Evaluation of measurement uncertainties in quantifying urinary aripiprazole and dehydroaripiprazole via isotope dilution–LC–MS/MS

Reliability of measurement data is particularly important in today’s world of globalization and trading across international borders. The acceptable and meaningful way of expressing the measurement result is to give the average value along with a range called measurement uncertainty at a confidence level within which the true value shall lie. Measurement uncertainty has specifically gained more importance with emphasis on decision rule as the decision-making criteria in ISO 17025: 2017 for accepting or rejecting a given sample. It is important for laboratory personnel to have knowledge in statistics apart from expertise in their field of testing and calibration to be able to correctly determine the factors that would contribute to the measurement uncertainty and the values of such contributions thereof. This chapter provides an overview of the evaluation and analysis of measurement uncertainty. The study also describes the strengths, weaknesses, opportunities, and threats (SWOT) analysis of the Monte Carlo simulation (MCS) in the evaluation of measurement uncertainty. Furthermore, the chapter also summarizes the implications and future prospects associated with the uncertainty methodology and recommends the wide usage of this in solving problems in various scientific filed.KeywordsMetrologyMeasurement uncertaintyProbability distribution functionSWOTCalibration

The definition in the ‘‘International Vocabulary of Metrology—Basic and general concepts and associated uncertainties (VIM)’’ [1] of ‘measurement result’ [2] refers to a ‘‘set of quantity values being attributed to a measurand together with any other available information’’. Note 2 to that definition [3] adds: ‘‘A measurement result is generally expressed as a single measured quantity value and a measurement uncertainty. ...’’ (terms in bold mean that they refer to concepts that are themselves defined in VIM). In the VIM, ‘‘Notes’’ are explanatory to definitions and are considered part of them. We discussed the ‘‘quality’’ of a measurement result previously [4–6]. Let us here take a special look at that most important intention we have when we carry out a measurement: the intended use of the result. If the quality of a measurement result is guaranteed by using a ‘measuring system’ [7], which is calibrated by means of an appropriate ‘calibrator’ [8], we could all agree that that would enable to obtain an acceptable result. Just about, but not quite. In daily measurements performed because of specific needs, the ‘measurement uncertainty’ in the measurement result should be small enough for the intended use of the result. However, there is no need that it be much smaller (hence requiring unnecessarily sophisticated and expensive procedures), nor much larger (making the measurement superfluous because leading to an inappropriate result). After all, it is because of the need for some specified use of the result that a measurement is made. Hence, it is logical that it must be designed as such on beforehand. The result should be consistent with the definition of the concept measurement result, whilst at the same time, the expected measurement uncertainty should be fit-for-the-intended-use of that result. In other words, the achieved uncertainty in the result should fall within an approximate (and pre-set) ‘target measurement uncertainty’ [9], which is decided before the measurement. Could it be that in a number of cases, we make too many measurements? Maybe. What more do we wish—or even need—than a measurement result falling within a pre-set target measurement uncertainty? Normally, a complete measurement uncertainty is composed of a combined Type A and Type B evaluation [10, 11]. Carrying out a ‘Type A evaluation of measurement uncertainty’ is easy. It is obtained from calculating a repeatability standard deviation and is usually not critical in most chemical measurement results as it is not generating the biggest component of the full final uncertainty in the result. The ‘Type B evaluation of measurement uncertainty’ usually constitutes the largest component of that full uncertainty and must be ‘‘evaluated’’ by the analyst. It is sufficient to verify that it is expected to fall within the pre-set target measurement uncertainty. If it would be expected to be much larger, there would be no need to make the measurement at all as the Type B uncertainty component is expected to be too large, rendering the result useless. ‘‘Fitness-for-intendeduse’’ of the measurement result is important as it prevents making too many measurements, or requiring too sophisticated measuring systems, all of which bring associated cost. On the other hand, evaluation of the Type B component of the expected uncertainty enables to ascertain whether the measurement is worth to be made at all, as the P. De Bievre (&) Kasterlee, Belgium e-mail: paul.de.bievre@skynet.be

Evaluation of the measurement uncertainty: Some common mistakes with a focus on the uncertainty from linear calibration

Propose a method for evaluating the measurement uncertainty of magnification error in metallographic microscope objective lens. Establish a measurement uncertainty evaluation model based on calibration methods and analyse the sources of each uncertainty. Combining measurement examples, this article elaborates on the evaluation of uncertainty in the measurement of magnification error of metallographic microscope objective lens.

