Assessing Measurement Uncertainty Research Articles

STATISTICAL TECHNIQUES IN PRECISION METROLOGY, APPLICATIONS AND BEST PRACTICES

Statistical techniques play a pivotal role in precision metrology, ensuring accurate measurements and reliable data analysis in various industries. This review delves into the applications and best practices of statistical techniques in precision metrology, highlighting their significance in enhancing measurement accuracy, reducing uncertainties, and optimizing manufacturing processes. In precision metrology, statistical methods are employed to analyze measurement data, assess measurement uncertainty, and make informed decisions regarding process control and quality assurance. One of the fundamental applications of statistical techniques is in experimental design, where methodologies such as Design of Experiments (DOE) aid in optimizing measurement processes by identifying influential factors and their interactions. Moreover, statistical process control (SPC) techniques like control charts are widely utilized in monitoring and maintaining measurement processes within specified limits, thereby ensuring consistency and reliability in metrology operations. These techniques enable early detection of deviations or anomalies, facilitating timely corrective actions to prevent the production of non-conforming products. Furthermore, the application of statistical analysis in uncertainty evaluation is crucial for quantifying the reliability of measurement results. Techniques such as Monte Carlo simulation and GUM (Guide to the Expression of Uncertainty in Measurement) provide systematic approaches for assessing and expressing measurement uncertainty, considering various sources of error and their contributions to the overall uncertainty budget. In addition to applications, adopting best practices in statistical techniques is essential for ensuring the effectiveness and efficiency of precision metrology processes. This includes proper data collection, adherence to statistical assumptions, selection of appropriate statistical models, and interpretation of results with caution. Overall, this review underscores the importance of statistical techniques in precision metrology, emphasizing their role in improving measurement accuracy, reducing variability, and enhancing overall quality in manufacturing processes. By implementing robust statistical methodologies and adhering to best practices, organizations can achieve higher levels of precision, consistency, and reliability in their metrology operations, ultimately leading to improved product quality and customer satisfaction.
 Keywords: Statistics, Precision Metrology, Best Practices, Application, Review.

Uncertainty: qualitative and quantitative aspects

The analysis the concept of uncertainty, its origin, interpretation in various scientific fields, sources of uncertainty, qualitative and quantitative aspects of this concept, as well as approaches to quantifying uncertainty are presented. Methods of historical and comparative analysis were used in the study. The main conclusion is the necessity of taking into account the presence of uncertainty and quantification of uncertainty of the results of mathematical modeling of objects and phenomena of the surrounding world in the same way as we do when assessing measurement uncertainty of experimental data. In is shown that the interval approach to estimating uncertainty of modeling results currently seems to be the most promising. The concept of uncertainty first proposed at the beginning of the last century refers to epistemic situations involving imperfect or unknown information. This concept had only a qualitative aspect for a long time. In the second half of the twentieth century, almost simultaneously with the development of a risk-based approach in the field of technological security, there was an interest in understanding uncertainty, its origin and typification. We are indebted to metrology for giving uncertainty a quantitative aspect, in which, instead of the measurement error paradigm, a measurement uncertainty paradigm was developed, and approaches (partly controversial) to its quantitative assessment were proposed. Uncertainty is an attribute of any data obtained both experimentally or theoretically (currently, usually by mathematical modeling). In the field of experimental research, specifying the uncertainty interval of the result has long been a scientific standard and routine. The time has come to make it mandatory for the results of theoretical research. To date, three alternative methods of quantitative estimation of uncertainty have been developed: probabilistic, fuzzy and interval methods. Methods for leveling the negative features of its initial «naive» version have been proposed in modern interval analysis. It seems to be the most promising method of quantifying uncertainty of the results of mathematical modeling today.

