Uncertainty Evaluation Procedure Research Articles

Uncertainty Evaluation of the TGA Oxidation Data

Thermogravimetric analysis (TGA) involves the measurement of the changes in mass that occur when a constant heat is applied to an unknown specimen as a function of time or temperature. It is used to evaluate thermal stability, oxidative stability, composition, and estimated lifetime, among other parameters. Given that accurate TGA data is important information for lifetime and stability evaluation of parts and products, an uncertainty evaluation procedure is required to ensure the reliability of the data. In this study, the uncertainty evaluation procedure was established according to the Guide to the Expression of Uncertainty in Measurement (GUM). The mathematically expression of the relationship between the measurand and the input quantities, evaluation of the standard uncertainty of each input estimate, determination of the combined standard uncertainty, and calculation of the expanded uncertainty were performed. The biggest factor affecting the uncertainty of TGA data is the uncertainty of correction factor caused by system calibration

Trans-conductance amplifier calibration protocol establishment – metrology ambiguities, constraints, and measurement uncertainty propagation analysis

The primary dilemma, when establishing calibration protocol for testing of any measurement transducer, is whether the concrete unit is going to be regarded as a standalone instrument, or it will be treated as a part of an integrated measurement system. The first approach would provide results that are applicable for broader further usage. The data obtained if the unit is calibrated within the measurement system, may be further used only for performance evaluation of the overall system. The concrete ambiguity is related to the appropriate quantity selection on the basis of which the measurements will be carried out, i.e., whether the measurand is the transducer’s output signal or its transformation coefficient. The determination of the quantity, which is supposed to be recorded, opens a further debate about the appropriate selection of measurement points and the uncertainty evaluation procedure, both in terms of dominant influential factors determination, and in overall uncertainty budget distribution modelling adequacy. In the concrete contribution, an originally developed protocol for high current trans-conductance amplifier examination will be presented, taking into account both perspectives for examination.

Value assignment and uncertainty evaluation for anion and single-element reference solutions incorporating historical information.

The National Institute of Standards and Technology, which is the national metrology institute of the USA, assigns certified values to the mass fractions of individual elements in single-element solutions, and to the mass fractions of anions in anion solutions, based on gravimetric preparations and instrumental methods of analysis. The instrumental method currently is high-performance inductively coupled plasma optical emission spectroscopy for the single-element solutions, and ion chromatography for the anion solutions. The uncertainty associated with each certified value comprises method-specific components, a component reflecting potential long-term instability that may affect the certified mass fraction during the useful lifetime of the solutions, and a component from between-method differences. Lately, the latter has been evaluated based only on the measurement results for the reference material being certified. The new procedure described in this contribution blends historical information about between-method differences for similar solutions produced previously, with the between-method difference observed when a new material is characterized. This blending procedure is justified because, with only rare exceptions, the same preparation and measurement methods have been used historically: in the course of almost 40 years for the preparation methods, and of 20 years for the instrumental methods. Also, the certified values of mass fraction, and the associated uncertainties, have been very similar, and the chemistry of the solutions also is closely comparable within each series of materials. If the new procedure will be applied to future SRM lots of single-element or anion solutions routinely, then it is expected that it will yield relative expanded uncertainties that are about 20 % smaller than the procedure for uncertainty evaluation currently in use, and that it will do so for the large majority of the solutions. However, more consequential than any reduction in uncertainty, is the improvement in the quality of the uncertainty evaluations that derives from incorporating the rich historical information about between-method differences and about the stability of the solutions over their expected lifetimes. The particular values listed for several existing SRMs are given merely as retrospective illustrations of the application of the new method, not to suggest that the certified values or their associated uncertainties should be revised.

Measurement uncertainty evaluation procedures and applications for various types of multichannel rotating-element spectroscopic ellipsometers.

A universal measurement uncertainty evaluation procedure is required for different types of multichannel rotating-element spectroscopic ellipsometers (RE-SEs) used in modern semiconductor industry. Herein, an improved uncertainty evaluation procedure, based on the universal measurement model functions and implicit function theorem, is introduced for unknown optical parameters of a sample. In addition, we develop a measurement standard instrument that can solve the error problems related to the basic principles of the multichannel RE-SEs used in the industrial field and present an example of applying the proposed uncertainty evaluation method to this standard instrument. Accordingly, the measurement performance for several types of real-time RE-SEs can be quantitatively compared. It can also be used for standardization, instrumentation, and measurement optimization.

