponential (TEE) distribution. For the TEE distribution, certain distributional properties and estimators of the model parameters are derived mathematically. The appraisal of the estimators of the TEE distribution is accomplished through a simulation study. Moreover, the applicability and virtuoso of the TEE distribution are exemplified via two data sets, which are taken from the music engineering (named Data 1) and reliability sector (named Data 2). By considering the p -value and three other important statistical tests/methods as diagnostic tools, we find that the TEE distribution is the most useful and optimal model for Data 1 and Data 2 compared to certain candidate probability distributions. [ABSTRACT FROM AUTHOR]

The objective of this study is to present a method for developing fragility curves for soil liquefaction that align with seismic hazards using Monte Carlo simulation. This approach can incorporate all uncertainties and variabilities in the input parameters. The seismic parameters, including earthquake magnitude (M) and associated peak ground acceleration (PGA), are jointly considered for the liquefaction assessment. The liquefaction potential and the resulting damages obtained by this method are more realistic. A case study is conducted using data from a sand-boil site in Yuanlin, Changhua County, where liquefaction occurred during the 1999 Chi-Chi earthquake in Taiwan. The findings indicate that the liquefaction potential index, IL, the post-liquefaction settlement, St, and the liquefaction probability index, PW, are all appropriate parameters for assessing liquefaction damages. The fragility curves for soil liquefaction developed through this method can support the performance-based earthquake engineering (PBEE) approach, provide guidance for liquefaction evaluation to the Taiwan Earthquake Loss Estimation System (TELES), and serve as a foundation for scenario simulation and an earthquake early warning system for liquefaction damages. [ABSTRACT FROM AUTHOR]

AbstractPerovskite scintillators have garnered significant interest in the realm of gamma-ray imaging in the past few years. Here, a comprehensive investigation into the gamma-ray imaging properties of CsPbBr3-PP composite scintillators is presented, wherein the Monte Carlo simulation approach offered by Geant4 is utilized. The primary focus is on the point spread function and modulation transfer function of the material, elucidating the nuanced interactions between gamma-ray energy, scintillator thickness, and their resultant imaging capabilities. A key aspect of this study is the exploration of the nonlinear and inverse effect of scintillator thickness and the energy of the photon beam on the imaging quality, highlighting the trade-offs between energy deposition and image resolution.This research underscores the importance of optimizing the scintillator design to balance these factors, catering to specific applications in high-energy detection and imaging. This work not only contributes significantly to the field of material sciences and radiographic imaging, but also provides practical insights for the development of more effective scintillator-based detectors. The findings of this study have broad implications for the design and application of perovskite scintillators in various high-tech industries and scientific research. [ABSTRACT FROM AUTHOR]

Process‐induced deformation (PID) arises in thermoset parts due to internal residual stress developed from their anisotropic properties, resulting in distortions. While passive numerical manufacturing control exists, active manufacturing control is crucial for enhancing the manufacturing process. The work focuses on diagnosing the polymerization reaction, known as the curing process, to consider the influence of uncertainties in thermal loading conditions on the behavior of cure kinetics. This is achieved using a Particle Filter approach, wherein a posterior distribution of cure evolution is recursively approximated based on observed measurements from characterization tests. The algorithm is designed to simultaneously perform the diagnosis and prognosis of the Degree of Cure and PID. This approach adopts the augmented cure formulation to address various scenarios with uncertainties in thermal loading conditions. It offers the advantage of providing comparable PID predictions with minimal computational costs. C‐shaped thermoset parts made of epoxy/carbon fibers with varying thicknesses are cured using the Manufacturing Recommended Curing Cycle, and the predictions with the developed algorithm are validated against experimental measures. Upon validation, the converged prognosis capability of the Particle Filter model is employed to assess the impact of thermal loading uncertainty on cure profiles, which, in turn, affects the final PIDs outcome. Highlights: A Bayesian sampling approach enables the estimation of cure kinetics parameters.The estimated stochastic parameters forecast the process‐induced deformations.The augmented Degree of Cure accounts for uncertainties linked to thermal loadings.Analysis on AS4/8552 C‐shaped parts shows the cure kinetics impact.The framework reduces the computational costs required for active control. [ABSTRACT FROM AUTHOR]

