Analysis of the Effect of Subgroup Size on the X-Bar Control Chart Using Forensic Science Laboratory Sample Influx Data

This paper analyzes the effect of subgroup size on the x-bar chart characteristics using sample influx (SIF) into forensic science laboratory (FSL). The characteristics studied include changes in out-or-control points (OCP), upper control limit UCLx, and zonal demarcations. Multi-rules were used to identify the number of out-of-control-points, Nocp as violations using five control chart rules applied separately. A sensitivity analysis on the Nocp was applied for subgroup size, k, and number of sigma above the mean value to determine the upper control limit, UCLx. A computer code was implemented using a FORTRAN code to create x-bar control-charts and capture OCP and other control-chart characteristics with increasing k from 2 to 25. For each value of k, a complete series of average values, Q(p), of specific length, Nsg, was created from which statistical analysis was conducted and compared to the original SIF data, S(t). The variation of number of out-of-control points or violations, Nocp, for different control-charts rules with increasing k was determined to follow a decaying exponential function, Nocp = Ae–α, for which, the goodness of fit was established, and the R2 value approached unity for Rule #4 and #5 only. The goodness of fit was established to be the new criteria for rational subgroup-size range, for Rules #5 and #4 only, which involve a count of 6 consecutive points decreasing and 8 consecutive points above the selected control limit (σ/3 above the grand mean), respectively. Using this criterion, the rational subgroup range was established to be 4 ≤ k ≤ 20 for the two x-bar control chart rules.

Research on aiming methods for small sample size shooting tests of two-dimensional trajectory correction fuse

The longitudinal dispersion of the projectile in shooting tests of two-dimensional trajectory corrections fused with fixed canards is extremely large that it sometimes exceeds the correction ability of the correction fuse actuator.The impact point easily deviates from the target,and thus the correction result cannot be readily evaluated.However,the cost of shooting tests is considerably high to conduct many tests for data collection.To address this issue,this study proposes an aiming method for shooting tests based on small sample size.The proposed method uses the Bootstrap method to expand the test data;repeatedly iterates and corrects the position of the simulated theoretical impact points through an improved compatibility test method;and dynamically adjusts the weight of the prior distribution of simulation results based on Kullback-Leibler divergence,which to some extent avoids the real data being"submerged"by the simulation data and achieves the fusion Bayesian estimation of the dispersion center.The experimental results show that when the simulation accuracy is sufficiently high,the proposed method yields a smaller mean-square deviation in estimating the dispersion center and higher shooting accuracy than those of the three comparison methods,which is more conducive to reflecting the effect of the control algorithm and facilitating test personnel to iterate their proposed structures and algorithms.;in addition,this study provides a knowledge base for further comprehensive studies in the future.

Frequentist and Bayesian Sample Size Determination for Single-Arm Clinical Trials Based on a Binary Response Variable: A Shiny App to Implement Exact Methods

Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct power functions to select the optimal sample size. We revise this approach when the focus is on testing a single binomial proportion. We consider exact methods and introduce a conservative criterion to account for the typical non-monotonic behavior of the power functions, when dealing with discrete data. The main purpose of this paper is to present a Shiny App providing a user-friendly, interactive tool to apply these criteria. The app also provides specific tools to elicit the analysis and the design prior distributions, which are the core of the two-priors approach.

Size and Shape of Sample Units in Native Forests and Plantations

The size and form of sampling units-SU have always been variables considered in planning and structuring forest inventories, being performed in forests or in plantations. The experimental work outlined to deal with the problem was conducted in an area of araucaria forest, in Sao Joao de Triunfo, PR, Brazil. The forms of sampling units circle, square and rectangular were evaluated, whose areas ranged from 200 m2 to 1000 m2. Time was recorded using a stopwatch and computed separately for locomotion and measurement. The power model was used to adjust the relations of the times of locomotion and measurement, as well as a hyperbolic one for the coefficient of variation, all taking as function of the SUs sizes. To achieve the analytical solution for the optimum size of the SU, it was necessary simulating the behavior of the three functions until the size of 10,000 m2. By taking the derivative of the combined function it was found the maximum point, which allowed optimizing the size of the SU in 600 m2 for the structured experimental conditions. This result proved the formulated hypothesis, performing even a critical analysis of the inclusion of other relevant variables, such as size of the area to be inventoried, number of SUs performed in one day of work, average distance between the SUs, average speeds for locomotion between SUs and for taking all respective measurements.

