Design and analysis of experiments in CMM measurement uncertainty study

In applying a coordinate measuring machine to measure a mechanical object, many factors affect the measurement uncertainty. Although a number of studies have been reported in evaluating measurement uncertainty, few have applied the factorial design of experiments (DOE) to examine the measurement uncertainty, as defined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM). This research applies the DOE approach to investigate the impact of the factors and their interactions on the uncertainty while following the fundamental rules of the GUM. The measurement uncertainty of the location of a hole measured by a coordinate measuring machine is used to demonstrate our methodology.     

Prediction of data variability in hand-arm vibration measurements

The long-term exposure to vibrations transmitted to the human upper limb by hand-held powered tools leads to a group of diseases commonly known as hand-arm vibration (HAV) syndrome. The risk deriving from the vibration exposure can be assessed with direct measurements, using data declared by the tool manufacturer or by retrieving measurements from specific databases. The discrepancies between data belonging to each of these three groups were evidenced in several studies. This paper analyzes the causes of the HAV measurements variability following the ISO GUM approach. The work process was modeled with a lumped parameter scheme of the tool-operator-measurement chain interactions. The measurement uncertainty has been identified propagating the uncertainties of the influencing parameters through the model. The soundness of the approach was verified by comparing the predicted and the observed variability in a specific case study. The major outcome of the proposed method is that the uncertainty budget allows understanding which parameters have to be controlled to limit data dispersion.     

Uncertainty analysis of positional deviations of CNC machine tools

The assessment of the measurement uncertainty is an indispensable task in all calibration procedures. By international accord, the evaluation is to be done in accordance with the ISO Guide to the Expression of Uncertainty in Measurement (GUM). To calibrate the positional deviations of computer numerically controlled (CNC) machine tools, calibration laboratories will usually follow the guidelines in ISO 230-2 International Standard. However, that standard does not address uncertainty. In this paper, we present an uncertainty evaluation scheme that is firmly grounded in the GUM, and can therefore be of use as a guide to develop appropriate uncertainty calculations in this and similar types of calibrations.     

空间直线度最小二乘评定结果的不确定度估计

评定模型的非线性和不可微给空间直线度最小二乘评定结果不确定度的估计带来困难,由空间直线度最小二乘评定模型出发,参照ISO国际测量不确定度表示指南,对影响不确定度估计的一些因素加以简化,推导了不确定估计公式。根据测量数据将推导公式估计结果与蒙特卡罗法运算的结果进行比较,结果表明采用本方法与蒙特卡罗方法获得的结果相符合,且本方法所用时间较少。     

Uncertainty evaluation associated with versatile automated gauging influenced by process variations through design of experiments approach

Recent advances in versatile automated gauging have enabled accurate geometric tolerance assessment on the shop floor. This paper is concerned with the uncertainty evaluation associated with comparative coordinate measurement using the design of experiments (DOE) approach. It employs the Renishaw Equator which is a software-driven comparative gauge based on the traditional comparison of production parts to a reference master part. The fixturing requirement of each production part to the master part is approximately ±1 mm for a comparison process with an uncertainty of ±2 μm. Therefore, a number of experimental designs are applied with the main focus on the influence of part misalignment from rotation between master and measure coordinate frames on the comparator measurement uncertainty. Other factors considered include measurement mode mainly in scanning and touch-trigger probing (TTP) and alignment procedure used to establish the coordinate reference frame (CRF) with respect to the number of contact points used for each geometric feature measured. The measurement uncertainty analysis of the comparator technique used by the Equator gauge commences with a simple measurement task using a gauge block to evaluate the three-dimensional (3D) uncertainty of length comparative coordinate measurement influenced by an offset by tilt in one direction (two-dimensional angular misalignment). Then, a specific manufactured measurement object is employed so that the comparator measurement uncertainty can be assessed for numerous measurement tasks within a satisfactory range of the working volume of the versatile gauge. Furthermore, in the second case study, different types of part misalignment including both 2D and 3D angular misalignments are applied. The time required for managing the re-mastering process is also examined. A task specific uncertainty evaluation is completed using DOE. Also, investigating the effects of process variations that might be experienced by such a device in workshop environments. It is shown that the comparator measurement uncertainties obtained by all the experiments agree with system features under specified conditions. It is also demonstrated that when the specified conditions are exceeded, the comparator measurement uncertainty is associated with the measurement task, the measurement strategy used, the feature size, and the magnitude and direction of offset angles in relation to the reference axes of the machine. In particular, departures from the specified part fixturing requirement of Equator have a more significant effect on the uncertainty of length measurement in comparator mode and a less significant effect on the diameter measurement uncertainty for the specific Equator and test conditions.     

