Comparison of Type I Error Rates of Siegel-Tukey and Savage Tests among Non-Parametric Tests

This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviation ratio of 1, was conducted for both small and large sample sizes. For small sample sizes, two main categories were established: equal and different sample sizes. Analyses were performed using Monte Carlo simulations with 20,000 repetitions for each scenario, and the simulations were evaluated using SAS software. For small sample sizes, the I. type error rate of the Siegel-Tukey test generally ranged from 0.045 to 0.055, while the I. type error rate of the Savage test was observed to range from 0.016 to 0.041. Similar trends were observed for Platykurtic and Skewed distributions. In scenarios with different sample sizes, the Savage test generally exhibited lower I. type error rates. For large sample sizes, two main categories were established: equal and different sample sizes. For large sample sizes, the I. type error rate of the Siegel-Tukey test ranged from 0.047 to 0.052, while the I. type error rate of the Savage test ranged from 0.043 to 0.051. In cases of equal sample sizes, both tests generally had lower error rates, with the Savage test providing more consistent results for large sample sizes. In conclusion, it was determined that the Savage test provides lower I. type error rates for small sample sizes and that both tests have similar error rates for large sample sizes. These findings suggest that the Savage test could be a more reliable option when analyzing variance differences.

Tests and error analysis of a self-positioning shearer operating at a manless working face

Self-positioning of a shearer is the key technology for mining with a man-less working face. In an underground coal mine all radio navigation; satellite positioning or celestial navigation methods have their limitations. We analyzed an inertial navi-gation system intended to guide the movement a shearer and designed a self-positioning device for the shearer. Simulation tests were also performed on the system. We analyzed the errors observed in these tests to show that the main reason for the low preci-sion of the self-positioning system is accumulated error in the inertial sensor. A Kalman filtering algorithm used in combination with the shearer motion model effectively reduces the measurement errors of the self-positioning system by compensating for gyroscopic drift. Finally, we built an error compensation model to reduce accumulated errors using continuous correction to provide self-positioning of the shearer within a certain range of accuracy.

Identification of Kinematic Errors of Five-axis Machine Tool Trunnion Axis from Finished Test Piece

Compared with the traditional non-cutting measurement,machining tests can more accurately reflect the kinematic errors of five-axis machine tools in the actual machining process for the users.However,measurement and calculation of the machining tests in the literature are quite difficult and time-consuming.A new method of the machining tests for the trunnion axis of five-axis machine tool is proposed.Firstly,a simple mathematical model of the cradle-type five-axis machine tool was established by optimizing the coordinate system settings based on robot kinematics.Then,the machining tests based on error-sensitive directions were proposed to identify the kinematic errors of the trunnion axis of cradle-type five-axis machine tool.By adopting the error-sensitive vectors in the matrix calculation,the functional relationship equations between the machining errors of the test piece in the error-sensitive directions and the kinematic errors of C-axis and A-axis of five-axis machine tool rotary table was established based on the model of the kinematic errors.According to our previous work,the kinematic errors of C-axis can be treated as the known quantities,and the kinematic errors of A-axis can be obtained from the equations.This method was tested in Mikron UCP600 vertical machining center.The machining errors in the error-sensitive directions can be obtained by CMM inspection from the finished test piece to identify the kinematic errors of five-axis machine tool trunnion axis.Experimental results demonstrated that the proposed method can reduce the complexity,cost,and the time consumed substantially,and has a wider applicability.This paper proposes a new method of the machining tests for the trunnion axis of five-axis machine tool.

APPROXIMATE POWER OF HETEROSCEDASTICITY TEST IN NONLINEAR MODELS WITH ARIMA（0,1,0） ERRORS

This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.

A Study on Measurement Error during Alternating Current Induced Voltage Tests on Large Transformers

The large transformer is pivotal equipment in an electric power supply system; Its partial discharge test and the induced voltage withstand test on large transformers are carried out at a frequency about twice the working frequency. If the magnetizing inductance cannot compensate for the stray capacitance, the test sample turns into a capacitive load and a capacitive rise exhibits in the testing circuit. For self-restoring insulation, a method has been recommended in IEC60-1 that an unapproved measuring system be calibrated by an approved system at a voltage not less than 50% of the rated testing voltage, and the result then be extrapolated linearly. It has been found that this method leads to great error due to the capacitive rise if it is not correctly used during a withstand voltage test under certain testing conditions, especiaUy for a test on high voltage transformers with large capacity. Since the withstand voltage test is the most important means to examine the operation reliability of a transformer, and it can be destructive to the insulation, a precise measurement must be guaranteed. In this paper a factor, named as the capacitive rise factor, is introduced to assess the rise. The voltage measurement error during the calibration is determined by the parameters of the test sample and the testing facilities, as well as the measuring point. Based on theoretical analysis in this paper, a novel method is suggested and demonstrated to estimate the error by using the capacitive rise factor and other known parame- ters of the testing circuit.