Simulation Program to Determine Sample Size and Power for a Multiple Logistic Regression Model with Unspecified Covariate Distributions

Binary logistic regression models are commonly used to assess the association between outcomes and covariates. Many covariates are inherently continuous, and have a variety of distributions, including those that are heavily skewed to the left or right. Existing theoretical formulas, criteria, and simulation programs cannot accurately estimate the sample size and power of non-standard distributions. Therefore, we have developed a simulation program that uses Monte Carlo methods to estimate the exact power of a binary logistic regression model. This power calculation can be used for distributions of any shape and covariates of any type (continuous, ordinal, and nominal), and can account for nonlinear relationships between covariates and outcomes. For illustrative purposes, this simulation program is applied to real data obtained from a study on the influence of smoking on 90-day outcomes after acute atherothrombotic stroke. Our program is applicable to all effect sizes and makes it possible to apply various statistical methods, logistic regression and related simulations such as Bayesian inference with some modifications.

Numerical study of point spread function of a fast neutron radiography system based on scintillating-fiber array

For a scintillating-fiber array fast-neutron radiography system,a point-spread-function computing model was introduced,and the simulation code was developed. The results of calculation show that fast-neutron radiographs vary with the size of fast neutron sources,the size of fiber cross-section and the imaging geometry. The results suggest that the following qualifications are helpful for a good point spread function: The cross-section of scintillating fibers not greater than 200 μm×200 μm,the size of neutron source as small as a few millimeters,the distance between the source and the scintillating fiber array greater than 1 m,and inspected samples placed as close as possible to the array. The results give suggestions not only to experiment considerations but also to the estimation of spatial resolution for a specific system.

Empirical Determination of the Tolerable Sample Size for Ols Estimator in the Presence of Multicollinearity (<i>ρ</i>)

This paper investigates the tolerable sample size needed for Ordinary Least Square (OLS) Estimator to be used when there is presence of Multicollinearity among the exogenous variables of a linear regression model. A regression model with constant term (β0) and two independent variables (with β1 and β2 as their respective regression coefficients) that exhibit multicollinearity was considered. A Monte Carlo study of 1000 trials was conducted at eight levels of multicollinearity (0, 0.25, 0.5, 0.7, 0.75, 0.8, 0.9 and 0.99) and sample sizes (10, 20, 40, 80, 100, 150, 250 and 500). At each specification, the true regression coefficients were set at unity while 1.5, 2.0 and 2.5 were taken as the hypothesized value. The power value rate was obtained at every multicollinearity level for the aforementioned sample sizes. Therefore, whether the hypothesized values highly depart from the true values or not once the multicollinearity level is very high (i.e. 0.99), the sample size needed to work with in order to have an error free estimation or the inference result must be greater than five hundred.

Cusp Catastrophe Polynomial Model: Power and Sample Size Estimation

Guastello’s polynomial regression method for solving cusp catastrophe model has been widely applied to analyze nonlinear behavior outcomes. However, no statistical power analysis for this modeling approach has been reported probably due to the complex nature of the cusp catastrophe model. Since statistical power analysis is essential for research design, we propose a novel method in this paper to fill in the gap. The method is simulation-based and can be used to calculate statistical power and sample size when Guastello’s polynomial regression method is used to do cusp catastrophe modeling analysis. With this novel approach, a power curve is produced first to depict the relationship between statistical power and samples size under different model specifications. This power curve is then used to determine sample size required for specified statistical power. We verify the method first through four scenarios generated through Monte Carlo simulations, and followed by an application of the method with real published data in modeling early sexual initiation among young adolescents. Findings of our study suggest that this simulation-based power analysis method can be used to estimate sample size and statistical power for Guastello’s polynomial regression method in cusp catastrophe modeling.

