A simulation-based investigation of the staircase method for fatigue strength testing

A critical evaluation of the statistics of the fatigue strength distribution as determined by the staircase (or up-and-down) method is presented. The effects of test parameters (namely, step size and sample size) were analyzed using numerical simulation to determine the accuracy of fatigue strength standard deviation calculations using traditional staircase statistics, resulting in a quantification of standard deviation bias as a function of step size and sample size. A non-linear correction was formulated to mitigate this standard deviation bias inherent in small-sample tests. In addition, the simulation was used to investigate the effectiveness of a bootstrapping algorithm on standard deviation estimates. The bootstrapping algorithm was found to significantly reduce the potential of large standard deviation errors in small-sample tests. Together, the use of the non-linear correction factor and the bootstrapping algorithm may allow an improved method to estimate the statistics of a material’s fatigue strength distribution using a small-sample staircase test strategy.     

Determination of Geometric Standard Deviation for Dissolution

The two important instances in which the scientist converts his/her experimental data to a logarithmic scale prior to computing the mean and standard deviation, are (i) when the distribution of the data is asymmetrical (e.g. percentage data) and (ii) when he/she intends to compare statistically the averages of two or more groups with unequal standard deviations. In either case, the mean is restored to its original scale by taking the antilog of the log mean, which is the geometric mean. However, this procedure cannot be applied for computing the geometric standard deviation. The author of reference(l) erroneously claims that the antilog of log standard deviation is the geometric standard deviation. This paper demonstrates the incorrectness of the procedure in reference (1), exhibits the exact statistical formula and introduces a novel method called “jackknife statistic” to confirm the results, based on the dissolution data associated with Product-C.     

升降法测试疲劳强度均值和标准偏差产生误差的原因

借助计算机模拟研究了应力台阶d与疲劳强度标准偏差σ 的比d/σ 、应力台阶数i及试样数量N对升降法测试疲劳强度均值μ 和标准偏差σ 的影响.结果表明:升降法测试疲劳强度均值的可靠度高于测试标准偏差的,同一试验条件下进行多次重复测试可以提高试验结果的可靠度.d/σ>3时,升降图难以满足D>0.3.标准偏差估计值(σ)的均...     

Determination of Geometric Standard Deviation for Dissolution

Abstract

The two important instances in which the scientist converts his/her experimental data to a logarithmic scale prior to computing the mean and standard deviation, are (i) when the distribution of the data is asymmetrical (e.g. percentage data) and (ii) when he/she intends to compare statistically the averages of two or more groups with unequal standard deviations. In either case, the mean is restored to its original scale by taking the antilog of the log mean, which is the geometric mean. However, this procedure cannot be applied for computing the geometric standard deviation. The author of reference(l) erroneously claims that the antilog of log standard deviation is the geometric standard deviation. This paper demonstrates the incorrectness of the procedure in reference (1), exhibits the exact statistical formula and introduces a novel method called “jackknife statistic” to confirm the results, based on the dissolution data associated with Product-C.     

Constructing Acceptance Limits for Multiple Stage Tests

Multiple stage tests are often used in the pharmaceutical industry (e.g., content uniformity, dissolution, disintegration). Acceptance limit methodology is given which assures that a future sample will have at least P% chance of passing a multiple stage test. For a given sample size, an associated acceptance region for the sample mean and standard deviation is found by (1) constructing a confidence region for the population mean and standard deviation, and (2) finding the probability of passing the test for each population mean and standard deviation in this confidence region. The acceptance region is the set of all sample means and standard deviations such that the probability of passing the test is greater than a specified P for all points in the confidence region.     

Process capability indices for skewed populations

This paper proposes a new method of constructing process capability indices (PCIs) for skewed populations. It is based on a weighted standard deviation method which decomposes the standard deviation of a quality characteristic into upper and lower deviations and adjusts the value of the PCI using decomposed deviations in accordance with the skewness estimated from sample data. For symmetric populations, the proposed PCIs reduce to standard PCIs. The performance of the proposed PCIs is compared with those of standard and other PCIs, and finite sample properties of the estimates are investigated using Monte Carlo simulation. Numerical studies indicate that considerable improvements over existing methods can be achieved by the use of the weighted standard deviation method when the underlying distribution is skewed. Copyright © 2002 John Wiley & Sons, Ltd.     