This study advances the application of the first‐to‐signal (FTS) concept to evaluate the effectiveness of multivariate charts when detecting shifts in the mean vector of a multivariate normally distributed process. Using Monte Carlo simulations, we estimate steady‐state average run‐length profiles and the probabilities of multivariate charts being the FTS an out‐of‐control state. Notably, our findings indicate that while the multivariate cumulative sum (MCUSUM) chart serves as a viable alternative to the multivariate exponentially weighted moving average (MEWMA) chart when detecting small shifts in the process mean vector, the latter surpasses the former in detecting moderate‐to‐large shifts. In addition, the Hotelling's T2$T^2$ chart outperforms the MEWMA and MCUSUM charts when detecting large shifts. [ABSTRACT FROM AUTHOR]

This paper investigates the stochastic nonlinear dynamic response of a single-degree-of-freedom dielectric elastomer generator under the combined action of harmonic excitation and stochastic disturbance. First, the nonlinear vibration model of a single-degree-of-freedom dielectric elastomer generator is established. The average method and fourth-order Runge–Kutta method are used to analyze the influence of pre-stretching, the initial membrane length, the charge amount, and the external excitation amplitude on the system response. Considering stochastic disturbance, the stochastic average method is applied to determine the probability density function (PDF) of the system’s steady-state response, and Monte Carlo numerical simulations are compared with the theoretical calculations for verification. The oscillation amplitude of the steady-state response can be increased by increasing the pre-stretching, harmonic excitation amplitude, and stochastic disturbance intensity. In the case of stochastic disturbance, as the intensity of the disturbance increases, the system becomes more likely to exhibit large amplitude responses for longer durations. [ABSTRACT FROM AUTHOR]

In this article, we propose a new adaptive exponentially weighted moving average (AEWMA) chart for monitoring the joint shifts in the location and scale parameters of the two‐parameter exponential distribution, namely the AEWMA‐II chart. A key feature of the proposed chart is its straightforward post‐signal diagnostics. The Monte Carlo simulation method is used to compute the steady‐state run‐length profiles of the proposed chart. The run‐length properties include the average run‐length and standard deviation of the run‐length. Through a comprehensive run‐length comparison, it is found that the AEWMA‐II chart performs better than the existing AEWMA chart. Moreover, with post‐signal diagnostics, the proposed chart also surpasses the existing chart. Finally, a real dataset is applied to illustrate the excellent performance and practical application of the proposed chart. [ABSTRACT FROM AUTHOR]

AbstractA high-altitude nuclear detonation releases a significant portion of energy as X-rays with a blackbody spectrum. Satellites are particularly vulnerable to prompt soft X-rays (~1 keV) absorbed within a few microns of the surface of the solar array, causing melting and evaporation of its materials. The absorption of soft X-rays in solar cell materials is studied using GEANT4 computer software. Energy deposition as a function of depth (depth-dose profile) is calculated for slab geometries of dielectric and metallic materials. The photo-absorption and Compton scattering of X-rays and the contribution of secondary radiation, such as photo-electrons, Auger-electrons, and fluorescence photons are taken into account. The effect of the production of secondary radiation on the distribution of deposited dose in the near-surface region of materials is investigated. The results presented in this work are validated against published data and provide valuable insights into X-ray absorption by solar cell materials, the redistribution of energy by secondary radiation, and the spatial scale of power density deposition that can be used as a source term for the further thermomechanical analysis of a material’s phase transformations and melting. [ABSTRACT FROM AUTHOR]

In this paper, a generalized autoregressive conditional heteroskedasticity model under skew-normal distributions is studied. A maximum likelihood approach is taken and the parameters in the model are estimated based on the expectation-maximization algorithm. The statistical diagnostics is made through the local influence technique, with the normal curvature and diagnostics results established for the model under four perturbation schemes in identifying possible influential observations. A simulation study is conducted to evaluate the performance of our proposed method and a real-world application is presented as an illustrative example. [ABSTRACT FROM AUTHOR]

