大锻件统计学Chi-square test的研究和应用

根据大锻件生产的特点和统计学的基本理论方法,首次深入浅出地论述了大锻件的Chi-square test,即X2检验,并给出了具体应用示例。该方法可用于大锻件工艺参数的科学分析和生产验证,可用于大锻件质量分析和判断,可帮助逐步建立起大锻件的工序能力,帮助实现稳定并提升大锻件工艺和质量控制水平。

Large Deviations and Moderate Deviations for the Chi-Square Test in Type Ⅱ Error

We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.

Data Consistency Tests through the Use of Neural Networks and Virial Equation. Application of the Proposed Methodology to Critical Study of Density Data

This paper focuses on a very important point which consists in evaluating experimental data prior to their use for chemical process designs. Hexafluoropropylene P, ρ, T data measured at 11 temperatures from 263 to 362 K and at pressures up to 10 MPa have been examined through a consistency test presented herein and based on the use of a methodology implying both neural networks and Virial equation. Such a methodology appears as very powerful to identify erroneous data and could be conveniently handled for quick checks of databases previously to modeling through classical thermodynamic models and equations of state. As an application to liquid and vapor phase densities of hexafluoropropylene, a more reliable database is provided after removing out layer data.

Use of Pearson’s Chi-Square for Testing Equality of Percentile Profiles across Multiple Populations

In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For example, it may be more informative to compare two or more populations with respect to their within population distributions by testing the hypothesis that their corresponding respective 10th, 50th, and 90th percentiles are equal. As a generalization of the median test, the proposed test statistic is asymptotically distributed as Chi-square with degrees of freedom dependent upon the number of percentiles tested and constraints of the null hypothesis. Results from simulation studies are used to validate the nominal 0.05 significance level under the null hypothesis, and asymptotic power properties that are suitable for testing equality of percentile profiles against selected profile discrepancies for a variety of underlying distributions. A pragmatic example is provided to illustrate the comparison of the percentile profiles for four body mass index distributions.

A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions

Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.

Consistency check of degradation mechanism between natural storage and enhancement test for missile servo system

Reliability enhancement testing(RET) is an accelerated testing which hastens the performance degradation process to surface its inherent defects of design and manufacture. It is an important hypothesis that the degradation mechanism of the RET is the same as the one of the normal stress condition. In order to check the consistency of two mechanisms, we conduct two enhancement tests with a missile servo system as an object of the study, and preprocess two sets of test data to establish the accelerated degradation models regarding the temperature change rate that is assumed to be the main applied stress of the servo system during the natural storage. Based on the accelerated degradation models and natural storage profile of the servo system, we provide and demonstrate a procedure to check the consistency of two mechanisms by checking the correlation and difference of two sets of degradation data. The results indicate that the two degradation mechanisms are significantly consistent with each other.

Thermodynamic Consistency Test for Binary Gas ＋ Water Equilibrium Data at Low and High Pressures

Phase equilibrium in binary gas + water mixtures over wide ranges of temperatures and pressures are modeled and tested for thermodynamic consistency. For modeling, the Peng-Robinson equation of state was used and the Wong-Sandler mixing rules were incorporated into the equation of state parameters. In the Wong-Sandler mixing rules the van Laar model for the excess Gibbs energy was applied. In addition, a reasonable and flexible method is applied to test the thermodynamic consistency of pressure-temperature-concentration(P-T-x) data of these binary mixtures.Modeling is found acceptable in all cases, meaning that deviations in correlating the pressure and the gas phase concentration are low. For all cases the thermodynamic consistency method gives a clear conclusion about consistency or inconsistency of a set of experimental P-T-x data.

Chi-Square Distribution: New Derivations and Environmental Application

We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.