Determination of dissolved oxygen in water by the Winkler method: Performance modelling and optimisation for environmental analysis

Dissolved oxygen concentration in water is a crucial parameter to assess the condition or evolution of an aquatic ecosystem health. This determination can be performed using an electrochemical sensor or the reference Winkler method that allows a more reliable measurement of this parameter. The comparison of dissolved oxygen values determined on two occasions or two samples requires calculating the measurement uncertainty. This uncertainty is also relevant to understand if the determination has adequately low uncertainty. This work describes the detailed assessment of dissolved oxygen determinations' performance aiming at the 'bottom-up' quantification and optimisation of the measurement uncertainty. The visual end-point detection's uncertainty was estimated by the difference between observed measurement precision and combined models of all precision components except the end-point detection. A user-friendly MS-Excel spreadsheet that allows applying the developed uncertainty evaluation procedure is made available as Supplementary Material. The determination of dissolved oxygen from analytical portions not lower than 50 mL is fit for environmental monitoring. It allows measurements between 0.3 mg L−1 and 14.6 mg L−1 with an expanded uncertainty between 0.36 mg L−1 and 0.74 mg L−1 for a 95% confidence level. This uncertainty allows differentiating dissolved oxygen values between 0.51 mg L−1 and 1.0 mg L−1 with less than a 5% probability of being wrongly assumed a relevant difference. The described uncertainty evaluation strategy can also be used in other titrimetric determinations.

Considering of the input quantities distributions in the procedure for measurement uncertainty evaluating on the example of resistance box calibration

The controversy over estimates of measurement uncertainty in the Guide to the Expression of Uncertainty in Measurement and Supplement 1 to it is considered. It is shown that possible ways to overcome these disagreements are to use the methods developed by the authors. Using the example of resistance calibration on a direct current, the features of taking into account the distribution of input values in the procedure for uncertainty evaluation when using the kurtosis method and low of propagation of expanded uncertainty are shown. A model of direct measurement of the resistance value of a resistance measure using a reference ohmmeter is written, the procedures for measurement uncertainty evaluation are described, and the uncertainty budgets are given. An example of measurement uncertainty evaluation at calibrating a resistance box P33 class 0.2 using a Fluke 8508 A digital multimeter is described. The expanded uncertainty of measurement for this example was estimated based on the NIST Uncertainty Machine web application, which showed good agreement with the estimates obtained by the methods considered.

Accounting for the kurtoses of input quantities in the procedure of evaluating measurement uncertainty using the example of weight calibration

Example 9.3.1.1 of JCGM-S1 “Mass calibration” is analyzed, which describes the comparison in air of reference and calibrated weights having the same nominal mass. JCGM-S1 compares uncertainty evaluation procedures based on the GUM uncertainty framework and the Monte Carlo method. The article uses the procedure developed by the authors and consists in decomposing the measurement model into a Taylor series of the second order taking into account the kurtoses of the distributions of input quantities. To facilitate the calculations, the finite increment method is used. To find expanded uncertainty, the kurtosis method is used. Good agreement between the results obtained by the proposed method and the result obtained by the Monte Carlo method is shown.

The power frequency voltage divider calibration device and its uncertainty

The power frequency high voltage divider is widely used to measure the power frequency high voltage and it is an important measuring instrument for high voltage test. Whether it is accurate or not directly affects the insulation monitoring level of power equipment closely related to the safety of power production, and it is of vital importance for power enterprises to ensure the measurement accuracy of power frequency high-voltage divider. The newly implemented JJG496-2016 <Verification procedure for high-voltage power divider> recommended three measurement methods: difference comparison, equal power bridge method and voltage ratio method. At present, only some literatures have introduced the measurement method using voltage ratio method and the measurement uncertainty evaluation procedure. This paper introduces a calibration device and measuring method of power frequency high voltage divider using the difference comparison method, and gives the uncertainty of the ratio difference and phase difference of power frequency high voltage divider obtained under the standard test environment.

Uncertainty Analysis of Stray Field Measurements by Quantitative Magnetic Force Microscopy

Magnetic force microscopy (MFM) measurements generally provide phase images which represent the signature of domain structures on the surface of nanomaterials. To quantitatively determine magnetic stray fields based on an MFM image requires calibrated properties of the magnetic tip. In this work, an approach is presented for calibrating a magnetic tip using a Co/Pt multilayered film as a reference sample which shows stable well-known magnetic properties and well-defined perpendicular band domains. The approach is based on a regularized deconvolution process in Fourier domain with a Wiener filter and the L-curve method for determining a suitable regularization parameter to get a physically reasonable result. The calibrated tip is applied for a traceable quantitative determination of the stray fields of a test sample which has a patial frequency spectrum covered by that of the reference sample. According to the "Guide to the expression of uncertainty in measurement", uncertainties of the processing algorithm are estimated considering the fact that the regularization influences significantly the quantitative analysis. We discuss relevant uncertainty components and their propagations between real domain and Fourier domain for both, the tip calibration procedure and the stray field calculation, and propose an uncertainty evaluation procedure for quantitative magnetic force microscopy.

