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.

Reliability Assessment for the Solenoid Valve of a High-Speed Train Braking System under Small Sample Size

Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant for safe operation. Traditional reliability assessment methods are only performed well under conditions of large sample size and complete failure data,which lead to large deviation under conditions of small sample size and zero?failure data. To improve this problem,a new Bayesian method is proposed. Based on the characteristics of the solenoid valve in the braking system of a high?speed train,the modified Weibull distribution is selected to describe the failure rate over the entire lifetime. Based on the assumption of a binomial distribution for the failure probability at censored time,a concave method is employed to obtain the relationships between accumulation failure prob?abilities. A numerical simulation is performed to compare the results of the proposed method with those obtained from maximum likelihood estimation,and to illustrate that the proposed Bayesian model exhibits a better accuracy for the expectation value when the sample size is less than 12. Finally,the robustness of the model is demonstrated by obtaining the reliability indicators for a numerical case involving the solenoid valve of the braking system,which shows that the change in the reliability and failure rate among the di erent hyperparameters is small. The method is provided to avoid misleading of subjective information and improve accuracy of reliability assessment under condi?tions of small sample size and zero?failure data.

Strategies on Sample Size Determination and Qualitative and Quantitative Traits Integration to Construct Core Collection of Rice (Oryza sativa)

The development of a core collection could enhance the utilization of germplasm collections in crop improvement programs and simplify their management. Selection of an appropriate sampling strategy is an important prerequisite to construct a core collection with appropriate size in order to adequately represent the genetic spectrum and maximally capture the genetic diversity in available crop collections. The present study was initiated to construct nested core collections to determine the appropriate sample size to represent the genetic diversity of rice landrace collection based on 15 quantitative traits and 34 qualitative traits of 2 262 rice accessions. The results showed that 50-225 nested core collections, whose sampling rate was 2.2%-9.9%, were sufficient to maintain the maximum genetic diversity of the initial collections. Of these, 150 accessions （6.6%） could capture the maximal genetic diversity of the initial collection. Three data types, i.e. qualitative traits （QT1）, quantitative traits （QT2） and integrated qualitative and quantitative traits （QTT）, were compared for their efficiency in constructing core collections based on the weighted pair-group average method combined with stepwise clustering and preferred sampling on adjusted Euclidean distances. Every combining scheme constructed eight rice core collections （225, 200, 175, 150, 125, 100, 75 and 50）. The results showed that the QTT data was the best in constructing a core collection as indicated by the genetic diversity of core collections. A core collection constructed only on the information of QT1 could not represent the initial collection effectively. QTT should be used together to construct a productive core collection.

Sample size effect on the dynamic torsional behaviour of the 2A12 aluminium alloy

In order to investigate the effect of sample size on the dynamic torsional behaviour of the 2A12 aluminium alloy. In this paper, torsional split Hopkinson bar tests are conducted on this alloy with different sample dimensions. It is found that with the decreasing gauge length and thickness, the tested yield strength increases. However, the sample innerlouter diameter has little effect on the dynamic torsional behaviour. Based on the finite element method, the stress states in the alloy with different sample sizes are analysed. Due to the effect of stress concentration zone （SCZ）, the shorter sample has a higher yield stress. Furthermore, the stress distributes more uniformly in the thinner sample, which leads to the higher tested yield stress. According to the experimental and simulation analysis, some suggestions on choosing the sample size are given as well.

Impacts of sample size for stomach content analysis on the estimation of ecosystem indices

This study used Ecopath model of the Jiaozhou Bay as an example to evaluate the effect of stomach sample size of three fish species on the projection of this model. The derived ecosystem indices were classified into three categories:(1) direct indices, like the trophic level of species, influenced by stomach sample size directly;(2)indirect indices, like ecology efficiency(EE) of invertebrates, influenced by the multiple prey-predator relationships;and(3) systemic indices, like total system throughout(TST), describing the status of the whole ecosystem. The influences of different stomach sample sizes on these indices were evaluated. The results suggest that systemic indices of the ecosystem model were robust to stomach sample sizes, whereas specific indices related to species were indicated to be with low accuracy and precision when stomach samples were insufficient.The indices became more uncertain when the stomach sample sizes varied for more species. This study enhances the understanding of how the quality of diet composition data influences ecosystem modeling outputs. The results can also guide the design of stomach content analysis for developing ecosystem models.