On the Different Ways to Handle the Trend of Disease Risk in Genetic Association Tests

Genetic association studies usually apply the simple chi-square (χ2)-test for testing association between a single-nucleotide polymorphism (SNP) and a particular phenotype, assuming the genotypes and phenotypes are independent. So, the conventional χ2-test does not consider the increased risk of an individual carrying the increasing number of disease responsible allele (a particular genotype). But, the association tests should be performed with the consideration of this disease risk according to the mode of inheritance (additive, dominant, recessive). Practical demonstration of the two possible methods for considering such order or trends in contingency tables of genetic association studies using SNP genotype data is the purpose of this paper. One method is by pooling the genotypes, and the other is scoring the individual genotypes, based on the disease risk according to the inheritance pattern. The results show that the p-values obtained from both the methods are similar for the dominant and recessive models. The other important features of the methods were also extracted using the SNP genotype data for different inheritance patterns.

CONSISTENCY OF MLE OF THE PARAMETER OF EXPONENTIAL LIFETIME DISTRIBUTION FOR RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION

In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.

Image segmentation by level set evolution with region consistency constraint

Image segmentation is a key and fundamental problem in image processing,computer graphics,and computer vision.Level set based method for image segmentation is used widely for its topology flexibility and proper mathematical formulation.However,poor performance of existing level set models on noisy images and weak boundary limit its application in image segmentation.In this paper,we present a region consistency constraint term to measure the regional consistency on both sides of the boundary,this term defines the boundary of the image within a range,and hence increases the stability of the level set model.The term can make existing level set models significantly improve the efficiency of the algorithms on segmenting images with noise and weak boundary.Furthermore,this constraint term can make edge-based level set model overcome the defect of sensitivity to the initial contour.The experimental results show that our algorithm is efficient for image segmentation and outperform the existing state-of-art methods regarding images with noise and weak boundary.

Practical integrated navigation fault detection algorithm based on sequential hypothesis testing

In detecting system fault algorithms,the false alarm rate and undectect rate generated by residual Chi-square test can affect the stability of filters.The paper proposes a fault detection algorithm based on sequential residual Chi-square test and applies to fault detection of an integrated navigation system.The simulation result shows that the algorithm can accurately detect the fault information of global positioning system（GPS）,eliminate the influence of false alarm and missed detection on filter,and enhance fault tolerance of integrated navigation systems.

Model Checking-Based Testing of Web Applications

A formal model representing the navigation behavior of a Web application as the Kripke structure is proposed and an approach that applies model checking to test case generation is presented. The Object Relation Diagram as the object model is employed to describe the object structure of a Web application design and can be translated into the behavior model. A key problem of model checking-based test generation for a Web application is how to construct a set of trap properties that intend to cause the violations of model checking against the behavior model and output of counterexamples used to construct the test sequences. We give an algorithm that derives trap properties from the object model with respect to node and edge coverage criteria.

On consistency and ranking of alternatives in uncertain AHP

This paper introduces uncertainty theory to deal with non-deterministic factors in ranking alternatives. The uncertain variable method (UVM) and the definition of consistency for uncertainty comparison matrices are proposed. A simple yet pragmatic approach for testing whether or not an uncertainty comparison matrix is consistent is put forward. In cases where an uncertainty comparison matrix is inconsistent, an algorithm is used to generate consistent matrix. And then the consistent uncertainty comparison matrix can derive the uncertainty weights. The final ranking is given by uncertainty weighs if they are acceptable;otherwise we rely on the ranks of expected values of uncertainty weights instead. Three numerical examples including a hierarchical (AHP) decision problem are examined to illustrate the validity and practicality of the proposed methods.