拉伸试验能力验证结果的稳健统计指定值及其不确定度

利用金属材料室温拉伸试验能力验证结果的中位值作为初始稳健平均值,用其稳健标准偏差对其进行修正得到修正后的稳健平均值及稳健标准偏差,以此方法反复修正直至稳定,得到能力验证结果的指定值,最后再根据稳定后的稳健标准偏差计算指定值的不确定度。结果表明:对该次拉伸试验结果进行二次修正后,其稳健平均值及稳健标准偏差均已稳定,分别为799和6.23 N·mm~(-2);因此该次金属材料室温拉伸试验能力验证结果的指定值为799 N·mm~(-2);该指定值的标准不确定度为0.7,N·mm~(-2)。     

Alternative statistical methods for spectral data processing: applications to laser-induced breakdown spectroscopy of gaseous and aerosol systems

A new spectral data processing scheme based on the standard deviation of collected spectra is compared with the traditional ensemble-averaging of laser-induced breakdown spectroscopy (LIBS)-based spectral data for homogenous (i.e., pure gas phase) systems and with a LIBS-based traditional conditional spectral analysis scheme for non-homogenous (e.g., aerosol system) analyte systems under discrete particle loadings. The range of conditions enables quantitative assessment of the analytical approaches under carefully controlled experimental conditions. In the homogeneous system with gaseous carbon dioxide producing the carbon atomic emission signal, the standard deviation method provided a suitable metric that is directly proportional to the analyte signal and compares favorably with a traditional ensemble averaging scheme. In contrast, the applicability of the standard deviation method for analysis of non-homogenous analyte systems (e.g., aerosol systems) must be carefully considered. It was shown both experimentally and via Monte Carlo simulations that the standard deviation approach can produce an analyte response that is monotonic with analyte concentration up to a point at which the analyte signal starts to transition from a non-homogeneous system to a homogeneous systems (i.e., around a 50% sampling point for aerosol particles). In addition, the standard deviation spectrum is capable of revealing spectral locations of non-homogeneously dispersed analyte species without a priori knowledge.     

Constructing Acceptance Limits for Multiple Stage Tests

Abstract

Multiple stage tests are often used in the pharmaceutical industry (e.g., content uniformity, dissolution, disintegration). Acceptance limit methodology is given which assures that a future sample will have at least P% chance of passing a multiple stage test. For a given sample size, an associated acceptance region for the sample mean and standard deviation is found by (1) constructing a confidence region for the population mean and standard deviation, and (2) finding the probability of passing the test for each population mean and standard deviation in this confidence region. The acceptance region is the set of all sample means and standard deviations such that the probability of passing the test is greater than a specified P for all points in the confidence region.     

三维稳定渗流的随机变分原理及有限元法

将渗透系数作为随机场引入泛函变分表达式中,应用小参数摄动法,推导建立了三维稳定渗流的随机变分原理和相应的随机有限元列式。并由此推导得到了水头、水力坡降的均值和方差表达式。为应用随机有限元方法对随机渗流进行分析提供了理论依据。最后,计算了一个典型堤防的水力坡降均值和标准差,分析了水力坡降标准差与渗透系数变异性之间的关系,结果表明此方法程序实施简便,计算效率较高。     

二厘米微波衰减标准装置不确定度的验证

采用传递比较法对二厘米微波衰减标准装置不确定度进行了验证。测量标准装置的重复性以组内实验标准偏差sn(A)定量表征，测量标准装置的稳定性用组间实验标准偏差sm定量表征。     

Calculation of refractive indices using Buchdahl's chromatic coordinate

In this paper we have completed an error analysis of the Buchdahl glass model for 813 glasses available from five manufacturers. A quadratic model has a standard deviation of 0.00002 and a maximum absolute error of 0.0001 in the visible spectral region. A cubic model has a standard deviation of 0.00005 and a maximum absolute error of 0.00026 over the full spectral region from 0.365 to 1.014 microm. A table giving the Buchdahl fitting coefficients for all the glasses, as well as the standard deviation and maximum error for each glass, is included for the quadratic model. The results indicate that the Buchdahl model is ideally suited for theoretical studies of refracting optical systems.     

一种测量透明平行平板折射率的新方法

通过测量激光细光束经平行平板玻璃所产生的位移,可确定平行平板的的折射率。本文阐述了该方法的测量原理,给出了测量公式,并详细分析了测量误差。计算机模拟计算结果表明,当平板厚度为50mm时,如果入射角测量标准偏差为1”,平板厚度和光线位移量测量标准偏差均为0.001mm,则折射率测量的标准偏差可达6×10~(-5),此时入射角约55°。     

On the uncertainty of a system reliability estimate

We study the uncertainty of a system reliability estimate, based on knowledge of the uncertainties at component level. For many purposes, the standard deviation of the system reliability serves as a satisfactory measure of uncertainty. The main purpose of the paper is to review and compare some computationally simple upper bounds for this standard deviation.     

