Estimation of the measurement uncertainty in the anisotropy test

The evaluation of the sheet metal drawability in mechanical shaping processes depends on a large number of analysis, among which the anisotropy evaluation. Nowadays, there is no Brazilian test laboratory accredited by the Metrology, Quality and Technology National Institute (INMETRO) to perform this analysis. So, the object of the present work is to establish a procedure for the estimation of the measurement uncertainty in the plastic anisotropy ratio of sheet metals, in accordance to the Guide to the Expression of Uncertainty in Measurement (GUM), aiming at the accreditation of this test in the Physical Metallurgy Laboratory. As results, we present the calculations performed and the uncertainty form proposed, and an analysis of which sources contributed the most for the uncertainty in the execution of a test. Finally, we propose improvement actions aiming at the reduction of the calculated uncertainty and the adequacy of the Measurement System for the desired application.     

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.     

Measurement uncertainty and metrological confirmation in quality-oriented organizations

The effect of measurement uncertainty on estimates and decisions performed under a regime of quality control and improvement, is considered in this paper. Standard statistical quality tools are analyzed such as control charts and instrument calibration procedures. Their performance is characterized under the assumption of both normally and uniformly distributed measurement uncertainty. Exact and approximate expressions are derived that allow the design of suitable procedures including the contribution of measurement uncertainty.     

随机模糊变量表示测量及测量不确定度

《测量不确定度表示指南》(GUM)这个技术规范已被广泛认可,且其测量值关联一个不确定度值的建议也被广泛采纳。然而,这个规范遵循一种固有的概率方法,其应用并不总是可行的,且因为一些技术和经济原因,在可行的情况下,其应用也并不是简单直接的。总结了一种更一般化的不确定度评定和表示的随机模糊变量RFVs方法,系统评述了其关键技术与难点,通过实例表明,RFVs方法在非线性测量函数中传递不确定度具有简单高效的特点,最后对该领域的研究扩展提出了两点建议,给出了使用RFVs扩展贝叶斯定理的初步探讨结果。RFVs方法基于数学可能性理论,从GUM及其基本概念和定义出发对GUM方法进行了扩展,具有明显的优势,该方法的广泛应用也证明了其远大的发展前景。     

Validation of the GUM using the Monte Carlo method when applied in the calculation of the measurement uncertainty of a compact prover calibration

This article presents the calibration of a compact prover using the weighing method. An evaluation of measurement uncertainty of the prover calibration has been developed using the GUM and Monte Carlo methodologies. A water draw kit was utilized to direct the liquid flow from the compact prover to a water container in order to weigh the transferred water mass on a balance. This amount of mass was used as reference for the calculation of the prover base volume. A modeling of the flow rate into the water draw kit as a function of time was conceived. This modeling was applied for calculating the error in the liquid volume of the water container due to the switching of two solenoid valves of the water draw kit. A mathematical model of the prover base volume has been developed. This model is non-linear and the two largest sources of uncertainty are related to the balance calibration certificate that together account for 31.84% of the uncertainty budget. This work showed that the GUM approach was validated by Monte Carlo method in the calculation of the measurement uncertainty of the calibration of a compact prover. The absolute differences of the respective endpoints of the coverage intervals of these two methods are less than 0.00023% of estimate of the prover base volume whose value is 151.427 dm³. This result was obtained for a coverage probability of 95% and ${10}^6$ Monte Carlo iterations. The density of the calibration water and its uncertainty have been calculated through an innovative approach.     

Evaluation of the uncertainty of an optical machine with a vision system for contact-less three-dimensional measurement

Optical machines with a vision system containing a video camera are designed to perform contact-less three-dimensional measurements. They are becoming more widely used in the industrial sector because of the many possibilities for automation they permit and because of the speed and economies in measurement tasks that can consequently be obtained. Within dimensional control these machines introduce significant characteristics of flexibility, savings and reliability. Therefore the purpose is to identify the principal metrological characteristics of such machines and so characterise the metrological traceability of the measurements obtained from them. The aim is to qualify each part of the optical machine as well as on the whole. Previously, no metrological traceability of this equipment has been provided in primary metrology, either at national (SIT—Sistema di Taratura in Italia—Calibration System in Italy) or at international level (EA–European co-operation for Accreditation). For this reason we develop a mathematical model that permits the evaluation of the measurement uncertainties in the use of such a device. The purpose is to obtain the certification of the measurement results furnished by the optical machine in as broad a context as possible. The experimental results of the tests are introduced for validating the proposed method. This paper provides the basis of the expression of the uncertainty of a measurement result obtained using the optical measurement machines and it shows the necessary requirements for the numerical evaluation of such uncertainty.     

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.     