Beep test评估11～15岁少年游泳运动员有氧能力的效度研究

目的:评估现有通过beep test估算VO_2max的公式在我国少年游泳运动员中的适用性,以及能否建立预测准确性更高的公式。斱法:28名男子和25名女子少年游泳运动员,年龄11~15岁,先进行beep test获得最快折返跑速度,随后通过递增负荷跑台测试获得VO_2max测试值。通过逐步回归法建立新的VO_2max估算公式,计算分别通过Léger、Barnett(a)、Barnett(b)、Matsuzaka和新公式的VO_2max估算值,采用差值比较、相关分析、误差分析和一致性分析进行各估算值的效度检验。结果:1)通过Léger、Barnett(a)、Barnett(b)和Matsuzaka公式得出的VO_2max估算值均显著低于测试值,%Error为(68.4~90.0)%,与测试值间的差值为7.63~9.02ml/kg/min,一致性界限为0.49~17.55 ml/kg/min。2)VO_2max的新预测公式为VO_2max=61.435+3.211S-2.003BMI-5.189×G(r=0.715,P=0.004,SEE=2.25 ml/kg/min),其中G表示性别(男=0,女=1),S为最快折返跑速度。3)新公式得出的VO_2max估算值与测试值无显著差异,%Error下降至16.1%,与测试值间的差值减少到0.02±3.09 ml/kg/min,一致性界限为-6.03~6.08 ml/kg/min。结论:beep test适用于我国少年游泳运动员有氧能力的评估,但现有VO_2max估算公式的效度水平一般。基于本研究所选取群体新建的估算公式有效提高了预测的准确性。

Consistency of Chi-Squared Test with Varying Number of Classes

The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.

The Values of the Prognostic Nutrition Index and the Patient Generated-Subjective Global Assessment during the Nutritional Assessment of Patients with Gastrointestinal Tumors

Objective To compare the value and consistency among the Patient Generated-Subjective Global Assessment(PG-SGA)and the Prognostic Nutrition Index(PNI)for assessing nutritional status in gastrointestinal tumor patients.Methods 251 patients from gastric cancer surgical ward from January 2019 to January 2020 were recruited through convenience sampling in this respective study.Nutritional screening and assessment were conducted for 251 gastrointestinal tumor patients using the nutritional risk screening 2002(NRS 2002)PG-SGA,and the PNI.PNI was calculated using the serum albumin level and the total lymphocyte count obtained from the patients’routine laboratory examination when they were admitted to the hospital.The receiver operating characteristic(ROC)of the PG SGA and the PNI were plotted with the NRS 2002 used as the gold standard,and the diagnostic value of the PG-SGA and PNI was reflected by the area under the curve(AUC),sensitivity,specificity and Youden index.We then determined the optimal cut-off for the PNI and tested the consistency of the PG-SGA and PNI.Results The optimal cut-off point for the PNI was calculated to be 50.78.The AUC of the PG-SGA was 0.908(95%CI 0.871-0.944).The sensitivity was 89.9%,specificity was 76.2%and the Youden index was 0.661.The AUC of the PNI was 0.594(95%CI 0.516-0.572).The sensitivity was 73.8%,specificity was 44.3%and the Youden index was 0.181.In the consistency test,the kappa value was 0.838(P<0.001).Conclusion The PNI is of limited value for assessing malnutrition,although it did have good consistency with the PG-SGA.The combination of the PNI and PG-SGA can be used for diagnosing assessing malnutrition in clinical practice.

Consistency analysis of accelerated degradation mechanism based on gray theory

A fundamental premise of an accelerated testing is that the failure mechanism under elevated and normal stress levels should remain the same. Thus, verification of the consistency of failure mechanisms is essential during an accelerated testing. A new consistency analysis method based on the gray theory is pro- posed for complex products. First of all, existing consistency ana- lysis methods are reviewed with a focus on the comparison of the differences among them. Then, the proposed consistency ana- lysis method is introduced. Two effective gray prediction models, gray dynamic model and new information and equal dimensional （NIED） model, are adapted in the proposed method. The process to determine the dimension of NIED model is also discussed, and a decision rule is expanded. Based on that, the procedure of ap- plying the new consistent analysis method is developed. Finally, a case study of the consistency analysis of a reliability enhancement testing is conducted to demonstrate and validate the proposed method.

A Note on Cochran Test for Homogeneity in Two Ways ANOVA and Meta-Analysis

In this paper, we generalize the proof of the Cochran statistic in the case of an ANOVA two ways structure that asymptotically follows a Chi-2. While construction of homogeneity statistics test usually resorts to the determination of the covariance matrix and its inverse, the Moore-Penrose matrix, our approach, avoids this step. We also show that the Cochran statistic in ANOVA two ways is equivalent to conventional homogeneity statistics test. In particular, we show that it satisfies the invariance property. Finally, we conduct empirical verification from a meta-analysis that confirms our theoretical results.