Dynamics and Attitude Error Analysis for Dock Test System of Small Satellite

To analyze the attitude errors of vertical docking test system of small satellite,the static error and kinematic error of test system are considered.The working principle of test system and coordinate of actuator are introduced.The model of friction torque on the joints and torque on docking mechanism are built.Dynamics equation of actuator is built by the Lagrange equation and the Nielsen equation.Under the condition of 24 different angle groups,the calculation of dynamics equation is built by using MATLAB/SIMULINK platform and the kinematic errors of actuator are obtained.The attitude error models of docking mechanism are built.Results shows that the main angle error sources of yaw,row,pitch are not identical.The attitude error of yaw angle can be decreased by compensating the angle error around xaxis.The attitude error of row angle mainly originates in the system error,and it can be eliminated by adjusting non-orthogonal degree.

TESTING OF CORRELATION AND HETEROSCEDASTICITY IN NONLINEAR REGRESSION MODELS WITH DBL(p,q,1) RANDOM ERRORS

Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.

On the Distribution of Type II Errors in Hypothesis Testing

When a statistical test of hypothesis for a population mean is performed, we are faced with the possibility of committing a Type II error by not rejecting the null hypothesis when in fact the population mean has changed. We consider this issue and quantify matters in a manner that differs a bit from what is commonly done. In particular, we define the probability distribution function for Type II errors. We then explore some interesting properties that we have not seen mentioned elsewhere for this probability distribution function. Finally, we discuss several Maple procedures that can be used to perform various calculations using the distribution.

Dynamic error research and application of an angular measuring system belonging to a high precision excursion test turntable

Angular measuring system is the most important component of a servo turntable in inertial test apparatus. Its function and precision determine the turntable＇ s function and precision. It attaches importance to research on inertial test equipment. This paper introduces the principle of the angular measuring system using amplitude discrimination mode. The dynamic errors axe analyzed from the aspects of inductosyn, amplitude and function error of double-phase voltage and wavefonn distortion. Through detailed calculation, theory is provided for practical application; system errors are allocated and the angular measuring system meets the accuracy requirement. As a result, the schedule of the angular measuring system can be used in practice.

Robust Principal Component Test in Gross Error Detection and Identification

Principle component analysis （PCA） based chi-square test is more sensitive to subtle gross errors and has greater power to correctly detect gross errors than classical chi-square test. However, classical principal com- ponent test （PCT） is non-robust and can be very sensitive to one or more outliers. In this paper, a Huber function liked robust weight factor was added in the collective chi-square test to eliminate the influence of gross errors on the PCT. Meanwhile, robust chi-square test was applied to modified simultaneous estimation of gross error （MSEGE） strategy to detect and identify multiple gross errors. Simulation results show that the proposed robust test can reduce the possibility of type Ⅱ errors effectively. Adding robust chi-square test into MSEGE does not obviously improve the power of multiple gross error identification, the proposed approach considers the influence of outliers on hypothesis statistic test and is more reasonable.

A flexible and robust soft-error testing system for microelectronic devices and integrated circuits

Single event effects(SEEs) induced by radiations become a significant challenge to the reliability for modern electronic systems. To evaluate SEEs susceptibility for microelectronic devices and integrated circuits(ICs), an SEE testing system with flexibility and robustness was developed at Heavy Ion Research Facility in Lanzhou(HIRFL). The system is compatible with various types of microelectronic devices and ICs, and supports plenty of complex and high-speed test schemes and plans for the irradiated devices under test(DUTs). Thanks to the combination of meticulous circuit design and the hardened logic design, the system has additional performances to avoid an overheated situation and irradiations by stray radiations. The system has been tested and verified by experiments for irradiating devices at HIRFL.