The use of measurement uncertainty and precision data in conformity assessment of automotive fuel products

In order to use a test result to decide whether it indicates compliance or non-compliance, it is necessary to take into account the dispersion of the values that can be attributed to the measurand. When dealing with conformity assessment of automotive fuel samples against European Union specification limits, this dispersion may be represented by uncertainty estimates based on either standard method precision data (ISO 4259 approach) or within laboratory precision data (intermediate precision approach). The present work presents possible decision rules based on these approaches and directly related to the required or acceptable level of probability of making a wrong decision. Acceptance limits for 95% and 99% confidence levels are calculated for all the properties of automotive fuels. Moreover, the effect of different approaches for defining guard bands, different levels of confidence or different number of replicate measurements is investigated using the results of the analyses of 769 diesel fuel samples for the determination of sulfur mass concentration.     

Quantifying impacts on the measurement uncertainty in flow calibration arising from dynamic flow effects

Traceability of the measurement units in fluid flow metering, as the state-of-the-art approach, is practiced as a so-called element-by-element method which relies upon the idealistic assumption that the measurement process in a flow calibration facility can be run under exact steady-state conditions, that is, absolutely no fluctuations of the flow quantities are assumed to occur during the flow measurement process. Practical experiences, combined with a model-based analytical view of the measurement process in a flow standard, have revealed that dynamic impacts on the measurement uncertainty due to flowrate fluctuations have to be taken into account, in addition to the steady-state traceability chain.     

Generalized expressions of second and third order for the evaluation of standard measurement uncertainty

The Guide to the Expression of Uncertainty in Measurement (GUM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the measurement function is strongly non-linear the use of this linear approximation may be inadequate and therefore higher order terms from the Taylor series cannot be neglected. The present paper aims to derive generalized expressions of second and third order for the evaluation of the estimate of a measurand and its associated standard uncertainty. A case study is given to illustrate an application of the proposed methods and the results obtained with the GUM method are compared to the corresponding ones when applying the method proposed in GUM Supplement 1.     

Evaluation of measurement uncertainty using mixed distribution for conducted emission measurements

For evaluation of measurement uncertainty for conducted emission measurements, we propose a new model which uses mixed distribution. Namely, evaluation of probability density function (PDF) for the measurand has been done using a Monte Carlo method and a modified least-squares method. As the Monte Carlo method required numerical calculation of approximate PDF values, pseudorandom number generator (PRNG) was developed for these requirements. For illustration, this work presents mixed distributions of two normal distributions, normal and rectangular distributions, and normal and also triangular distributions in case of conducted emission measurements. The results obtained by the Monte Carlo method and the modified least-squares method are compared to the corresponding results when applying the standard Guide to the Expression of Uncertainty in Measurement (GUM) procedure.     

Evaluation of the standard measurement uncertainty due to the ISO50 surface determination method for dimensional computed tomography

Surface determination is the process by which a CT volume is converted from an image-based representation of an object to a surface-based representation. The process of surface determination relies on well-established image processing algorithms, but these algorithms are not exact, surface determination therefore contributes a component of uncertainty to X-ray CT based dimensional measurements. The purpose of this work is to develop a method for quantifying the standard uncertainty due to surface determination such that this standard uncertainty can be combined with other standard uncertainties in order to calculate the combined standard uncertainty for X-ray CT based dimensional measurements. The proposed method relies on evaluating the mode and the 68% dispersion of the air and material grey values of a given CT data-set. These values are propagated through the ISO50 threshold calculation to give the standard uncertainty of the ISO50 threshold value from which the standard uncertainty due to the ISO50 surface determination method can be evaluated. The proposed method is verified numerically and then demonstrated experimentally for dimensional measurements of an aluminium workpiece, a polymer workpiece, and a steel additively manufactured workpiece. The results show that the measurement uncertainty due to the ISO50 surface determination method is largest for dimensions that have both internal and external surfaces such as wall thicknesses, followed by dimensions such as internal and external diameters, whilst dimensions that are not sensitive to surface determination, for example centre-to-centre distances have the smallest uncertainty due to the ISO50 surface determination method.     

Evaluating a task-specific measurement uncertainty for gear measuring instruments via Monte Carlo simulation

Evaluating the measurement uncertainty for gears with analytical or experimental methods is usually very time- and cost-consuming. In this paper we therefore present a Monte Carlo based method for evaluating the measurement uncertainty of gear measurements on gear measuring instruments, the VCMM-Gear, which is based on the method of the VCMM for coordinate measuring machines. Necessary extensions of the mathematical model of the measurement process in order to consider the significant uncertainty influences from rotary tables, workpiece clamping and scanning are described. Additionally the statistical reliability of the evaluated measurement uncertainty and the consideration of systematic error contributions to the measurement uncertainty are discussed. Finally the results of some first verification measurements are presented, giving a reliable impression of the capability and suitability of the VCMM-Gear.     

强直流计量标准装置量值传递与溯源方法

强直流电流在工业领域有着广泛的应用.论述了强直流计量标准装置的工作原理、量值传递与溯源方法,重点对校验方法及电流变比准确度进行了不确定度评定.旨在建立强直流电流量值传递与溯源体系,即实验室参考标准(0.0005级)、现场传递标准(0.02级)、现场工作标准(0.05级)装置及其量值测试、评定与溯源方法,该方法含盖自校、互校及与其他国内标准比对的全过程,为直流能耗准确计量、节能减排提供科学的强直流计量方法和手段.     