Windowed Fourier transform for fringe pattern analysis: theoretical analyses

A windowed Fourier ridges (WFR) algorithm and a windowed Fourier filtering (WFF) algorithm have been proposed for fringe pattern analysis and have been demonstrated to be versatile and effective. Theoretical analyses of their performances are of interest. Local frequency and phase extraction errors by the WFR and WFF algorithms are analyzed in this paper. Effectiveness of the WFR and WFF algorithms will thus be theoretically proven. Consider four phase-shifted fringe patterns with local quadric phase [c(20)=c(02)=0.005 rad/(pixel)(2)], and assume that the noise in these fringe patterns have mean values of zero and standard deviations the same as the fringe amplitude. If the phase is directly obtained using the four-step phase-shifting algorithm, the phase error has a mean of zero and a standard deviation of 0.7 rad. However, when using the WFR algorithm with a window size of sigma(x)=sigma(y)=10 pixels, the local frequency extraction error has a mean of zero and a standard deviation of less than 0.01 rad/pixel and the phase extraction error in the WFR algorithm has a mean of zero and a standard deviation of about 0.02 rad. When using the WFF algorithm with the same window size, the phase extraction error has a mean of zero and a standard deviation of less than 0.04 rad and the local frequency extraction error also has a mean of zero and a standard deviation of less than 0.01 rad/pixel. Thus, an unbiased estimation with very low standard deviation is achievable for local frequencies and phase distributions through windowed Fourier transforms. Algorithms applied to different fringe patterns, different noise models, and different dimensions are discussed. The theoretical analyses are verified by numerical simulations.     

On t and EWMA t charts for monitoring changes in the process mean

The performance of an X‐bar chart is usually studied under the assumption that the process standard deviation is well estimated and does not change. This is, of course, not always the case in practice. We find that X‐bar charts are not robust against errors in estimating the process standard deviation or changing standard deviation. In this paper we discuss the use of a t chart and an exponentially weighted moving average (EWMA) t chart to monitor the process mean. We determine the optimal control limits for the EWMA t chart and show that this chart has the desired robustness property. Copyright © 2009 John Wiley & Sons, Ltd.     

Uncertainty Analysis of Evaporation Rate in Magnetic Suspension Balance/Diffusion-Tube Humidity Generator

An analysis method for the uncertainty of a small evaporation rate in a magnetic suspension balance/diffusion-tube humidity generator has been developed. Using experimentally obtained data, the uncertainty is evaluated as a function of measurement time. It is found that the observed standard deviation of the evaporation rate in a region of short measurement time (short term) is inversely proportional to the measurement time, and that in a region of long measurement time (long term) the standard deviation does not vary markedly with increasing measurement time. The behavior of the observed standard deviation in the short term is attributable mainly to the uncertainty of the balance reading, and that in the long term to the variability of room temperature. The results of the investigation show that the use of only least-squares analysis leads to underestimation of the uncertainty.     

关于灵敏系数命题的证明及应用

提出了“灵敏系数等于输入量导出的输出量的标准偏差和输入量自身标准偏差之比”的命题,并用数学逻辑给予了证明。     

Reduced-noise-displacement measurements with a correlated differential photodiode sensor

A measured displacement resolution of <3 nm is demonstrated with a common cathode differential photodetector combined with a laser-diode optical source and a fiber-optic collimator. Resolution, standard deviation, and differences between maxima and minima values for the residuals of the least-squares fit suggest that a coherent laser-diode source temporally correlates photoelectron flux between adjacent detector segments, suggesting reduced signal variance and associated electronic (shot) noise. For otherwise similar systems, the laser-diode source provides approximately an order of magnitude reduction in standard deviation compared with a light-emitting-diode source, which implies an equivalently improved measured (including standard deviation) resolution. Combined variances for correlated and uncorrelated detectors and their measured variances are outlined. The measured resolution is a sum of both the (ideal) mathematical variance based on the detector noise (millivolts) divided by the system sensitivity (millivolts per nanometer, and the standard deviation of the noise (nanometers).     

基准转换标准器在多系统集成中的应用

使用经纬仪、激光跟踪仪进行协同测量时需要对不同测量系统的测量基准进行基准转换,传统基准转换手段较为繁琐耗时.针对此问题,设计了一种新型便携式基准转换标准器,该标准器由基准转换组件、转向组件和三脚架组成,通过基准板上的测量靶点及立方镜构建坐标系,实现基准转换.经验证:该标准器在不同姿态下的平均位置偏差小于0.01 mm,...