Dimensional measuring of parts as function of temperature variation and FEM study

The components of astructure can be made in many different areas by many suppliers, before being brought together as a single final. Measuring geometry and geometric dimensions of a structure is an essential process in establishing product quality. Dimensional measurement is often affected by several human or physical factors, of which temperature is an essential factor in introducing deviations. Often the expected results are out of specification due to temperature variation. Paper aims to present the effects due to temperature variations in dimensional measurement as well as way to solve problems. One of the problems in the measurement process is the lack of repeatability in measuring tolerated dimensions. The study presents measurements in the conditions of volumetric thermal expansion of AMCs and measured parts, which are directly influenced by temperature. The need to verify the accuracy of measurements and control of equipment is an important step for quality departments in this industry because the quality of production is based on the target of “zero defects” so the need to know about the condition of equipment is extremely important. In specific cases in addition to the normal calibration which is according to international standard ISO 10360-2: 2009 as a mandatory application, the same standard determines the need to perform re-verification tests according to user specifications, looking for deviations that should not occurs in systematic errors. Also, the international standard ISO 17025: 2005 which defines the general requirements for testing and calibration components of laboratories, in point 5.5.10 of the technical requirements it is said that intermediate checks are necessary to maintain confidence in the calibration status of equipment, these checks having to be done according to a specific procedure. Three techniques for assessing measurement uncertainty are presented in ISO 15530-; they can be used alone or in combinations. The first of these is known as sensitivity analysis and is described in the ISO Guide for Expressing Uncertainty in Measurement. Modeling and simulation can help evaluate the size of a part as a function of temperature. The article presents in the second part this method which offers values very close to the experimental ones and which may in the future simulate the values of the measurements where the experimental part is difficult to be done.

A method for assessing the uncertainty of a secondary dynamic pressure standard using shock tube

Pressures are often measured in fast transient regimes, even if the transducers are not calibrated in dynamic regimes. If the solutions proposed for primary calibration of the dynamic response of pressure sensors must be fully recognised, secondary methods are also needed to disseminate the standard to final users. A method for assessing measurement uncertainty, carried out by comparison with a reference transducer, traceable to primary standard, is proposed here. A typical application is gas pressure measurement. This paper follows and supplements the work done on the Mach number method in 2018. For this work the reference transducer is calibrated by the ‘collective standard method’ currently used in the ‘Laboratoire de Métrologie Dynamique’( LNE/ENSAM). This primary standard uses steps of pressure as inputs for dynamic pressure calibration that are generated by shock tubes (STs) and fast-opening devices (FODs). The uncertainty on dynamic sensitivity is evaluated from the quasi-static to the low, medium and high-frequency range (up to 10 kHz) using bandwidth comparisons. To calibrate a secondary standard transducer in gas, the method also requires one or two step generators: an ST for high-frequency range calibration and a FOD for the low-frequency range. Concerning the main results of this paper, the transducer to be calibrated and the reference transducer are placed symmetrically on the endplate of an ST. The amplitude of the pressure step generated by the tube is used to excite the transducers. Finally, the uncertainty on the sensitivity in dynamic conditions is determined by comparison with a model expected to be exhaustive. The results are provided as an uncertainty budget assigned frequency by frequency. The question asked in this work concerns the measurand used in secondary calibration: can a pressure step generated by a non-ideal ST be used in the process of calibration by comparison, i.e. for a secondary dynamic calibration? A method is proposed. Since the secondary method is derived directly from the primary one, this paper recaps the primary dynamic calibration method in gas and the budget of the associated uncertainty. Then the paper presents a secondary method and options to overcome the principal default identified in the ST frequency range, namelythe non-uniform pressure fields existing in the tube.

Evaluation of the clinical chemistry tests analytical performance by using different models and specifications

Abstract Background The importance of managing analytical quality in clinical laboratories is known. Goal-setting models are critical for analytical quality management, along with correctly implemented error models. However, the methods used to determine analytical performance and more importantly, the relevant analytical quality goals are open to discussion. Our aim was to compare the analytical performance characteristics of routine clinical chemistry tests with different goal-setting models which was proposed by various establishments. In addition, to provide a perspective to Turkish total analytical error (TAE) circular letter that compulsory to calculate from 2016. Materials and methods This study was performed by the data obtained from the internal and external quality control of clinical chemistry tests which were measured by Roche Cobas c501 biochemistry analyzer. TAE calculated with TAE% = 1.65 ×(CV%) + Bias% formula. Nordtest uncertainty model was used in the calculation of measurement uncertainty (MU). In this context, total analytical error was evaluated with biological variation (BV), RCPA, CLIA and Turkish allowable total error (ATE) goals. Measurement uncertainty was evaluated with only permissible measurement uncertainty (pU%) goal. Results In our study, RCPA goals are the most stringent, followed by the BVEuBIVAS, BVRicos, pU%, CLIA and finally the ATETurkey goals coming in last. In cumulatively, BVEuBIVAS goals were 18.3% lower than BVRicos for evaluated parameters. Conclusion The balance between applicability and analytical assurance of goals should be well ensured when determining goal-setting models. Circular letter (2016/18) creates awareness to the analytical quality management but still open to development. Biological variation dependent total allowable error model never designed to be used as benchmarks for measurement uncertainty and it is not methodologically appropriate for assessing measurement uncertainty which was estimated by the Nordtest method. Also considered that, the use of “permissible MU” is more methodologically appropriate in the evaluation of measurement uncertainty.