Sample size re-estimation without un-blinding for time-to-event outcomes in oncology clinical trials

Sample size re-estimation is essential in oncology studies. However, the use of blinded sample size reassessment for survival data has been rarely reported. Based on the density function of the exponential distribution, an expectation-maximization（EM） algorithm of the hazard ratio was derived, and several simulation studies were used to verify its applications. The method had obvious variation in the hazard ratio estimates and overestimation for the relatively small hazard ratios. Our studies showed that the stability of the EM estimation results directly correlated with the sample size, the convergence of the EM algorithm was impacted by the initial values, and a balanced design produced the best estimates. No reliable blinded sample size re-estimation inference can be made in our studies, but the results provide useful information to steer the practitioners in this field from repeating the same endeavor.

Influence of parental sample sizes on the estimating genetic parameters in cultured clam Meretrix meretrix based on factorial mating designs

The precise and accurate knowledge of genetic parameters is a prerequisite for making efficient selection strategies in breeding programs.A number of estimators of heritability about important economic traits in many marine mollusks are available in the literature,however very few research have evaluated about the accuracy of genetic parameters estimated with different family structures.Thus,in the present study,the effect of parent sample size for estimating the precision of genetic parameters of four growth traits in clam M.meretrix by factorial designs were analyzed through restricted maximum likelihood（REML） and Bayesian.The results showed that the average estimated heritabilities of growth traits obtained from REML were 0.23-0.32 for 9 and 16 full-sib families and 0.19-0.22 for 25 full-sib families.When using Bayesian inference,the average estimated heritabilities were0.11-0.12 for 9 and 16 full-sib families and 0.13-0.16 for 25 full-sib families.Compared with REML,Bayesian got lower heritabilities,but still remained at a medium level.When the number of parents increased from 6 to 10,the estimated heritabilities were more closed to 0.20 in REML and 0.12 in Bayesian inference.Genetic correlations among traits were positive and high and had no significant difference between different sizes of designs.The accuracies of estimated breeding values from the 9 and 16 families were less precise than those from 25 families.Our results provide a basic genetic evaluation for growth traits and should be useful for the design and operation of a practical selective breeding program in the clam M.meretrix.

Minimum sample size estimates for trials in inflammatory bowel disease:A systematic review of a support resource

BACKGROUND Of 25%of randomised controlled trials(RCTs)on interventions for inflammatory bowel disease(IBD)have no power calculation.AIM To systematically review RCTs reporting interventions for the management of IBD and to produce data for minimum sample sizes that would achieve appropriate power using the actual clinical data.METHODS We included RCTs retrieved from Cochrane IBD specialised Trial register and CENTRAL investigating any form of therapy for either induction or maintenance of remission against control,placebo,or no intervention of IBD in patients of any age.The relevant data was extracted,and the studies were grouped according to the intervention used.We recalculated sample size and the achieved difference,as well as minimum sample sizes needed in the future.RESULTS A total of 105 trials were included.There was a large discrepancy between the estimated figure for the minimal clinically important difference used for the calculations(15%group differences observed vs 30%used for calculation)explaining substantial actual sample size deficits.The minimum sample sizes indicated for future trials based on the 25 years of trial data were calculated and grouped by the intervention.CONCLUSION A third of intervention studies in IBD within the last 25 years are underpowered,with large variations in the calculation of sample sizes.The authors present a sample size estimate resource constructed on the published evidence base for future researchers and key stakeholders within the IBD trial field.

A STATISTICAL INVESTIGATION OF FATIGUE CRACK INITIATION AND GROWTH PROCESS BASED UPON A LARGE SAMPLE SIZE EXPERIMENT

After finishing 102 replicate constant amplitude crack initiation and growth tests on Ly12-CZ aluminum alloy plate, a statistical investigation of the fatigue crack initiation and growth process is conducted in this paper. According to the post-mortem fractographic examination by scanning electron microscopy (SEM), some qualitative observations of the spacial correlation among fatigue striations are developed to reveal the statistical nature of material intrinsic inhomogeneity during the crack growth process. From the test data, an engineering division between crack initiation and growth is defined as the upper limit of small crack. The distributions of crack initiation life N-i, growth life N, and the statistical characteristics of crack growth rate da/dN are also investigated. It is hoped that the work will provide a solid test basis for the study of probabilistic fatigue, probabilistic fracture mechanics, fatigue reliability and its engineering applications.