Sensitivity and Specificity Analysis Relation to Statistical Hypothesis Testing and Its Errors: Application to Cryptosporidium Detection Techniques

The use of Statistical Hypothesis Testing procedure to determine type I and type II errors was linked to the measurement of sensitivity and specificity in clinical trial test and experimental pathogen detection techniques. A theoretical analysis of establishing these types of errors was made and compared to determination of False Positive, False Negative, True Positive and True Negative. Experimental laboratory detection methods used to detect Cryptosporidium spp. were used to highlight the relationship between hypothesis testing, sensitivity, specificity and predicted values. The study finds that, sensitivity and specificity for the two laboratory methods used for Cryptosporidium detection were low hence lowering the probability of detecting a “false null hypothesis” for the presence of cryptosporidium in the water samples using either Microscopic or PCR. Nevertheless, both procedures for cryptosporidium detection had higher “true negatives” increasing its probability of failing to reject a “true null hypothesis” with specificity of 1.00 for both Microscopic and PCR laboratory detection methods.

Characterizing prediction errors of a new tree height model for cut-to-length Pinus radiata stems through the Burr TypeⅫdistribution

Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionally normal but are rather leptokurtic and heavy-tailed.This feature was merely noticed in previous studies but never thoroughly investigated.This study characterized the prediction error distribution of a newly developed such tree height model for Pin us radiata(D.Don)through the three-parameter Burr TypeⅫ(BⅫ)distribution.The model’s prediction errors(ε)exhibited heteroskedasticity conditional mainly on the small end relative diameter of the top log and also on DBH to a minor extent.Structured serial correlations were also present in the data.A total of 14 candidate weighting functions were compared to select the best two for weightingεin order to reduce its conditional heteroskedasticity.The weighted prediction errors(εw)were shifted by a constant to the positive range supported by the BXII distribution.Then the distribution of weighted and shifted prediction errors(εw+)was characterized by the BⅫdistribution using maximum likelihood estimation through 1000 times of repeated random sampling,fitting and goodness-of-fit testing,each time by randomly taking only one observation from each tree to circumvent the potential adverse impact of serial correlation in the data on parameter estimation and inferences.The nonparametric two sample Kolmogorov-Smirnov(KS)goodness-of-fit test and its closely related Kuiper’s(KU)test showed the fitted BⅫdistributions provided a good fit to the highly leptokurtic and heavy-tailed distribution ofε.Random samples generated from the fitted BⅫdistributions ofεw+derived from using the best two weighting functions,when back-shifted and unweighted,exhibited distributions that were,in about97 and 95%of the 1000 cases respectively,not statistically different from the distribution ofε.Our results for cut-tolength P.radiata stems represented the first case of any tree species where a non-normal error distribution in tree height prediction was described by an underlying probability distribution.The fitted BXII prediction error distribution will help to unlock the full potential of the new tree height model in forest resources modelling of P.radiata plantations,particularly when uncertainty assessments,statistical inferences and error propagations are needed in research and practical applications through harvester data analytics.

An improved four-dimensional variation source term inversion model with observation error regularization

Aiming at the Four-Dimensional Variation source term inversion algorithm proposed earlier,the observation error regularization factor is introduced to improve the prediction accuracy of the diffusion model,and an improved Four-Dimensional Variation source term inversion algorithm with observation error regularization(OER-4DVAR STI model)is formed.Firstly,by constructing the inversion process and basic model of OER-4DVAR STI model,its basic principle and logical structure are studied.Secondly,the observation error regularization factor estimation method based on Bayesian optimization is proposed,and the error factor is separated and optimized by two parameters:error statistical time and deviation degree.Finally,the scientific,feasible and advanced nature of the OER-4DVAR STI model are verified by numerical simulation and tracer test data.The experimental results show that OER-4DVAR STI model can better reverse calculate the hazard source term information under the conditions of high atmospheric stability and flat underlying surface.Compared with the previous inversion algorithm,the source intensity estimation accuracy of OER-4DVAR STI model is improved by about 46.97%,and the source location estimation accuracy is improved by about 26.72%.