At present, several measuring instruments are commercially available in the market for accurate and precise pressure measurements. In case of electromechanical type pressure sensors, the evaluation of measurement uncertainty is always a tedious task for researchers due to lack of availability of the suitable and well-defined mathematical model. In order to harmonize the method of evaluation of measurement uncertainty associated with measuring instruments, “The Guide to the Expression of Uncertainty in measurement,” published by International Standard Organization, is a major directional guide which is equally important in pressure metrology. The present paper describes the various uncertainty propagation models developed for the evaluation of measurement uncertainty associated with direct pressure indicating devices (DPIDs). A detailed comparative study is presented while using Monte Carlo simulation, least square fitting and calibration factor methods for the evaluation of measurement uncertainty using a DPID. In order to judge the feasibility and practical applicability of these contemporary methods, it is demonstrated through an example of a case study on the results thus obtained on a DPID that results using three different approaches are in excellent agreement and quite comparable.

Internet Protocol Packet Delay Variation measurements in communication networks: How to evaluate measurement uncertainty?

The evaluation of measurement uncertainties has been widely applied to the calibration of measurement instruments, whereas its application to tests, despite increasing requirements, is a more recent phenomenon. The generalization of the evaluation of measurement uncertainties to tests has been a gradual process, in line with changes in the requirements of the normative framework that regulates the accreditation of tests laboratories and also as the perceived good practices have evolved. The sole identification of the relevant sources of uncertainty was followed by the requirement to provide a simplified estimate of the measurement uncertainty, and it is now an accepted requirement to properly evaluate the expanded measurement uncertainty associated with any tests. In this study, the evaluation of measurement uncertainty associated with the determination of sulfate in water will be attempted using a procedure that includes linear regression, with the regression parameters provided with associated uncertainties, and a Monte Carlo method applied as a validation tool of the conventional mainstream evaluation method, concerning the approximations in terms of linearization of the model and the assumed shape of the output distribution introduced by this approach.

Several instruments are available in the market for the accurate and precise measurement of pressure. Due to numerous influencing elements and the lack of a well-defined mathematical model, calculating the uncertainty in the category of electromechanical pressure transducers has long been a laborious task for researchers. The “Guide to the Expression of Uncertainty in Measurement (GUM)” and “Guidelines on the Calibration of Electromechanical Manometers (Calibration Guide EURAMET/Version 4.1)” are the main directional guides for harmonizing the method of evaluation of measurement uncertainty associated with pressure measuring instruments. The present chapter describes the various uncertainty estimation models developed for the evaluation of measurement uncertainty associated with the electromechanical type of pressure transducers. For the evaluation of the measurement uncertainty of such pressure measuring equipment, a thorough comparative study using Least Square Fitting (LSF), Monte Carlo simulation (MCS), and EURAMET approach is presented. It is shown through an example of a case study on a digital pressure transducer (DPT) up to the pressure range of 800 MPa. The results obtained using three different approaches are in excellent agreement and quite comparable, allowing us to assess the viability and practical applicability of these modern techniques.