Numerical Analysis and Measurement of Electric field Strength inside GTEM Cell at GSM Frequencies

A miniaturised gigahertz transverse electromagnetic (GTEM) cell is designed and fabricated to generate uniform electric (E-) field, essential for studying the radio frequency exposure effect on tissue equivalent liquids at global system for mobile (GSM) communication frequencies (914 MHz and 2.10 GHz). The simulation procedure is discussed and its results are compared with measurement data. The E-field strength inside the GTEM cell is scanned using a microstrip based E-field probe and complete uncertainty evaluation procedure is discussed. Theoretically, simulated and measured E-field strength is reported with expanded uncertainty.

An Improved Budget Allocation Procedure for Selecting the Best-Simulated Design in the Presence of Large Stochastic Noise

Motivated by the increasing practical needs for simulation optimization of modern industrial systems, this paper proposes an efficient ranking and selection (R&S) procedure for selecting the best-simulated design from a finite set of alternatives in the presence of large stochastic noise. To obtain the correct selection under a limited simulation budget, the proposed procedure sequentially allocates the budget to minimize the evaluated uncertainty values of the selection through a two-step process based on the existing uncertainty evaluation (UE) procedure. This two-step process reduces the inefficiency of the underlying UE procedure while keeping its high robustness to noise, thereby achieving improved the efficiency for the proposed procedure in a noisy environment. This improved efficiency is demonstrated in comparative experiments with other R&S procedures on several benchmark problems. In particular, the experimental results of three practical optimization problems emphasize the necessity of the proposed procedure.

Statistical analysis of parameter estimation of a probabilistic crack initiation model for Alloy 182 weld considering right-censored data and the covariate effect

Abstract To ensure the structural integrity of nuclear power plants, it is essential to predict the lifetime of Alloy 182 weld, which is used for welding in nuclear reactors. The lifetime of Alloy 182 weld is directly related to the crack initiation time. Owing to the large time scatter in most crack initiation tests, a probabilistic model, such as the Weibull distribution, has mainly been adopted for prediction. However, since statistically more advanced methods than current typical methods may be applied, we suggest a statistical procedure for parameter estimation of the crack initiation time of Alloy 182 weld, considering right-censored data and the covariate effect. Furthermore, we suggest a procedure for uncertainty evaluation of the estimators based on the bootstrap method. The suggested statistical procedure can be applied not only to Alloy 182 weld but also to any material degradation data set including right-censored data with covariate effect.

A simulation-based probabilistic framework for lithium-ion battery modelling

State-of-the-art researches on the modelling of lithium-ion batteries for electric vehicle have been conducted based on the physics and empirical-based models to estimate their states. However, less attention has been paid to evaluating the mechanical strength of the batteries when the battery pack is subjected to sudden external impact or crash. The present work, therefore, proposes a simulation-based probabilistic framework that combines artificial neural network and a moment-based uncertainty evaluation technique utilising the finite element model of a lithium-ion battery to evaluate its mechanical strength. The study was based on the following inputs: displacement, temperature and strain rate of the battery, and their uncertainties when the battery is subjected to sudden impact. The artificial neural network outperforms other well-known modelling methods, such as the radial basis function neural network and polynomial regression, for the global mechanical strength modelling, and the probability distribution obtained from the proposed uncertainty evaluation procedure is shown to be accurate. Further analysis employing the framework reveals that the mean mechanical strength of the battery decreases with increasing temperature, but increases with increasing displacement and strain rate. It was also found that the displacement and temperature have similarly high influence on the mechanical strength of the battery compared to the strain rate. The proposed framework and presented findings can help battery manufacturers improve the road safety of electric vehicles.

Uncertainty Evaluation of the Calibration of Dial Indicator Calibrators by Laser Interferometer

This paper describes the uncertainty evaluation procedure for a dial indicator calibrator calibration in accordance with the ISO/IEC Guide 98-3:2008. The effects of error sources on this calibratio...