基于傅里叶变换与统计检验的圆度误差分离技术研究

采用傅里叶变换及数理统计假设检验的方法对圆度误差进行分离。针对圆轮廓的高精度测量数据,通过最小区域法拟合圆心。应用傅里叶变换将圆轮廓信号转换成谐波信号,从理想圆轮廓模型出发,逐步添加傅里叶分量,迭代过程中通过偏F检验构造包含未知系统形状误差的主导性模型。通过自相关法检验、卡方检验及J-B检验获取残余的显著性傅里叶分量,进一步构建显著性模型,实现圆度误差中系统误差的分离。通过数控加工16个圆孔的实验数据分析,证明了该方法可以对圆度误差进行有效分离。

五轴数控机床旋转轴综合误差测量与辨识

针对五轴数控机床旋转轴的运动误差和几何误差的综合评估问题,在不考虑直线轴运动误差影响的情况下,提出了一种采用R-test测量仪的测量及其辨识方法。首先,测量过程按照参考球的两种不同高度设置进行,仅移动旋转轴,而不移动直线轴。其次,利用R-test测量仪对旋转轴的运动精度进行了测量。此外,假设旋转轴位置几何误差和工作台上参考球的设置误差是影响测量结果的因素,并通过最小二乘法对这些因素进行分离。采用IBS公司的R-test测量仪,对米克朗公司UCP800Duro立式五轴加工中心C轴的运动误差和几何误差进行了测量实验。研究结果表明,该方法能够正确识别旋转轴的运动误差和几何误差,可以有效地综合评估旋转轴的运动精度,并有助于进一步提高旋转工作台的精度。

导弹命中精度的序贯截尾概率圆检验方法

针对圆概率偏差检验难以直接计算的问题,提出序贯截尾概率圆检验方法,以目标点为中心,绘制两个同心圆,其中小圆以内区域为接受域,大圆以外区域为拒绝域,中间区域为继续试验域,在此基础上定义了序贯检验的基本决策规则,给出了双方风险及平均试验次数计算模型,提出了两种不同的决策阈值优化计算模型,通过求解优化问题确定接受域及拒绝域半径。利用数值仿真分析了两种不同决策阈值计算方法下检验方案中的各类参数,其中以平均试验次数最小为优化目标的计算模型具有更好的工程实用性。

用于数据采集器测试的时间脉冲插值分析方法

地震数据采集器时间服务精度是评价设备性能的重要指标,一般使用标准时间源输出的时间脉冲信号采样数据进行分析计算,但受仪器采样率限制,时间偏差测试分辨率不高。设计了基于一阶差分和直方图分析的脉冲信号上升沿识别、高低电位分析和时间偏差分析算法,研究使用非线性插值分析方法对地震数据采集器采集的标准时间脉冲信号进行波形升采样恢复,并基于所提算法进行实验分析和讨论,在提高地震数据采集器时间偏差测试分辨率的同时,规范了测试数据处理方法和流程。

纵切自动车床环境温度变化误差试验研究

为研究环境温度变化对纵切自动车床热误差的影响,本文以RTS20瑞士型纵切自动车床为试验载体,通过环境温度变化误差(ETVE)试验装置,开展了恒主轴转速(5000 rpm)变环境温度、变主轴转速(0~8000 rpm)变环境温度的热误差试验,对环境温度对热误差的影响进行了研究分析。结果表明:在相同主轴转速下,环境温度变化影响着车床结构各部位的温升,进而影响热误差;在随机主轴转速下,主轴轴承等温度测点的温升受转速变化的影响,热误差的增长与关键测点温度具有相同变化周期,但不具有相同变化趋势,即温度快速升高时热误差并不一定也正向增长;空调开启后各测点温度有明显降低,最高降幅可达3℃,热误差随之也有明显降低趋势,最高降幅达6μm。

100 V输入宽频带电压比例校验系统研究

提出一种基于数字采集装置的50 Hz~10 kHz电压比例校验系统,由电压比例变换和数字采集装置构成。数字采集装置采用了通道切换技术,极大提高数字采集装置测量比例误差的准确度。电压比例变换部分由级联型感应分压器、隔离互感器及高、低压精密电压跟随器构成。为了降低分布参数引起的附加误差,设计了采用双绞线结构的双级隔离互感器;该双级互感器在10 kHz范围内幅值误差不大于5×10^(-6),相位误差不超过10μrad。利用双封装运算放大器特性匹配特征,补偿电压跟随器电路的相位响应,显著提升了低压和高压复合型电压跟随器的相位特性,10 kHz范围内,跟随器的幅值误差不大于10×10^(-6),相位误差不大于20μrad。测量结果表明,校验系统具有较好的测量准确度,50 Hz时的测量偏差不大于1×10^(-6)和1μrad,10 kHz范围内,比值误差偏差不大于80×10^(-6),相位误差偏差不大于60μrad,可满足不同频率场景下的电压比例误差测量需求。