Removing divergence of JCGM documents from the GUM (1993) and repairing other defects

The mission of the Joint Committee for Guides in Metrology (JCGM) is to maintain and promote the use of the Guide to the Expression of Uncertainty in Measurement (GUM) and the International Vocabulary of Metrology (VIM, second edition). The JCGM has produced the third edition of the VIM (referred to as VIM3) and a number of documents; some of which are referred to as supplements to the GUM. We are concerned with the Supplement 1 (GUM-S1) and the document JCGM 104. The signal contribution of the GUM is its operational view of the uncertainty in measurement (as a parameter that characterizes the dispersion of the values that could be attributed to an unknown quantity). The operational view promulgated by the GUM had disconnected the uncertainty in measurement from the unknowable quantities true value and error. The GUM-S1 has diverged from the operational view of the uncertainty in measurement. Either the disparities should be removed or the GUM-S1 should not be referred to as a supplement to the GUM. Also, the GUM-S1 has misinterpreted the Bayesian concept of a statistical parameter and the VIM3 definitions of coverage interval and coverage probability are mathematically defective. We offer practical suggestions for revising the GUM-S1 and the VIM3 to remove their divergence from the GUM and to repair their defects.     

Comparison of GUM and Monte Carlo methods for evaluating measurement uncertainty of perspiration measurement systems

Measurement uncertainty is an important parameter to express measurement results including means and reliability. The uncertainty analysis of the biomedical measurement system needs to be established. A perspiration measurement system composed of several sensors was developed. We aim to estimate the measurement uncertainty of this system with several uncertainty sources, including airflow rate, air density, and inlet and outlet absolute humidity. Measurement uncertainty was evaluated and compared by the Guide to the expression of the uncertainty in measurement (GUM) method and Monte Carlo simulation. The standard uncertainty for the perspiration measurement system was 6.81 × 10⁻⁶ kg/s and the uncertainty percentage <10%. The major source of the uncertainty was airflow rate, and inlet and outlet absolute humidity. The Monte Carlo simulation could be executed easily with available spreadsheet software programs of the Microsoft Excel. GUM and Monte Carlo simulation did not differ in measurement uncertainty with precision to two decimal places. However, the sensitivity coefficient derived by GUM provided useful information to improve measurement performance, which was not evaluated with the Monte Carlo simulation method.     

Uncertainty of measurement by Monte-Carlo simulation and metrological reliability in the evaluation of electric variables of PEMFC and SOFC fuel cells

The aim of this work is presenting results of uncertainty of measurement calculations applied to both a low temperature PEMFC (proton exchange membrane fuel cell) and a high temperature SOFC (solid oxide fuel cell) by using Monte Carlo method simulations. The intention is correlating electric voltage, obtained in the technical literature, and energetic efficiency of the fuel cells studied in this work. In order to validate the Monte Carlo results achieved a comparison with the procedure for the evaluation of the uncertainty of measurement existing in the GUM 95 ”Guide to the Expression of Uncertainty in Measurement” (by BIPM, IEC, IFCC, ISO, IUPAC, IUPAP and OIML) is made. A reasoning of the balancing of the sources of uncertainty is presented as well. In last, it is discussed why the calibration process and traceability of the voltmeter are key factors in providing reliable metrological results in the production of electricity by fuel cell technology. This work is the first part of a broader study from which the next steps will be the validation of these presented simulations by fuel cell bench tests and the planning and development of Brazilian Conformity Assessment programs for PEMFC and SOFC fuel cells afterwards.     

电子级氮气中超痕量杂质的质谱分析方法及测量不确定度评估

采用大气压电离质谱（APIMS）技术及标准添加法建立了一种电子级氮气中超痕量杂质的分析方法。以高效纯化后氮气中的5种杂质（CO、CH₄、H₂、O₂和CO₂）作为检测对象,以动态稀释后的标准气体作为参考进行回归分析,标准气体依据ISO 6142及ISO导则34规定的重量法在实验室制备,同时采用蒙特卡洛（MCM）法及《不确定度表示指南》描述的GUM法对本方法的不确定度进行评定。结果表明：在0~1 nmol/mol范围内,5种杂质的校准曲线呈现出良好的线性关系,线性相关系数R²均大于0.998;方法的灵敏度高,检出限可达几至几十pmol/mol水平,扩展不确定度为37%（k=2）,通过与文献中报道的数据相比,CH₄和CO的检出限分别改善了1个和2个数量级,H₂、O₂、CO₂则与文献的报道值基本一致。本方法能够满足对相关电子气体中杂质的分析要求,并可为量值溯源提供参考依据。     