This study examines population and small sample properties of the standardized fifth and sixth moments – the "higher moments" – for assessing univariate normality against bimodal and selected unimodal alternatives. Population parameters and distributions for selected bimodal mixtures are calculated and contrasted with those for the normal distribution. Using Gram-Charlier series expansion methods, an omnibus goodness of fit test incorporating the higher moments is specified and Monte Carlo simulation used to compare test power with parametric tests based on the standardized third and fourth sample moments: the asymptotic and size corrected versions of the Jarque-Bera score test and the omnibus D'Agostino K2 test. The studentized range and directional tests using the third through sixth moments are also considered. The results demonstrate that incorporating the fifth and sixth moments can provide enhanced parametric normality test power for bimodal normal mixture alternatives but not for various unimodal alternatives. [ABSTRACT FROM AUTHOR]

Recently, several control charts have been proposed in the statistical process monitoring literature based on a belief statistic. In this article we compare the zero‐state average run‐lengths and conditional expected delay profiles of the exponentially weighted moving average (EWMA) and belief statistic‐based (BSB) charts. We show that an ordinary EWMA chart is far better than the BSB chart when detecting delayed shifts in the mean of a normally distributed process. [ABSTRACT FROM AUTHOR]

Optical fiber X-ray sensors have the potential to realize real-time dose monitoring of precision radiotherapy. However, an over-response phenomenon can occur when using an optical fiber sensor (OFXS) filled with inorganic scintillator (Gd2O2S:Tb) to measure the off-axis ratio (OAR) curve. The aim of this paper is to study the mechanism responsible for the over-response. Due to the complex particle distribution present in water phantoms, the Monte Carlo-based code GEANT4 was used to model the response of the scintillator. The energy response of the scintillator to photons and electrons was initially simulated, which subsequently allowed the OAR curve to be simulated and the results were compared with experiment. To analyze the energy distribution of particles in different positions, electron spectroscopy was simulated together with the photon spectrum at the position from the central axis to a distance of 14.5 cm away from the center. Finally, three metal (Al, Cu, Sn) caps were made for the OFXS to prevent the low-energy photons penetrating the OFXS, and the OARs measurements were repeated. The results show that the scintillator exhibits higher sensitivity to photons with energy below 0.5 MeV, while for electrons, the scintillator has a higher sensitivity to high-energy electrons. Simulations for electron spectroscopy and the photon spectrum show that there are many low-energy photons with relatively few low-energy electrons. The OARs measured using the OFXS with metal caps show that the over-response can be mitigated using a high-Z metal cap. The measurements demonstrate that the OAR cure measured using an OFXS fitted with a Sn cap exhibits the closest response to that measured using an IC. [ABSTRACT FROM AUTHOR]

In this paper, a new regression estimator is proposed as an alternative to the ridge estimator in the case of multicollinearity in Bell regression model, called an almost unbiased ridge estimator. Also, we provide the theoretical properties of the new almost unbiased ridge estimator, and some theorems showing under which conditions that the almost unbiased ridge estimator is superior to its competitors. We consider a comprehensive simulation study to demonstrate the superiority of the almost unbiased ridge estimator compared to the usual Bell ridge estimator and the maximum likelihood estimator. The usefulness and superiority of the introduced regression estimator is shown via a real-world data example. According to the results of the simulation study and real-world data example, we conclude that the new almost unbiased ridge regression estimator is superior to its competitors in terms of the mean square error criterion. [ABSTRACT FROM AUTHOR]

In various applied disciplines, the modeling of continuous data often requires the use of flexible continuous distributions. Meeting this demand calls for the introduction of new continuous distributions that possess desirable characteristics. This paper introduces a new continuous distribution. Several estimators for estimating the unknown parameters of the new distribution are discussed and their efficiency is assessed through Monte Carlo simulations. Furthermore, the process capability index S pmk is examined when the underlying distribution is the proposed distribution. The maximum likelihood estimation of the S pmk is also studied. The asymptotic confidence interval is also constructed for S pmk . The simulation results indicate that estimators for both the unknown parameters of the new distribution and the S pmk provide reasonable results. Some practical analyses are also performed on both the new distribution and the S pmk . The results of the conducted data analysis indicate that the new distribution yields effective outcomes in modeling lifetime data in the literature. Similarly, the data analyses performed for S pmk illustrate that the new distribution can be utilized for process capability indices by quality controllers. [ABSTRACT FROM AUTHOR]