Assessing 3D paediatric foot morphology using low-dose biplanar radiography: Parameter reproducibility and preliminary values

BackgroundThe physical examination and weight-bearing radiography are the two main available methods for assessing the feet and lower limbs. The anatomy and function of these two structures interact with each other. These two assessment methods are affected by subjectivity and projection bias. Low-dose biplanar radiography (LDBR) is now a promising alternative for evaluating the lower limbs in children. At present, however, the foot cannot be assessed using LDBR. The objective of this study was to work towards developing a new method for 3D radiographic analysis of the paediatric foot during weight-bearing, first by determining the reproducibility of landmarks defined by LDBR then by reporting the values of the calculated radiographic parameters. HypothesisA new radiographic method based on LDBR can be used to obtain a 3D evaluation of the foot in paediatric patients. Patients and methodsTwo biplanar radiographs in perpendicular planes were obtained simultaneously in a standardised position using the EOS system (EOS® Imaging, Paris, France) in each of 10 healthy children. To assess measurement uncertainty, two observers performed 3D reconstructions of each of the 10 feet three times (60 reconstructions). The standard error of reproducibility of the anatomic landmarks and clinical parameters was computed. Measurement uncertainty was then estimated based on the 95% confidence interval (95%CI). To obtain reference values, the mean±SD of each variable was computed after checking that the data were normally distributed. ResultsReproducibility was high for the anatomical landmarks of interest, calcaneal pitch angle, tibio-calcaneal angle on the lateral view, and first metatarsal pitch angle (95%CI<5%). The values of these angles in the study population are reported. Discussion and conclusionThe data reported here pave the way towards developing new parameters for describing 3D foot morphology and for simultaneously assessing the lower limb and foot in the standing position. Level of evidenceI.

Assessing measurement uncertainty in meteorology in urban environments

Measurement uncertainty in meteorology has been addressed in a number of recent projects. In urban environments, uncertainty is also affected by local effects which are more difficult to deal with than for synoptic stations. In Italy, beginning in 2010, an urban meteorological network (Climate Network®) was designed, set up and managed at national level according to high metrological standards and homogeneity criteria to support energy applications. The availability of such a high-quality operative automatic weather station network represents an opportunity to investigate the effects of station siting and sensor exposure and to estimate the related measurement uncertainty. An extended metadata set was established for the stations in Milan, including siting and exposure details. Statistical analysis on an almost 3-year-long operational period assessed network homogeneity, quality and reliability. Deviations from reference mean values were then evaluated in selected low-gradient local weather situations in order to investigate siting and exposure effects. In this paper the methodology is depicted and preliminary results of its application to air temperature discussed; this allowed the setting of an upper limit of 1 °C for the added measurement uncertainty at the top of the urban canopy layer.

Evaluation of a high-precision gear measuring machine for helix measurement using helix and wedge artifacts

High-precision gears are required for advanced motion and power transmission. The reliability of the measured value becomes important as the gear accuracy increases, and the establishment of a traceability system is needed. Therefore, a high-precision gear measuring machine (GMM) with a smaller uncertainty is expected to improve the gear calibration uncertainty. For this purpose, we developed a prototype of a high-precision GMM that adopts a direct drive mechanism and other features. Then, the high measurement capability of the developed GMM was verified using gear artifacts. Recently, some new measurement methods using simple shapes such as spheres and planes have been proposed as standards. We have verified the tooth profile measurement using a sphere artifact and reported the results that the developed GMM had a high capability in tooth profile measurement. Therefore, we attempted to devise a new evaluation method for helix measurement using a wedge artifact (WA) whose plane was treated as the tooth flank, and the high measurement capability of the developed GMM was verified. The results will provide a part of information to fully assess measurement uncertainty as our future work. This paper describes the evaluation results of the developed GMM for helix measurement using both a helix artifact and the WA, and discusses the effectiveness of the WA as a new artifact to evaluate the GMMs.