Spatial Interpolation and Sample Size Optimization for Soil Copper(Cu) Investigation in Cropland Soil at County Scale Using Cokriging

Knowledge on spatial distribution and sampling size optimization of soil copper （Cu） could lay solid foundations for environmetal quality survey of agricultural soils at county scale. In this investigation, cokriging method was used to conduct the interpolation of Cu concentraiton in cropland soil in Shuangliu County, Sichuan Province, China. Based on the original 623 physicochmically measured soil samples, 560, 498, and 432 sub-samples were randomly selected as target variable and soil organic matter （SOM） of the whole original samples as auxiliary variable. Interpolation results using Cokriging under different sampling numbers were evaluated for their applicability in estimating the spatial distribution of soil Cu at county sacle. The results showed that the root mean square error （RMSE） produced by Cokriging decreased from 0.9 to 7.77%, correlation coefficient between the predicted values and the measured increased from 1.76 to 9.76% in comparison with the ordinary Kriging under the corresponding sample sizes. The prediction accuracy using Cokriging was still higher than original 623 data using ordinary Kriging even as sample size reduced 10%, and their interpolation maps were highly in agreement. Therefore, Cokriging was proven to be a more accurate and economic method which could provide more information and benefit for the studies on spatial distribution of soil pollutants at county scale.

Application of statistical analysis of sample size:How many occupant responses are required for an indoor environmental quality(IEQ)field study

Determining required sample size is one of the critical pathways to reproducible,reliable and robust results in human-related studies.This paper aims to answer a fundamental but often overlooked question:what sample size is required in surveys of occupant responses to indoor environmental quality(IEQ).The statistical models are introduced in order to promote determining required sample size for various types of data analysis methods commonly used in IEQ field studies.The Monte Carlo simulations are performed to verify the statistical methods and to illustrate the impact of sample size on the study accuracy and reliability.Several examples are presented to illustrate how to determine the value of the parameters in the statistical models based on previous similar research or existing databases.The required sample size including“worst”and“optimal”cases in each condition is obtained by this method and references.It is indicated that 385 is a“worst case”sample size to be adequate for a subgroup analysis,while if the researcher has an estimate of the study design and outcome,the“optimal case”sample size can potentially be reduced.When the required sample size is not achievable,the uncertainty in the result can properly interpret via a confidence interval.It is hoped that this paper would fill in the gap between statistical analysis of sample size and IEQ field research,and it can provide a useful reference for researchers when planning their own studies.

Effect of sample size on the response of DEM samples with a realistic grading

This paper shows that for DEM simulations of triaxial tests using samples with a grading that is repre- sentative of a real soil, the sample size significantly influences the observed material response. Four DEM samples with identical initial states were produced： three cylindrical samples bounded by rigid wails and one bounded by a cubical periodic cell, When subjected to triaxial loading, the samples with rigid boundaries were more dilative, stiffer and reached a higher peak stress ratio than the sample enclosed by periodic boundaries. For the rigid-wall samples, dilatancy increased and stiffness decreased with increasing sample size, The periodic sample was effectively homogeneous, The void ratio increased and the contact density decreased close to the rigid walls, This heterogeneity reduced with increasing sample size. The positions of the critical state lines （CSLs） of the overall response in e-log p＇ space were sensitive to the sample size, although no difference was observed between their slopes. The critical states of the interior regions of the rigid-wall-bounded samples approached that of the homogeneous periodic sample with increasing sample size. The ultimate strength of the material at the critical state is independent of sample size.

An evaluation of the effects of sample size on estimating length composition of catches from tuna longline fisheries using computer simulations

Length composition analysis can provide insights into the dynamics of a fish population.Accurate quantification of the size structure of a population is critical to understand the status of a fishery and how the population responds to environmental stressors.A scientific observer program is a reliable way to provide such accurate information.However,100%observer coverage is usually impossible for most fisheries because of logistic and financial constraints.Thus,there is a need to evaluate observer program performance,identify suitable sample sizes,and optimize the allocation of observation efforts.The objective of this study is to evaluate the effects of sample size on the quality of length composition data and identify an optimal coverage rate and observation ratio to improve the observation efficiency using an onboard observer data set from China's tuna longline fishery in the western and central Pacific Ocean.We found that the required sample size varies with fish species,indices used to describe length composition,the acceptable accuracy of the estimates,and the allocation methods of sampling effort.Ignoring other information requirements,1000 individuals would be sufficient for most species to reliably quantify length compositions,and a smaller sample size could generate reliable estimates of mean length.A coverage rate of 20%would be sufficient for most species,but a lower coverage rate(5%or 10%)could also be effective to meet with the accuracy and precision requirement in estimating length compositions.A nonrandom effort allocation among fishing baskets within a set could cause the length composition to be overestimated or underestimated for some species.The differences in effective sample sizes among species should be included in the consideration for a rational allocation of observation effort among species when there are different species management priorities.