AbstractIn this article, the parameter estimation of several commonly used two-parameter lifetime distributions, including the Weibull, inverse Gaussian, and Birnbaum–Saunders distributions, based on joint progressively Type-II right-censored sample is studied. Different numerical methods and algorithms are used to compute the maximum likelihood estimates of the unknown model parameters. These methods include the Newton–Raphson method, the stochastic expectation–maximization (SEM) algorithm, and the dual annealing (DA) algorithm. These estimation methods are compared in terms of accuracy (e.g. the bias and mean squared error), computational time and effort (e.g. the required number of iterations), the ability to obtain the largest value of the likelihood, and convergence issues by means of a Monte Carlo simulation study. Recommendations are made based on the simulated results. A real data set is analyzed for illustrative purposes. These methods are implemented in Python, and the computer programs are available from the authors upon request. [ABSTRACT FROM AUTHOR]

Multicollinearity, a critical issue in regression analysis that can severely compromise the stability and accuracy of parameter estimates, arises when two or more variables exhibit correlation with each other. This paper solves this problem by introducing six new, improved two-parameter ridge estimators (ITPRE): NATPR1, NATPR2, NATPR3, NATPR4, NATPR5, and NATPR6. These ITPRE are designed to remove multicollinearity and improve the accuracy of estimates. A comprehensive Monte Carlo simulation analysis using the mean squared error (MSE) criterion demonstrates that all proposed estimators effectively mitigate the effects of multicollinearity. Among these, the NATPR2 estimator consistently achieves the lowest estimated MSE, outperforming existing ridge estimators in the literature. Application of these estimators to a real-world dataset further validates their effectiveness in addressing multicollinearity, underscoring their robustness and practical relevance in improving the reliability of regression models. [ABSTRACT FROM AUTHOR]

This research article presents a methodology for estimating the multicomponent reliability based on progressively first-failure censored samples, where the underlying distribution of stress and strength is modelled using the power Lindley distribution. The classical and Bayesian estimation methods are utilized for estimating the multicomponent reliability. In the Bayesian estimation, the Markov Chain Monte Carlo approximation method is employed to obtain the posterior mean under a generalized entropy loss function. Various intervals including asymptotic confidence, bootstrap-p confidence, bootstrap-t confidence, Bayesian credible, and highest posterior density credible intervals are computed. A simulation study is conducted to evaluate the performance of the proposed methodology. Also, two different real data applications are presented to illustrate the practicality of the approach. [ABSTRACT FROM AUTHOR]

A novel method for assessing the seismic resilience of railway stations is introduced. With this method, a railway station is divided into five constituent systems. The structural components, nonstructural components, and especially professional equipment that affect the functions in each system are identified and analyzed. Significantly, a new calculation method for seismic resilience indices, encompassing repair cost, repair time, casualties, and resilience grade, is proposed. Additionally, the complete seismic resilience assessment process is outlined. Furthermore, a case study was conducted on a typical railway station in China to demonstrate the application of this new seismic resilience assessment method. [ABSTRACT FROM AUTHOR]

According to existing literature, the ordinary least squares (OLS) estimators are not the best in presence of multicollinearity. The inability of OLS estimators against multicollinearity has paved the way for the development of various ridge type estimators for circumventing the problem of multicollinearity. In this paper improved two-parameter ridge (ITPR) estimators are proposed. A simulation study is used to evaluate the performance of proposed estimators based on minimum mean squared error (MSE) criterion. The simulative results reveal that, based on minimum MSE, ITPR2 was the most efficient estimator compared to the considered estimators in the study. Finally, a real-life dataset is analyzed to demonstrate the applications of the proposed estimators and also checked their efficacy for mitigation of multicollinearity. [ABSTRACT FROM AUTHOR]