Assessing measurement uncertainty on trihalomethanes prediction through kinetic models in water supply systems

Disinfection of drinking water through chlorine is commonly used in many countries for reducing pathogenic infection problems, but it may pose a risk to human health due to the formation of some by-products, such as trihalomethanes (THMs). For an adequate management of the disinfection process, it is useful to have models capable of simulating THMs concentrations in water supply systems. However, a crucial aspect is the reliability of their performances when used on real systems and the knowledge of the uncertainty of their predictions. The objective of the present paper is to investigate the simulation of THMs formation through calibrated kinetic models, along with the assessment of the measurement uncertainty on the parameters' estimate and on the model predictions. In particular, a first-order, a second-order and a two-phase kinetic model are considered, while the effect of measurement uncertainty is mainly investigated through the first-order second moment (FOSM) method. The analysis performed on a real case study shows that the three considered models have similar performances in terms of predicted concentrations, which suggests using the simplest first-order one. Moreover, the FOSM results reveal that the first-order model is less affected by measurement uncertainty.

Assessing measurement uncertainty in CMM measurements: comparison of different approaches

Manufactured parts are affected by size and form errors, which need to be assessed against geometrical and dimensional tolerances in order to meet the functional requirements they have been conceived for. The compliance assessment of workpieces with specifications depends on measurements and is unavoidably affected by several uncertainty contributions. According to the geometrical product specifications and verification (GPS), measurement uncertainty consists of method and implementation uncertainty. Literature proposes different approaches for the evaluation of implementation uncertainty, however a standardized method has not been yet achieved. This paper makes an analysis of the various elements to be considered when choosing a specific approach: in the implementation uncertainty of circular features. The most common manufacturing signatures affecting circular profiles were considered, together with the number of points necessary for a reliable estimation of implementation uncertainty.

Chemometrics in f-element speciation: a metrological challenge?

The UV–Vis spectra of the f-elements, especially the lanthanides, are known for their rather sharp absorption bands showing systematic and reproducible changes upon coordination with suitable ligands. These absorption bands have been used as indicators allowing interpretation of the processes in solution. Modern absorption spectrometers in combination with digital recording of the spectra allow a precise collection of a large number of absorptions for many samples. The number of absorption thus collected easily amounts to several thousands of individual data. Chemometric techniques, especially factor analysis, are occasionally used to extract information from these data sets on basis of Bouguer–Lambert–Beer law. Recent studies indicate the sensitivity of parameter values obtained from uncritical use of chemometric techniques to various influence and nuisance factors. On the basis of selected examples, the effects of parameter correlations, residual correlations, and measurement uncertainty introduced by volume operations are demonstrated. Using the ISO Guide to the Expression of Uncertainty as a convention for assessing measurement uncertainty, formation constants lg K derived from UV–Vis spectra of f-elements should be associated with a measurement uncertainty u of at least u = 0.15 (k = 1).

A systematic approach to assessing measurement uncertainty for CO 2 emissions from coal-fired power plants – Missing contributions from the Theory of Sampling (TOS)

An augmented measurement uncertainty approach for CO 2 emissions from coal-fired power plants with a focus on the often forgotten contributions from sampling errors occurring over the entire fuel-to-emission pathway is presented. Current methods for CO 2 emission determination are evaluated in detail, from which a general matrix scheme is developed that includes all factors and stages needed for total CO 2 determination, which is applied to the monitoring plan of a representative medium-sized coal-fired power plant. In particular sampling involved significant potential errors, as identified and assessed by the Theory of Sampling (TOS), which also shows how these can be eliminated and/or minimised. Since coal-related CO 2 emission calculations not only require analytical results of the carbon content of coal itself but also of the by-products fly ash and bottom ash, sampling procedures of these three materials were also given full attention. A systematic error (bias) is present in the current sampling approach, which increases the present uncertainty estimate unnecessarily. For both primary sampling and analytical sample extraction steps, random variations, which hitherto only have been considered to a minor extent, have now also been fully quantified and included in the overall uncertainty. Elimination of all identified sampling errors lead to modified CO 2 determination procedures, which indicate that the actual CO 2 emission is approximately 20,000 t higher than the present estimate. Based on extensive empirical sampling experiments, a fully comprehensive uncertainty estimate procedure has been devised. Even though uncertainties increased (indeed one particular factor is substantially higher, the so-called “emission factor”), the revised CO 2 emission budget for the case plant complies with the official pre-determined uncertainty levels maxima in the EU guidelines.