240 nm AlGaN-based deep ultraviolet micro-LEDs:size effect versus edge effect

240 nm AlGaN-based micro-LEDs with different sizes are designed and fabricated.Then,the external quantum efficiency(EQE)and light extraction efficiency(LEE)are systematically investigated by comparing size and edge effects.Here,it is revealed that the peak optical output power increases by 81.83%with the size shrinking from 50.0 to 25.0μm.Thereinto,the LEE increases by 26.21%and the LEE enhancement mainly comes from the sidewall light extraction.Most notably,transversemagnetic(TM)mode light intensifies faster as the size shrinks due to the tilted mesa side-wall and Al reflector design.However,when it turns to 12.5μm sized micro-LEDs,the output power is lower than 25.0μm sized ones.The underlying mechanism is that even though protected by SiO2 passivation,the edge effect which leads to current leakage and Shockley-Read-Hall(SRH)recombination deteriorates rapidly with the size further shrinking.Moreover,the ratio of the p-contact area to mesa area is much lower,which deteriorates the p-type current spreading at the mesa edge.These findings show a role of thumb for the design of high efficiency micro-LEDs with wavelength below 250 nm,which will pave the way for wide applications of deep ultraviolet(DUV)micro-LEDs.

Towards an Effective Communication in the Care of Patients with Long Term Disease in Kenya via Cybernetic—A Systematic Review

In this paper, to effectively treat chronic disorders and improve the standard of care, effective communication between patients and healthcare professionals was essential. The aim of the study was to review the literature on how good communication might improve treatment outcomes for Kenyan patients with chronic and terminal illnesses and to determine whether Cybernetic electronic communication can improve those outcomes even more. We uncovered the history of treatment outcomes for chronic and terminal diseases in this research study, both with and without communication at the core of the patient’s care plan. We discussed the importance of good communication in the treatment of patients with chronic and terminal illnesses and why it is a momentous endeavor comparable to medical diagnosis and treatment for the long-term health of patients. To locate pertinent material for the background literature study, we carried out a comprehensive literature search. Although the preliminary literature review was a continuation of the introduction research, it also highlighted the paucity of local Kenyan literature and suggested that improved communication might help patients with chronic and terminal illnesses have better treatment outcome. Methodology maintained the literature search, as a systematic literature review focused on core of the study, making separate sections of the same body necessary. This ensured that a methodological literature search section is as comprehensive as possible. We used an integrated PRISM model to limit a comprehensive literature search and a systematic literature review design as part of the overall process. Non-probability sampling and snowball approaches on literary papers over the previous 17 years were used in this arrangement. Since this was a multidisciplinary study, the four experts who also serve as authors were chosen from within their respective fields of expertise to design the study. They created search strategies, generated key words, looked up keywords in database engines, assessed the results of the literature using the PRISMA logical model, looked over successful literature, and triangulated their findings. The conclusions of the experts individually revealed a convergence of thoughts, beliefs, and practices across. The study concluded that even though there isn’t much research done in Kenya on the same subject;what is available illustrates how crucial good communication is for patients with chronic illnesses. The study’s findings also highlighted the positive effects of effective communication between patients and healthcare professionals on treatment plan adherence, patient satisfaction, and overall health outcomes. The results also noted that in order to improve patient care and outcome, Kenyan healthcare workers should underscore developing their communication skills. The study also found that the incorporation of cybernetics is crucial if a truly effective communication is required so as to enable centered care for patients with long-term diseases in Kenya. The goal of the Cybernetics is to activate genuinely effective communication in the care of Patients with long-term disease in Kenya. This study is organized to begin with an abstract, followed by keywords, an introduction, literature review, methodology, findings, discussion, and finally conclusions.

Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam

The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) microbeam.Size-dependent constitutive equations,which can capture the size effect of the SMP,are proposed based on the modified couple stress theory (MCST).The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam theory.An SMP microbeam model,which includes the formulations of deflection,strain,curvature,stress and couple stress,is developed by using the principle of minimum potential energy and the separation of variables together.The sizedependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam model.Results show that the size effects of the SMP microbeam are significant when the dimensionless height is small enough.However,they are too slight to be necessarily considered when the dimensionless height is large enough.The bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height,while the couple stress level declines with the increasing dimensionless height.The larger the dimensionless height is,the more obvious the viscous property and shape memory effect of the SMP microbeam are.The Poisson ratio has obvious influence on the size-dependent behaviors of the SMP microbeam.The paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine,microelectronic devices and micro-electro-mechanical system (MEMS) self-assembling.

Power Analysis and Sample Size Determination for Crossover Trials with Application to Bioequivalence Assessment of Topical Ophthalmic Drugs Using Serial Sampling Pharmacokinetic Data

Objective To develop methods for determining a suitable sample size for bioequivalence assessment of generic topical ophthalmic drugs using crossover design with serial sampling schemes.Methods The power functions of the Fieller-type confidence interval and the asymptotic confidence interval in crossover designs with serial-sampling data are here derived.Simulation studies were conducted to evaluate the derived power functions.Results Simulation studies show that two power functions can provide precise power estimates when normality assumptions are satisfied and yield conservative estimates of power in cases when data are log-normally distributed.The intra-correlation showed a positive correlation with the power of the bioequivalence test.When the expected ratio of the AUCs was less than or equal to 1, the power of the Fieller-type confidence interval was larger than the asymptotic confidence interval.If the expected ratio of the AUCs was larger than 1, the asymptotic confidence interval had greater power.Sample size can be calculated through numerical iteration with the derived power functions.Conclusion The Fieller-type power function and the asymptotic power function can be used to determine sample sizes of crossover trials for bioequivalence assessment of topical ophthalmic drugs.

Semi-supervised LIBS quantitative analysis method based on co-training regression model with selection of effective unlabeled samples

The accuracy of laser-induced breakdown spectroscopy(LIBS) quantitative method is greatly dependent on the amount of certified standard samples used for training. However, in practical applications, only limited standard samples with labeled certified concentrations are available. A novel semi-supervised LIBS quantitative analysis method is proposed, based on co-training regression model with selection of effective unlabeled samples. The main idea of the proposed method is to obtain better regression performance by adding effective unlabeled samples in semisupervised learning. First, effective unlabeled samples are selected according to the testing samples by Euclidean metric. Two original regression models based on least squares support vector machine with different parameters are trained by the labeled samples separately, and then the effective unlabeled samples predicted by the two models are used to enlarge the training dataset based on labeling confidence estimation. The final predictions of the proposed method on the testing samples will be determined by weighted combinations of the predictions of two updated regression models. Chromium concentration analysis experiments of 23 certified standard high-alloy steel samples were carried out, in which 5 samples with labeled concentrations and 11 unlabeled samples were used to train the regression models and the remaining 7 samples were used for testing. With the numbers of effective unlabeled samples increasing, the root mean square error of the proposed method went down from 1.80% to 0.84% and the relative prediction error was reduced from 9.15% to 4.04%.

An Improved Algorithm for Imbalanced Data and Small Sample Size Classification

Traditional classification algorithms perform not very well on imbalanced data sets and small sample size. To deal with the problem, a novel method is proposed to change the class distribution through adding virtual samples, which are generated by the windowed regression over-sampling (WRO) method. The proposed method WRO not only reflects the additive effects but also reflects the multiplicative effect between samples. A comparative study between the proposed method and other over-sampling methods such as synthetic minority over-sampling technique (SMOTE) and borderline over-sampling (BOS) on UCI datasets and Fourier transform infrared spectroscopy (FTIR) data set is provided. Experimental results show that the WRO method can achieve better performance than other methods.