The methodology flaws in Hinman's acupuncture clinical trial, Part Ⅲ: Sample size calculation

In the October 2014 publication of JAMA,Dr.Hinman and colleagues published the study＂Acupuncture for Chronic Knee Pain：A Randomized Clinical Trial,＂in which the authors concluded that＂in patients older than50 years with moderate or severe chronic knee pain,neither laser nor needle acupuncture conferred benefi t over sham for pain or function.Our fi ndings do not support acupuncture[1]

ANALYSIS OF THE IMPACT OF SAMPLE SIZE, ATTRIBUTE VARIANCE AND WITHIN-SAMPLE CHOICE DISTRIBUTION ON THE ESTIMATION ACCURACY OF MULTINOMIAL LOGIT MODELS USING SIMULATED DATA

Literature review indicates that sample size, attribute variance and within-sample choice distribution of alternatives are important considerations in the estimation of multinomial logit （MNL） models, but their impacts on the estimation accuracy have not been systematically studied. Therefore, the objective of this paper is to provide an empirical examination to the above issues through a set of simulated discrete choice preference and rank ordered preference datasets. In this paper, the utility coefficients, alternative specific constants （ASCs）, and the mean and standard deviation of the four attributes for a set of seven hypothetical alternatives are specified as a priori. Then, synthetic datasets, with varying sample size, attribute variance and within-sample choice distribution are simulated. Based on these datasets, the utility coefficients and ASCs of the specified MNLs are re-estimated and compared with the original values specified as the priori. It is found that （1） the estimation accuracy of utility parameters increases as the sample size increases; （2） the utility coefficients can be re-estimated with reasonable accuracy, but the estimates of the ASCs are confronted with much larger errors; （3） as the variances of the alternative attributes increase, the estimation accuracy improves significantly; and （4） as the distribution of chosen choices becomes more balanced across alternatives within sample datasets, the hit-ratio decreases. The results indicate that （a） under a similar setting presented in this paper, a large sample consisting of a few thousand observations （3000 - 4000） may be needed in order to provide reasonable estimates for utility coefficients, particularly for ASCs; （b） a larger, but realistic attribute space is preferred in the stated preference survey design; and （c） choice datasets with unbalanced ＂chosen＂ choice frequency distribution is preferred, in order to better capture the elasticity between the ＂perceived utility＂ associated with alternative＇s attributes.

Power analysis,sample size calculation for testing the largest binomial probability

A procedure is developed for power analysis and sample size calculation for a class of complex testing problems regarding the largest binomial probability under a combination of treatments.It is shown that the asymptotic null distribution of the likelihood-ratio statistic is not parameterfree,but χ_(1)^(2) is a conservative asymptotic null distribution.A nonlinear Gauss-Seidel algorithm is proposed to uniquely determine the alternative for the power and sample size calculation given the baseline binomial probability.An example from an animal clinical trial is discussed.

Sample size and power analysis for stepped wedge cluster randomised trials with binary outcomes

In stepped wedge cluster randomised trials(SW-CRTs),clusters of subjects are randomly assigned to sequences,where they receive a specific order of treatments.Compared to conventional cluster randomised studies,one unique feature of SW-CRTs is that all clusters start from control and gradually transition to intervention according to the randomly assigned sequences.This feature mitigates the ethical concern of withholding an effective treatment and reduces the logistic burden of implementing the intervention at multiple clusters simultaneously.This feature,however,presents challenges that need to be addressed in experimental design and data analysis,i.e.,missing data due to prolonged follow-up and complicated correlation structures that involve between-subject and longitudinal correlations.In this study,based on the generalised estimating equation(GEE)approach,we present a closed-form sample size formula for SW-CRTs with a binary outcome,which offers great flexibility to account for unbalanced randomisation,missing data,and arbitrary correlation structures.We also present a correction approach to address the issue of under-estimated variance by GEE estimator when the sample size is small.Simulation studies and application to a real clinical trial are presented.

Metal Corrosion Rate Prediction of Small Samples Using an Ensemble Technique

Accurate prediction of the internal corrosion rates of oil and gas pipelines could be an effective way to prevent pipeline leaks.In this study,a proposed framework for predicting corrosion rates under a small sample of metal corrosion data in the laboratory was developed to provide a new perspective on how to solve the problem of pipeline corrosion under the condition of insufficient real samples.This approach employed the bagging algorithm to construct a strong learner by integrating several KNN learners.A total of 99 data were collected and split into training and test set with a 9:1 ratio.The training set was used to obtain the best hyperparameters by 10-fold cross-validation and grid search,and the test set was used to determine the performance of the model.The results showed that theMean Absolute Error(MAE)of this framework is 28.06%of the traditional model and outperforms other ensemblemethods.Therefore,the proposed framework is suitable formetal corrosion prediction under small sample conditions.

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.