Impulse response characterization of anechoic and hemi-anechoic chambers.

Characterization of a measurement environment is an important component of assessing measurement uncertainty. The traditional technique in anechoic and hemi‐anechoic chambers is qualification through draw‐away testing: deviation from square‐law spreading is estimated along various radials, for broadband noise and occasionally for tones. All locations within a volume for which the deviations are below certain criteria are considered “qualified” for testing, and measured results from these locations are typically not corrected for the influence of the room. The draw‐away test is tedious and time consuming and does not yield the information that is actually desired: precision of measurements for a particular source‐receiver pair. Impulse response methods are considerably more rapid and provide a wealth of information in postprocessing including amplitude, phase, and time‐delay factors for both steady‐state and transient sounds, across arbitrary frequency ranges. This paper will explain how the impulse response characterization can be obtained and how it can be used to improve precision of measurements in anechoic and hemi‐anechoic environments.

Micro-PIXE characterization of reference samples intended for QA/QC of k0 NAA

Cellulose cylinders and circular filter papers spiked with known amounts of standard element solutions were prepared for studying some aspects of assessing measurement uncertainty of NAA and the elemental distribution measured by micro-PIXE analysis. Results for the cylinders showed strongly non-homogeneous distribution of the elements, both in radial and vertical directions, dominantly caused by osmosis driven transport of added liquid solution from the centre to the edges. Results for the thin cellulose filter paper disks exhibited weaker peaking of the standard element concentrations at the edges in comparison with the thick cylinders.

A simple algorithm for the absolute calibration of flatness using a three flat test

Absolute calibration of the reference flats installed in flatness interferometers is important to reduce measurement uncertainty and keep traceability of flatness measurement. A three flat test is a common method to derive absolute shape of flatness, but in the calculation process complicated least square calculations are required. A simple arithmetic formula is proposed to derive the absolute shape of the flat followed by experimental results to validate the formula and assess measurement uncertainty.

Assessing measurement uncertainty of first‐order degradation rates in heterogeneous aquifers

The principal idea of this paper is to simulate and evaluate the determination of first‐order degradation rate constants at heterogeneous contaminated sites under realistic conditions. First, a set of heterogeneous and contaminated synthetic aquifers is generated; second, the spreading of a solute plume subject to first‐order degradation is simulated. Third, this plume is investigated using “monitoring wells” placed along the presumed plume center line. Using only piezometric heads, concentrations and hydraulic conductivities obtained at these monitoring wells, first‐order degradation rate constants are calculated by methods typically used in field applications. The estimated rate constants are compared to the “real” value known from the simulations. This comparison is conducted for different degrees of heterogeneity, represented by lognormally distributed random conductivity fields. The results indicate that, with increasing degree of heterogeneity, “measured” degradation rate constants become uncertain with a high variability around the true constant. Measured rate constants tend to overestimate the true constant by up to one order of magnitude. A sensitivity analysis of the influences of source width, transport velocity, and dispersivity shows that (1) with increasing source width, measured rate constants decrease their relative error and increase their accuracy; (2) the choice of dispersivity can produce both over‐ and under‐estimation of the true rate constant; and (3) that large‐scale measurements of hydraulic conductivity yield better estimates of flow velocities as compared to local scale measurements. These results explain in part the high variability of field measured degradation rate constants reported in the literature.

Capability in Rockwell C Scale Hardness.

A measurement system is capable if it produces measurements with uncertainties small enough for demonstration of compliance with product specifications. To establish the capability of a system for Rock-well C scale hardness, one must assess measurement uncertainty and, when hardness is only an indicator, quantify the relation between hardness and the product property of real interest. The uncertainty involves several components, which we designate as lack of repeatability, lack of reproducibility, machine error, and indenter error. Component-by-component assessment leads to understanding of mechanisms and thus to guidance on system upgrades if these are necessary. Assessment of some components calls only for good-quality test blocks, and assessment of others requires test blocks that NIST issues as Standard Reference Materials (SRMs). The important innovation introduced in this paper is improved handling of the hardness variation across test-block surfaces. In addition to hardness itself, the methods in this paper might be applicable to other local measurement of a surface.