Sample Size Determination and Statistical Hypothesis Testing for Core Centration in Press Coated Tablets

A novel statistical approach to evaluate the manufacturing quality of press coated tablets in terms of the centering of their core is presented. We also provide a formula to determine the necessary sample size. This approach is applied to real data.

Experimental study on the size effect on the equation of state of concretes under shock loading

Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for.

Numerical study of size effect in concrete penetration with LDPM

Projectile size effect is of great importance since the scaling researches are extensively applied to concrete penetration investigations. This paper numerically deals with the projectile size effect on penetration resistance via the recently developed Lattice Discrete Particles Model(LDPM) which is featured with mesoscale constitutive laws governing the interaction between adjacent particles to account for cohesive fracture, strain hardening in compression and compaction due to pore collapse. Simulations of two different penetration tests are carried to shed some light on the size effect issue. The penetration numerical model is validated by matching the projectile deceleration curve of and predicting the depth of penetration(DOP). By constant velocity penetration simulations, the target resistance is found to be dependent on the projectile size. By best fitting numerical results of constant velocity penetration, a size effect law for target resistance is proposed and validated against literature data. Moreover, the size effect is numerically obtained in the projectile with longer extended nose part meanwhile the shorter extended nose is found to improve the DOP since the projectile nose is sharpened.

Estimating the Size of an Injecting Drug User Population

This article describes a sampling and estimation scheme for estimating the size of an injecting drug user (IDU) population by combining classical sampling and respondent-driven sampling procedures. It is designed to use the information from harm reduction programs, especially, Needle Exchange Programs (NEPs). The approach involves using respondent-driven sampling design to collect a sample of injecting drug users who appear at site of NEP in a certain period of time and to obtain retrospective self-report data on the number of friends among the IDUs and number of needles exchanged for each sampled injecting drug user. A methodology is developed to estimate the size of injecting drug users who have ever used the NEP during the fixed period of time, and which allows us to estimate the proportion of injecting drug users in using NEP. The size of the IDU population is estimated by dividing the total number of IDUs who using NEPs during the period of time by the estimated proportion of IDUs in the group. The technique holds promise for providing data needed to answer questions such as “What is the size of an IDU population in a city?” and “Is that size changing?” and better understand the dynamics of the IDU population. The methodology described here can also be used to estimate size of other hard-to-reach population by using information from harm reduction programs.

Fracture Response of Reinforced Concrete Deep Beams Finite Element Investigation of Strength and Beam Size

This article presents a finite element analysis of reinforced concrete deep beams using nonlinear fracture mechanics. The article describes the development of a numerical model that includes several nonlinear processes such as compression and tension softening of concrete, bond slip between concrete and reinforcement, and the yielding of the longitudinal steel reinforcement. The development also incorporates the Delaunay refinement algorithm to create a triangular topology that is then transformed into a quadrilateral mesh by the quad-morphing algorithm. These two techniques allow automatic remeshing using the discrete crack approach. Nonlinear fracture mechanics is incorporated using the fictitious crack model and the principal tensile strength for crack initiation and propagation. The model has been successful in reproducing the load deflections, cracking patterns and size effects observed in experiments of normal and high-strength concrete deep beams with and without stirrup reinforcement.

Unimolecular Dissociation of H⁺<sub style="margin-left:-6px;">2n+1</sub>Hydrogen Clusters: Measured Cross Sections and Theoretically Calculated Rate Constants

In this paper, we studied the process of dissociation unimolecular of the evaporation of H+2n+1 hydrogen clusters according to size, using the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The rate constants k(E) were determined with the use of statistical theory of unimolecular reactions using various approximations. In our work, we used the products frequencies instead of transitions frequencies in the calculation of unimolecular dissociation rates obtained by three models RRKM. The agreement between the experimental cross section ratio and calculated rate ratio with direct count approximation seems to be reasonable.