An uncertainty model has been proposed which is based on the black-box concept to evaluate the uncertainty of measurement and calibration in high voltage pulse divider. The initial model was proposed in principle, unnecessary variables in the formula could be omissible in the calibration experiment. For the model absent of uncertainty originating from calibration document, and resolving power of oscilloscope, the correction components which belong to the black-box model would be introduced to the formula to perfect the model. The uncertainties were combined after perfection of model according to the law of propagation of uncertainty. The results are compared with that combined from relative uncertainty. It is shown that the uncertainty combined from relative uncertainty will be correct if this model is only composed of multiplication and division of different variables, or addition and subtraction of different variables are also permitted if the mathematical expectation values of these items equal to zero. This is proven by calculating the voltage potential between two different positions according to the measured voltage pulse at those positions and analyzing the attenuation represented by dB scales. In the calibration experiment of high voltage divider, the combined standard uncertainty of dividers scaling factor is obtained by evaluating Type A standard uncertainty of the ratio of output to input. The influence of dispersion from signal source output on evaluation of standard uncertainty can be weakened with this method.

Measurement uncertainty is an indispensable factor to describe the precision of measurement value. Evaluation of measurement uncertainty, however, is the obstacle for most of tests and measurements because of its complexity of modeling and calculation. Meanwhile, almost all current automatic uncertainty evaluation technologies are lack of customized measurement modeling, control flexibility, data sharing, or result comparison. Aimed at such issues, we propose uncertainty evaluation and calculation technologies and develop an accordant system based on cloud computing. According to the experiment result, the technologies and system are useful and efficient.

Spreadsheet for designing valid least-squares calibrations: A tutorial

Measurement of grating pitch by optical diffraction is one of the few methods currently available for establishing traceability to the definition of the meter on the nanoscale; therefore, understanding all aspects of the measurement is imperative for accurate dissemination of the SI meter. A method for evaluating the component of measurement uncertainty associated with coherent scattering in the diffractometer instrument is presented. The model equation for grating pitch calibration by optical diffraction is an example where Monte Carlo (MC) methods can vastly simplify evaluation of measurement uncertainty. This paper includes discussion of the practical aspects of implementing MC methods for evaluation of measurement uncertainty in grating pitch calibration by diffraction. Downloadable open-source software is demonstrated.

The archetypal procedure in Type A evaluation of measurement uncertainty involves making <em>n</em> observations of the same quantity, taking the sample figure <em>s</em>² to be an unbiased estimate of the underlying variance and quoting the figure <em>s</em> / sqrt(<em>n</em>) as the relevant standard uncertainty. Although this procedure is theoretically valid when the sample size <em>n</em> is fixed, it is not necessarily valid when <em>n</em> is chosen in response to the growing dataset. In fact, when the experimenter makes observations until a certain level of uncertainty in the mean is reached, the bias in the estimation of the variance can be as much as -45 %. Likewise, the usual nominal 95 % confidence interval can have a level of confidence as low as 88 %. This issue is discussed and techniques are suggested so that Type A evaluation of uncertainty becomes as accurate as is implied. The 'objective Bayesian' approach to this issue is discussed and an associated unacceptable phenomenon is identified.

The Guide to the Expression of Uncertainty in Measurement (GUM) is the de facto standard for the evaluation of measurement uncertainty in metrology. Recently, evaluation of measurement uncertainty has been proposed on the basis of probability density functions (PDFs) using a Monte Carlo method. The relation between this PDF approach and the standard method described in the GUM is outlined. The Monte Carlo method required for the numerical calculation of the PDF approach is described and illustrated by its application to two examples. The results obtained by the Monte Carlo method for the two examples are compared to the corresponding results when applying the GUM.

The knowledge power quality levels, through objective approach, is based on the accumulation as measurement information. For a more complete characterization of power quality parameters it is necessary that the measurement process to include in the set of specific operations and evaluation of measurement uncertainty. Measurement uncertainty is a specific parameter of measurement method and conditions under which measurements are made. By this way, IEC 61000–4 series regulations Electromagnetic compatibility include a number of clarifications concerning the purpose of determinations, the level of accuracy and the level of uncertainty to be measured power quality parameters. The issue of evaluation of measurement uncertainty of power quality parameters, is presented in this article as a methodology, exemplified experimentally by measuring the nominal voltage supply, dips and swell in power distribution networks.