Evaluation of aspects affecting measurement of three-axis accelerometers

In order to set integrated procedures involving geotechnical and structural aspects finalized to buildings diagnostics, uncertainty aspects are discussed concerning three-axis accelerometers and inclinometers for a distributed sensor network. This network allows to operate in a selective manner, preferring the most critical situations. To this aim, the main aspects affecting the measurement uncertainty of sensors to be used for building diagnostic should be known. As the firstly step of the uncertainty evaluation procedure, we focused on the calibration of sensors used for the task. The requirement of low cost and complexity of sensors and test benches was considered. Experimental results show that satisfactory calibration accuracy could be achieved, also for the low frequency range, 0–10Hz. Systematic errors are minimized and main parameters affecting uncertainty are identified, such as: the motion positioning of the accelerometer with respect to the vertical axis, the imposed motion law, the parameter used as the reference and, finally, the real radial positioning of the sensor. Requirements to be satisfied by the sensor are also analysed.

Evaluation of an optical coordinate measuring machine for measuring grated structures

The use of optical coordinate measuring machines (CMMs) in industrial metrology shows great potential due to a high measurement speed and non-contact working principle. However, at present measurements performed by different users present too large variations. The uncertainty contributions are difficult to quantify and standard uncertainty evaluation procedures are needed. In order to address this issue, we have investigated the uncertainty sources of commercial optical CMMs. We present a comparison on chessboard standards between three different vision systems. The influence of critical measurement parameters on image formation and analysis is discussed.

The GUM, Bayesian inference and the observation and measurement equations

In this paper, we compare uncertainty evaluation procedures based on the measurement and observation equation approaches applied to a class of models covering many practical measuring systems. We derive general conditions for when the two approaches give the same distributions associated with the measurand and give examples of how and where they differ. We argue that while it is possible to interpret the measurement equation approach as determining a state of knowledge distribution for the measurand, for some problems there are conceptual, and for highly nonlinear models, practical difficulties with this interpretation. These conceptual difficulties do not arise if the measurement equation approach is interpreted as characterising the behaviour of a measuring system. The discussion presented here is relevant to the revision of the GUM, currently being undertaken by the Joint Committee for Guides in Metrology.

Covariance Propagation for the Uncertainty Estimation in Stereo Vision

Stereo vision has emerged as an effective approach for contactless 3-D measurements. This paper presents a methodology for the propagation of the measurement uncertainty through stereo-vision calibration and measurement algorithms, according to international standards. The proposed procedure is compared to the reference statistical procedure for uncertainty evaluation, and the results are presented and discussed. The results proved that the proposed procedure was able to estimate the standard uncertainty even at considerable working distances from the calibrated volume with negligible processing times and far more accurately than the theoretical simplified models commonly adopted.

Uncertainty evaluation procedure and intercomparison of bell provers as a calibration system for gas flow meters

Many NMIs (national measurement institutes) and calibration laboratories worldwide use a bell prover as a calibration system for gas flow meters. The basic definition and procedure to estimate the bell prover uncertainty have been given in previous studies. After the announcement of a mutual recognition agreement (MRA) in 1998 by the BIPM (Bureau International des Poids at Mesures), many NMIs have needed to have more details of uncertainty evaluation procedure of the bell prover. In this study, more details of the test procedure of bell prover uncertainty are presented with a modification of position of the temperature and the pressure sensor to measure more exact values. The other modification is to use three precise guide rods with bearings to make the pressure in the bell more stable. Furthermore, a laser interferometer is used to enhance the measurement accuracy of the testing time and the traveling length of the bell. The uncertainty of the bells estimated by the procedure given in this study is 0.13% at the confidence level of 95%, rather than 0.17% of the previous one. Recently, the results of CCM.FF-K6, which is an international comparison of NMIs organized by the CIPM (Comité International des Poids et Mesures), show that the uncertainty of the KRISS (Korea Research Institute of Standards and Science) bell prover estimated by this study is reasonable.

Metrological performance of optical coordinate measuring machines under industrial conditions

An increasing number of manufactured parts are measured in industry using non-contact measuring systems. The paper describes an industrial comparison of coordinate measuring machines (CMMs) equipped with optical sensors, performed in Europe from August 2007 to January 2009 involving 21 optical CMMs. Participants, mainly small–medium size industrial companies, were asked to measure a set of calibrated artefacts with measurement tasks of different complexity. They include both 1D/2D standards (glass scale and optomechanical hole plate) and 3D injection moulded workpieces of different colours (four plastic Lego bricks). In addition to the evaluation of actual metrological performances of optical CMMs in industry, an important aim of the comparison was to investigate the validity of measurement uncertainty statements provided by participants. The focus of this investigation was on the additional error sources that emerge when using optical CMMs. Results demonstrate that: (i) the interactions of optical sensors with material and surface of parts are among the most important error sources; (ii) the users of optical CMMs in most cases are not aware of the magnitude of these effects; (iii) specific uncertainty evaluation procedures, suitable for industrial users of optical coordinate measurements, are needed.