Aims: Abiraterone treatment requires regular drug intake under fasting conditions due to pronounced food effect, which may impact patient adherence. The aim of this prospective study was to evaluate adherence to abiraterone treatment in patients with prostate cancer. To achieve this aim, an abiraterone population pharmacokinetic model was developed and patients' adherence has been estimated by comparison of measured levels of abiraterone with population model‐based simulations. Methods: A total of 1469 abiraterone plasma levels from 83 healthy volunteers collected in a bioequivalence study were analysed using a nonlinear mixed‐effects model. Monte Carlo simulation was used to describe the theoretical distribution of abiraterone pharmacokinetic profiles at a dose of 1000 mg once daily. Adherence of 36 prostate cancer patients treated with abiraterone was then evaluated by comparing the real abiraterone concentration measured in each patient during follow‐up visit with the theoretical distribution of profiles based on simulations. Patients whose abiraterone levels were ˂5th or ˃95th percentile of the distribution of simulated profiles were considered to be non‐adherent. Results: Based on this evaluation, 13 patients (36%) have been classified as non‐adherent. We observed significant association (P =.0361) between richness of the breakfast and rate of non‐adherence. Adherent patients reported significantly better overall condition in self‐assessments (P =.0384). A trend towards a higher occurrence of adverse effects in non‐adherent patients was observed. Conclusions: We developed an abiraterone population pharmacokinetic model and proposed an advanced approach to medical adherence evaluation. Due to the need for administration under fasting conditions, abiraterone therapy is associated with a relatively high rate of non‐adherence. [ABSTRACT FROM AUTHOR]

Purpose: Special properties and recent advances in the synthesis and biomolecular functionalization of gold nanoparticles (GNPs) have led to the evolution of their use in biomedical applications such as photon radiotherapy. Simulation-based studies on the effect of various parameters that govern the dose enhancement due to utilizing GNPs have facilitated the progress of knowledge in this field. Due to their flexibility and easier accessibility compared with experimental works, simulations have the potential to be considered for pre-clinical tests and, therefore, should be close to the realistic conditions as much as possible. Materials and methods: To this aim, the present work investigates the effect of the presence of GNPs that are accumulated in the cytoplasm of the constituent cells in healthy tissues of a human eye phantom, inspired by the published experimental results which report that non-target tissues also receive the drugs containing GNPs. The GNPs' concentrations are assumed to decrease by moving from the tumor toward the depth of the phantom through a suggested pattern. The MCNPX Monte Carlo code is used for the simulations. Results: The results show that for four concentrations tested, the dose enhancement factor in the shallower layer reaches 6, and decreases to 1.2 in the last layer. The dose enhancements are also examined for critical structures of the iris, cornea, sclera, and lens, showing maximum deviations of about 3 to 200% compared with the absence of GNPs in the healthy tissue. Considering the reported doses to the lens by clinical institutions, the effect of penetration of GNPs to deep layers on treatment time is also investigated. Conclusions: The results show that the penetration of GNPs from the tumor toward healthy tissues strongly controls the dose enhancement over the various eye structures and emphasizes the importance of modeling the GNPs' distribution in the medium on the overall dose enhancement. Considering the current challenges in the clinical use of GNPs, more effort needs to be made to reach an effective endpoint in treatment. [ABSTRACT FROM AUTHOR]

One of the critical quandaries in real-world production management systems is uncertainty in the product demand, which is closely associated to the product price. This uncertain behavior of demand affects production decisions in a system. In this context, this study develops a decision support framework for an imperfect serial production management system under uncertainty. The proposed framework is analyzed considering price-dependent uncertain demand and random defective rate in the system, thus considering both internal and external uncertainties of the system. Three distinct production models are formulated considering different types of uncertain relations among the product demand and market price. Closed form solutions of the decisions are obtained through hybrid of simulation and analytical optimization and are tested through an experimental case analysis. @RISK of Palisade Suite is utilized for simulation and to capture the uncertainty in defective proportion and demand elasticity parameters by creating several possibilities. [ABSTRACT FROM AUTHOR]

The mean residual lifetime (MRL) of a unit is its expected additional lifetime provided that it has survived until time t. The MRL estimation problem has been frequently addressed in the literature since it has wide applications in statistics, reliability and survival analysis. In this paper, we consider the problem of estimating the MRL in ranked set sampling when actual quantifications of a concomitant variable are available. To exploit the additional information of the concomitant variable, we introduce several MRL estimators based on some regression techniques. We then compare them with the standard MRL estimator in simple random sampling using Monte Carlo simulation and a real dataset from the Surveillance, Epidemiology, and End Results Program. Our results indicate the superiority of the procedures that we have developed when the quality of ranking is fairly good. [ABSTRACT FROM AUTHOR]