An MCMC algorithm based on GUM Supplement 1 for uncertainty evaluation

This paper describes a simple Markov chain Monte Carlo algorithm for evaluating measurement uncertainty according to Bayesian principles. The algorithm has two phases, the first coinciding with the Monte Carlo method described in GUM Supplement 1 (GUMS1), the second a simple Metropolis–Hastings algorithm. The second phase can be regarded as a post-processing add-on to the GUMS1 calculation and can be used whenever a GUMS1 approach is adopted. The algorithm allows users freedom to choose their preferred prior distribution for the measurand, rather than that implicitly assigned in the GUMS1 approach, thereby avoiding some of the problems that can arise when applying GUMS1 to certain types of measurement model. The post-processing can be implemented in a few lines of software, so that many of the practical difficulties in implementing Bayesian approaches to measurement uncertainty evaluation are largely removed.     

光学原子力显微镜中的蒙特卡罗方法

扫描探针显微镜(Scanning probe microscopy,SPM)是显微镜的一个分支,它利用物理探针扫描标本形成样本表面图像.而原子力显微镜(Atomic force microscopy,AFM)是SPM中一种多功能的表面成像和测量工具,对导电、不导电、真空中、空气中或流体中的各种样本均可测量.原子力显微镜最面临的最大挑战之一是评估其在表面测量过程中所伴随的不确定度.本研究通过XYZ Phase的标定,对一台光学原子力显微镜进行了校准.该方法旨在克服在评估一些无法实验确定的不确定部件时遇到的困难,如尖端表面相互作用力和尖端几何.运用蒙特卡罗方法来确定根据相关容差和概率密度函数(PDFs)随机绘制参数而引起的相关不确定度.整个过程遵循《测量不确定度表示指南》(GUM)补编2.经本方法验证,原子力显微镜的评估不确定度为10nm左右.     

激光跟踪仪多边测量的不确定度评定

激光跟踪仪多边测量是大型高端装备制造现场溯源的重要手段,正确评定其不确定度是确保制造过程量值统一、结果可靠的关键。本文提出了一种准确、快速的激光跟踪仪多边测量的不确定度评定方法。从仪器误差、环境干扰及靶球制造误差等方面分析激光跟踪仪多边测量的不确定度来源。针对多边测量的输出量为多维向量的特点,重点研究基于多维不确定度传播律(GUM法)的不确定度合成方法,同步评定目标点坐标和跟踪仪站位的不确定度。最后,介绍了点到点长度的不确定度计算方法。实验表明:GUM法评定的不确定度结果与蒙特卡洛法(MCM法)的结果相比,坐标不确定度偏差小于0.000 2 mm,相关系数偏差小于0.01,满足数值容差,且GUM法用时仅为MCM法的0.08%;点到点长度测试的En值均小于1。因此,基于GUM法评定激光跟踪仪多边测量的不确定度具有可行性及高效性,且评定结果正确、可靠。     

Implementation of unscented transform to estimate the uncertainty of a liquid flow standard system

First-order partial derivatives of a mathematical model are an essential part of evaluating the measurement uncertainty of a liquid flow standard system according to the Guide to the expression of uncertainty in measurement (GUM). Although the GUM provides a straight-forward method to evaluate the measurement uncertainty of volume flow rate, the first-order partial derivatives can be complicated. The mathematical model of volume flow rate in a liquid flow standard system has a cross-correlation between liquid density and buoyancy correction factor. This cross-correlation can make derivation of the first-order partial derivatives difficult. Monte Carlo simulation can be used as an alternative method to circumvent the difficulty in partial derivation. However, the Monte Carlo simulation requires large computational resources for a correct simulation because it considers the completeness issue whether an ideal or a real operator conducts an experiment to evaluate the measurement uncertainty. Thus, the Monte Carlo simulation needs a large number of samples to ensure that the uncertainty evaluation is as close to the GUM as possible. Unscented transform can alleviate this problem because unscented transform can be regarded as a Monte Carlo simulation with an infinite number of samples. This idea means that unscented transform considers the uncertainty evaluation with respect to the ideal operator. Thus, unscented transform can evaluate the measurement uncertainty the same as the uncertainty that the GUM provides.     