Improvement and uncertainty evaluation of mercury sealed piston prover using laser interferometer

Many NMIs (National Measurement Institute) and calibration laboratories are using a mercury sealed piston prover as calibration system for gas flow meter. But it has problems in deciding measuring volume, traveling time of piston and generating low flow rate below 10 cc/min. In this study, a new structure of a piston prover is designed and its flow measurement uncertainty is evaluated according to ISO/IEC 17025. A laser interferometer, instead of optical sensors used in a typical piston prover, is employed to measure testing time and moving distance of the piston, accurately. A new material of the piston is used to eliminate contaminated particles from the material of the piston body. Uncertainty is calculated by evaluating various uncertainty factors which have influence on gas flow measurement. The expanded uncertainty of the piston prover is 0.11% at the confidence level of 95%. The uncertainty evaluation procedure of this study would be useful in flow measurement uncertainty determination of other types of gas flow measurement systems.     

Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error

Measurement uncertainty is one of the most important concepts in geometrical product specification (GPS). The “Guide to the expression of uncertainty in measurement (GUM)” is the internationally accepted master document for the evaluation of uncertainty. The GUM method (GUMM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the mathematical model of measurand is strongly non-linear the use of this linear approximation may be inadequate. Supplement 1 to GUM (GUM S1) has recently been proposed based on the basis of probability density functions (PDFs) using the Monte Carlo method (MCM). In order to solve the problem that the number of Monte Carlo trials needs to be selected priori, adaptive Monte Carlo method (AMCM) described in GUM S1 is recommended to control over the quality of the numerical results provided by MCM.The measurement and evaluation of cylindricity errors are essential to ensure proper assembly and good performance. In this paper, the mathematical model of cylindricity error based on the minimum zone condition is established and a quasi particle swarm optimization algorithm (QPSO) is proposed for searching the cylindricity error. Because the model is non-linear, it is necessary to verify whether GUMM is valid for the evaluation of measurement uncertainty of cylindricity error. Then, AMCM and GUMM are developed to estimate the uncertainty. The procedure of AMCM scheme and the validation of GUMM using AMCM are given in detail. Practical example is illustrated and the result shows that GUMM is not completely valid for high-precision evaluation of the measurement uncertainty of cylindricity error if only the first-order terms in the Taylor series approximation are taken into account. Compared with conventional methods, not only the proposed QPSO method can search the minimum zone cylindricity error precisely and rapidly, but also the Monte Carlo simulation is adaptive and AMCM can provide control variables (i.e. expected value, standard uncertainty and lower and higher coverage interval endpoints) with an expected numerical tolerance. The methods can be extended to the evaluation of measurement uncertainty of other form errors such as roundness and sphericity errors.     

测量误差与测量不确定度的比较应用

文章详细介绍了测量误差和测量不确定度的基本概念以及两者之间的关系,阐述了采用测量不确定度评定测量结果的质量的必然性,旨在正确地了解掌握其实质、以便在工作中能正确地应用测量不确定度的评定与表示。     

机器视觉非接触测量系统在线校准及不确定度分析

高精度、大面阵CCD和CMOS传感器件的出现,使得机器视觉非接触测量技术得到越来越广泛的应用。本研究以典型机器视觉非接触测量模型为研究对象,通过对其原理、测量数学模型和计量特性进行了阐述和分析,创新性提出了一种机器视觉非接触测量系统的在线校准方法,分析并确立了测量过程中的不确定度来源,并对校准结果进行了不确定度评定。实验表明,机器视觉非接触测量系统在线校准方法具备两个优点：一是易操作性,优化了测量标准的追溯关系;二是校准精度高,在95％的置信概率下。校准系统不确定度为0．008mm。     

Laser tracker performance quantification for the measurement of involute profile and helix measurements

Standard-conforming measurements for a large involute gear were performed with a manually operated laser tracker system and the corresponding task-specific measurement uncertainties were estimated. Especially, readers using laser trackers for inspecting large involute gears will get information of a taskspecific measurement performance for the first time, which significantly differs from the laser tracker machine specification. To ensure unambiguous and repeatable measurement results, user-friendly auxiliary tools are used, which allows the operator to probe the measurement points according to existing guidelines and standards. Measurements were taken on a robust and highly accurate large involute gear measurement standard of the Physikalisch-Technische Bundesanstalt (PTB) under laboratory conditions. The size of this gear measurement standard complies with those gears used in wind power plants. The external gear materializes a left and a right hand gear as well as a spur gear. The obtained results of profile, helix and surface measurements are presented. These research activities were carried out at the PTB in the department of coordinate metrology.     

Repeatability and Reproducibility techniques for the analysis of measurement systems

This research was conducted with the aim of analyzing two of the main metrological characteristics of any measurement system: Repeatability and Reproducibility. Both of these features play an important role in the analysis of the measurements and they can give us a lot of information about who and what influences any measuring system. The analysis of Repeatability and Reproducibility is generally carried out through the use of the study Gage R&R. This study permits to understand which are the decisive factors in a measurement system, and, definitively, if the process is stable, that is under statistical control or out of statistical control.