This paper develops a new approach for reliability-based design (RBD) of tunnel face support pressure from a quantile value perspective. A surrogate model is constructed to calculate the collapse pressures of the random samples generated by a single run of Monte Carlo simulation (MCS). The cumulative distribution function (CDF) of the collapse pressure is then obtained and the support pressure aiming at a target failure probability is chosen as the upper quantile value of the collapse pressures. The proposed approach does not require repetitive reliability analyses compared to the existing methods. Moreover, a direct relationship between the target failure probability and the required support pressure is established. An illustrative example is used to demonstrate the implementation procedure. The accuracy of the reliability-based support pressures is verified by direct MCS incorporating with three-dimensional numerical simulations. Finally, the influencing factors, including the sample size of MCS, the correlation coefficient between random variables, the choice of experimental points, and the surrogate model, are investigated. This method can play a complementary role to available approaches due to its advantages of simplicity and efficiency. [ABSTRACT FROM AUTHOR]

A geotextile-reinforced retaining wall is a geotechnical structure with many design parameters. Hence, the uncertainty of the input parameters considerably affects the design of these structures. On the other hand, when the number of uncertain parameters increases, the time of this analysis increases drastically. Accordingly, the current study used an analytical method, namely, jointly distributed random variables (JDRV) method, that requires less running time than the simulation methods for stochastic analysis. For this purpose, stochastic analysis of the geotextile-reinforced retaining wall was carried out based on the limit equilibrium method (LEM), with soil parameters considered as uncertain variables. To verify the results, the probability density functions (PDFs) of the wall safety factors were compared with the Monte Carlo simulation (MCS). Next, to assess the effect of the external and internal stability modes on system reliability, the system reliability index was determined using the sequential compounding method (SCM). The results of the system reliability analysis revealed that, among the reliability indices of the components, the minimum values are attributed to the bearing capacity. The correlation between the rupture and pullout safety factors exhibited the maximum correlation, indicating that they are more dependent components than others. Based on the stochastic sensitivity analysis, the internal friction angle emerged as the most influential in the external and internal safety factors. [ABSTRACT FROM AUTHOR]

Generalized linear mixed models (GLMMs) have great potential to deal with count data in single-case experimental designs (SCEDs). However, applied researchers have faced challenges in making various statistical decisions when using such advanced statistical techniques in their own research. This study focused on a critical issue by investigating the selection of an appropriate distribution to handle different types of count data in SCEDs due to overdispersion and/or zero-inflation. To achieve this, I proposed two model selection frameworks, one based on calculating information criteria (AIC and BIC) and another based on utilizing a multistage-model selection procedure. Four data scenarios were simulated including Poisson, negative binominal (NB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB). The same set of models (i.e., Poisson, NB, ZIP, and ZINB) were fitted for each scenario. In the simulation, I evaluated 10 model selection strategies within the two frameworks by assessing the model selection bias and its consequences on the accuracy of the treatment effect estimates and inferential statistics. Based on the simulation results and previous work, I provide recommendations regarding which model selection methods should be adopted in different scenarios. The implications, limitations, and future research directions are also discussed. [ABSTRACT FROM AUTHOR]

Researchers increasingly study short-term dynamic processes that evolve within single individuals using N = 1 studies. The processes of interest are typically captured by fitting a VAR(1) model to the resulting data. A crucial question is how to perform sample-size planning and thus decide on the number of measurement occasions that are needed. The most popular approach is to perform a power analysis, which focuses on detecting the effects of interest. We argue that performing sample-size planning based on out-of-sample predictive accuracy yields additional important information regarding potential overfitting of the model. Predictive accuracy quantifies how well the estimated VAR(1) model will allow predicting unseen data from the same individual. We propose a new simulation-based sample-size planning method called predictive accuracy analysis (PAA), and an associated Shiny app. This approach makes use of a novel predictive accuracy metric that accounts for the multivariate nature of the prediction problem. We showcase how the values of the different VAR(1) model parameters impact power and predictive accuracy-based sample-size recommendations using simulated data sets and real data applications. The range of recommended sample sizes is smaller for predictive accuracy analysis than for power analysis. [ABSTRACT FROM AUTHOR]