Uncertainty evaluation of multivariate quantities: A case study on electrical impedance

The paper discusses the evaluation of the uncertainty of a multivariate quantity using the Law of Propagation of Uncertainty defined in the Guide to the Expression of Uncertainty in Measurement (GUM) and a Monte Carlo method according to the GUM’s Supplement 2. The quantity analysed is the electrical impedance, which is not a scalar but a complex quantity. The used measuring method allows the evaluation of the impedance and of its uncertainty in different ways and the corresponding results are presented, compared and discussed. For comparison purposes, results of the impedance uncertainty obtained using the NIST Uncertainty Machine are also presented.     

Can coverage factor 2 be interpreted as an equivalent to 95% coverage level in uncertainty estimation? Two case studies

The GUM modelling, its Bayesian modification and the Monte Carlo method (MCM) to estimate the uncertainty are compared in two practical measurement situations (finding reference value of relative humidity and a generic chemical instrumental analysis procedure). The results of the three approaches agree very well when there are no dominant input quantities with type A evaluated uncertainty estimated from small number of repeated measurements. In the opposite case the GUM gives underestimated expanded uncertainties (by up to 20–25%), compared to both other approaches. Analysis of the practical measurement situations reveals that even in the case of several dominating input quantities of similar uncertainty contributions, if one of them is distributed according to the t-distribution and has a low number (3–4) of degrees of freedom, the output quantity cannot be safely assumed Normally distributed and in such a case coverage factor 2 is not an equivalent to 95% coverage level.     

Aide in decision-making: contribution to uncertainties in three-dimensional measurement

The authorities of the standards organization International Organization of Standardization (ISO) advocate mastering any uncertainties in all parts of the industrialization process. In the three-dimensional (3D) measurement process, uncertainty is usually obtained at the end of a battery of tests. It is defined as a whole because it includes several types of errors, known systematic components, unknown systematic components and random components. Automated calculations of uncertainty can be made based on statistics. This method is based on statistical concepts, which are in accordance with “The Guide to the expression of the uncertainty in measurement” (GUM). It also enables us to generate uncertainties on the verification of ISO specifications (or specs in the ISO directives). In the course of this article, a usage will be presented that takes the knowledge of uncertainties into account: this usage will help the operator to take a decision on the conformance of a mechanical part in reference to its conformance to geometric tolerance.     

基于蒙特卡罗法与GUM法的直线度测量不确定度评定

由于形位误差测量的复杂性和测量结果评定的多样性,导致在实际测量结果中形位误差的不确定度评定成了难题。通过GUM法和蒙特卡罗法对直线度的测量不确定度进行评定。首先,根据最小二乘法得到直线度的误差模型;然后采用GUM方法对测量结果进行不确定度评定,采用蒙特卡罗仿真方法对测量值进行模拟仿真,从而得到直线度误差的不确定度;设置实验对比,通过数据分析验证了蒙特卡罗方法评定的可行性,为形位误差测量结果不确定度评定提供了更加简便的方法。     

面向任务的测量不确定度评估原理和方法

坐标测量机是典型的面向任务的测量设备,测量任务的改变将引入不同的测量不确定度。怎样评估坐标机面向任务的测量不确定度,目前我国还没有这方面专门的技术规范。参考ISO/TS15530系列标准,介绍了坐标测量机面向任务的不确定度评估原理和方法。     

Uncertainty budgeting for range calibration

The Guide to the Expression of Uncertainty in Measurement (GUM) established a general procedure to evaluate measurement uncertainty. The Guide covers only the evaluation of a single result or a set of individual results. Modern measuring instruments and procedures operate over a wide range of values. Therefore in practice a calibration procedure is needed that is valid for this range. The procedure should include an evaluation of uncertainty associated with the calibration results and for the subsequent measurements performed with the calibrated instrument. Traditionally regression analysis is used for this purpose. In this paper we will discuss some weaknesses of the regression approach and suggest an alternative. We show that for instruments with a linear response function the regression can be replaced by 2-point calibration. We introduce a limit of the deviation from linearity to address observed deviations from a linear response function of the instrument. To improve an existing instrument with a non-linear response function a combination of the instrument and a correction function can be treated as a virtual linear measuring device and a 2-point calibration can be applied. As an example we use the calibration of a pressure sensor to illustrate the procedure. The approach can be used for instruments and measurement procedures with a linear or non-linear response function.