Determining the compositional structure and dimensionality of psychological constructs lies at the heart of many research questions in developmental science. Structural equation modeling (SEM) provides a versatile framework for formalizing and estimating the relationships among multiple latent constructs. While the flexibility of SEM can accommodate many complex assumptions on the underlying structure of psychological constructs, it makes a priori estimation of statistical power and required sample size challenging. This difficulty is magnified when comparing non-nested SEMs, which prevents the use of traditional likelihood-ratio tests. Sample size estimates for SEM model fit comparisons typically rely on generic rules of thumb. Such heuristics can be misleading because statistical power in SEM depends on a variety of model properties. Here, we demonstrate a Monte Carlo simulation approach for estimating a priori statistical power for model selection when comparing non-nested models in an SEM framework. We provide a step-by-step guide to this approach based on an example from our memory development research in children. [ABSTRACT FROM AUTHOR]

The proportional hazard regression models are widely used statistical tools for analyzing survival data and estimating the effects of covariates on survival times. It is assumed that the effects of the covariates are constant across the time. In this paper, we propose a novel extension of the proportional hazard model by incorporating an exponentiated-Weibull distribution to model the baseline line hazard function. The proposed model offers more flexibility in capturing various shapes of failure rates and accommodates both monotonic and non-monotonic hazard shapes. The performance evaluation of the proposed model and comparison with other commonly used survival models including the generalized log–logistic, Weibull, Gompertz, and exponentiated exponential PH regression models are explored using simulation results. The results demonstrate the ability of the introduced model to capture the baseline hazard shapes and to estimate the effect of covariates on the hazard function accurately. Furthermore, two real survival medical data sets are analyzed to illustrate the practical importance of the proposed model to provide accurate predictions of survival outcomes for individual patients. Finally, the survival data analysis reveal that the model is a powerful tool for analyzing complex survival data. [ABSTRACT FROM AUTHOR]

Background/Objectives: To date, population pharmacokinetic (PK) studies of vancomycin on healthy Korean adults have not been conducted. This study aimed to investigate the PK properties of vancomycin in healthy volunteers and to identify optimal dosing regimens based on the area under the concentration–time curve (AUC) in adult patients with normal renal function. Methods: We conducted a prospective clinical study, analysing PK samples from 12 healthy participants using noncompartmental analysis and non-linear mixed-effects modelling. The population PK parameters derived were employed in Monte Carlo simulations to evaluate the adequacy of the current dosing regimen and to formulate dosing recommendations. Results: The PK profiles were optimally described by a two-compartment model, with body weight and age as significant covariates affecting total clearance. The simulations indicated that to achieve a therapeutic target—defined as an AUC at steady-state over 24 h of 400–600 mg·h/L—daily doses ranging from 60 to 70 mg/kg are necessary in adults with normal renal function. Conclusions: This study underscores the need to actively adjust dosage and administration based on a vancomycin PK model that adequately reflects the demographic characteristics of patients to meet both safety and efficacy standards. [ABSTRACT FROM AUTHOR]

Coordinate measuring machines are widely used in the industrial field due to their ease of automation. However, estimating the measurement uncertainty is a delicate task, especially when controlling for deviation, given the large number of factors that influence the measurement. A precise estimate of the uncertainty is crucial to avoid incorrect conformity assessments. The purpose of this study is to control geometrical-form tolerance specifications, taking into consideration their associated uncertainty. A surface fitting model based on the least squares criterion is proposed, allowing one to obtain the variance–covariance matrix by iterative calculation according to the Levenberg–Marquard optimization method. The form deviation is then evaluated following the Geometrical Product Specifications (GPS) Standard, and its associated uncertainty is estimated using the guide to the expression of uncertainty in measurement (GUM) propagation of the uncertainty law. Finally, the conformity assessment is performed based on the measured deviation and its associated uncertainty. Different results for the measurement of straightness, flatness, circularity, roundness, and cylindricity are presented and detailed. This model is thereafter validated by a Monte Carlo simulation, and interlaboratory comparisons of the obtained results were performed, which showed satisfactory outcome. This contribution is of great use to manufacturing companies and metrology laboratories, allowing them to meet the normative guidelines, which stipulates that each measurement result must be accompanied by its associated uncertainty. [ABSTRACT FROM AUTHOR]

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This paper addresses the practical issue of load frequency control (LFC) in multi-area power systems with degraded actuators and sensors under cyber-attacks. A time-varying approximation model is developed to capture the variability in component degradation paths across different operational scenarios, and an optimal controller is constructed to manage stochastic degradation across subareas simultaneously. To assess the reliability of the proposed scheme, both Monte Carlo simulation and particle swarm optimization techniques are utilized. The methodology distinguishes itself by four principal attributes: (i) a time-varying degradation model that broadens the application from single-area to multi-area systems; (ii) the integration of physical constraints within the degradation model, which enhances the realism and practicality compared to existing methods; (iii) the sensor suffers from fault data injection attacks; and (iv) an optimal controller that leverages particle swarm optimization to effectively balance reliability and system performance, thereby improving both stability and reliability. This method has demonstrated its effectiveness and advantages in mitigating load disturbances, achieving its objectives in just one-third of the time required by established benchmarks. The case study validates the applicability of the proposed approach and demonstrates its efficacy in mitigating load disturbance amidst stochastic degradation in actuators and sensors under FDIA cyber-attacks. [ABSTRACT FROM AUTHOR]

This study aimed to reduce the methane (CH4) emissions originating from dam lake treatment using malt dust-derived biochar, which is an agro-industrial byproduct of the brewery industry. Optimum operating and water quality parameters for CH4 reduction were determined using statistical analyses based on the Box–Behnken design method. Also, a Monte Carlo simulation was performed to determine the correlation between CH4 emissions and operating parameters. According to the simulation, dissolved oxygen (DO) and the oxidation–reduction potential (ORP) had the highest correlation with CH4 emissions, with values of 92.03% and 94.57%, respectively. According to the Box–Behnken design methodology, the optimum operating parameters were 4 mg/L of dissolved oxygen, −359 mV of ORP, and 7.5 pH for the minimum CH4 emissions. There was a reported reduction of up to 19.4% in CH4 emissions for the dam lake treatment using malt dust-derived biochar. Finally, a new methane capture index, based on the biochar application (MCI), was developed and validated. The largest methane capture capacity was related to the malt dust-derived biochar produced at the lowest temperature (M1). [ABSTRACT FROM AUTHOR]

Nested simulation has been an active area of research in recent years, with an important application in portfolio risk measurement. While majority of the literature has been focusing on the continuous case where portfolio loss is assumed to follow a continuous distribution, monetary losses of a portfolio in practice are usually measured in discrete units, oftentimes due to the practical consideration of meaningful decimal places for a given level of precision in risk measurement. In this paper, we study a nested simulation procedure for estimating conditional Value-at-Risk (CVaR), a popular risk measure, in the case where monetary losses of the portfolio take discrete values. Tailored to the discrete nature of portfolio losses, we propose a rounded estimator and show that when the portfolio loss follows a sub-Gaussian distribution or has a sufficiently high-order moment, the mean squared error (MSE) of the resulting CVaR estimator decays to zero at a rate close to Γ − 1 , much faster than the rate of the CVaR estimator in the continuous case which is Γ − 2 / 3 , where Γ denotes the sampling budget required by the nested simulation procedure. Performance of the proposed estimator is demonstrated using numerical examples. [ABSTRACT FROM AUTHOR]

In this short note, we reevaluate the run-length performance of the EWMA and exponentiated EWMA (Exp-EWMA) charts using the conditional expected delay metric. It is found that the enhancements offered by the Exp-EWMA chart over the EWMA chart in the zero-state setup are marginal. Given its simplicity in implementation and its ability to encompass the functionality of the Exp-EWMA chart in detecting delayed shifts in the process mean, the EWMA chart remains the preferred choice over the Exp-EWMA chart. [ABSTRACT FROM AUTHOR]