Software Tools for Evaluation of Measurement Models for Complex-valued Quantities in Accordance with Supplement 2 to the GUM

Tsui, Cho-man; Yan, Aaron Y. K.; Li, Hing-wah

doi:10.1080/19315775.2012.11721608

Cited by 7 publications

(5 citation statements)

References 3 publications

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“…E15 Voltage Reflection Coefficient. Tsui et al (2012) consider the voltage reflection co efficient Γ = S 22 − S 12 S 23 ∕S 13 of a microwave power splitter, defined as a function of el ements of the corresponding three-port scattering matrix (S-parameters). Exhibit 22 repro duces the measurement results for the S-parameters listed in Tsui et al (2012, Table 5).…”

Section: Prob Densitymentioning

confidence: 99%

Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results

Possolo¹

2015

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Measurement is an informative assignment of value to quantitative or qualitative properties involving comparison with a standard (§2). Property values that are imperfectly known are modeled as random variables whose probability distributions describe states of knowledge about their true values (§3). Procedure (1) Measurand & Measurement Model. Define the measurand (property intended to be measured, §2), and formulate the measurement model (§4) that relates the value of the measurand (output) to the values of inputs (quantitative or qualitative) that determine or influence its value. Measurement models may be: • Measurement equations (§6) that express the measurand as a function of inputs for which estimates and uncertainty evaluations are available (Example E3); • Observation equations (§7) that express the measurand as a function of the pa rameters of the probability distributions of the inputs (Examples E2 and E14). (2) Inputs. Observe or estimate values for the inputs, and characterize associated uncer tainties in ways that are fit for purpose: at a minimum, by standard uncertainties or similar summary characterizations; ideally, by assigning fully specified probability dis tributions to them, taking correlations between them into account (§5). (3) Uncertainty Evaluation. Select either a bottom-up approach starting from an uncer tainty budget (or, uncertainty analysis), as in TN1297 and in the GUM, or a top-down approach, say, involving a proficiency test (§3f). The former typically uses a measure ment equation, the latter an observation equation. (3a) If the measurement model is a measurement equation, and • The inputs and the output are scalar (that is, real-valued) quantities: use the NIST Uncertainty Machine (NUM, uncertainty.nist.gov) (§6); • The inputs are scalar quantities and the output is a vectorial quantity: use the results of the Monte Carlo method produced by the NUM as illustrated in Example E15, and reduce them using suitable statistical analysis software (§6); • Either the output or some of the inputs are qualitative: use a custom version of the Monte Carlo method (Example E6). (3b) If the measurement model is an observation equation: use an appropriate statistical method, ideally selected and applied in collaboration with a statistician (§7). (4) Measurement Result. Provide an estimate of the measurand and report an evaluation of the associated uncertainty, comprising one or more of the following (§8): • Standard uncertainty (for scalar measurands), or an analogous summary of the dispersion of values that are attributable to the measurand (for non-scalar measurands); • Coverage region: set of possible values for the measurand that, with specified probability, is believed to include the true value of the measurand; • Probability distribution for the value of the measurand, characterized either analytically (exactly or approximately) or by a suitably large sample drawn from it.

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Section: Prob Densitymentioning

confidence: 99%

Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results

Possolo¹

2015

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“…It is possible to use the original ICM in situations where the two SPRTs cannot be placed close together (e.g., in a metal block calibrator) by swapping the two SPRTs as follows to obtain the parameter A in equation (7). (i)…”

Section: Comparison Of the Scl Approach With The Original Icmmentioning

confidence: 99%

“…A summary of the uncertainties contributed by the components is in Table 7. Alternatively, an in-house developed software [7] enables us to encode the measurement model in equations ( 1) to (6) using VBA in Microsoft Excel and calculate the uncertainty using Monte-Carlo method [6].…”

Section: Sensitivity Coefficientmentioning

confidence: 99%

Implementation of instantaneous comparison methods in temperature gradient evaluation of stirred liquid temperature baths

Cheung¹,

Tsui²,

Lam³

et al. 2023

J. Phys.: Conf. Ser.

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Temperature gradient is an important performance indicator of a stirred liquid bath. Its evaluation requires measuring the temperature differences between different bath positions. A common way to do that is to place two SPRTs at two positions and measure their resistances against a standard resistor (R SPRT1/R S and R SPRT2/R S) sequentially (the sequential method). A drawback of this method is the existence of a time gap between the two measurements rendering the results susceptible to temporal temperature variation. The instantaneous comparisons method offers a better solution by measuring the resistance ratio of two SPRTs directly (R SPRT1/R SPRT2) and deriving their temperature difference at the same moment eliminating the time gap. To implement this method at the Standards and Calibration Laboratory (SCL) of Hong Kong, the resistance ratio of SPRT1 to a standard resistor (R SPRT1/R s) is firstly measured to determine the initial bath temperature. After that, the resistance ratios of SPRT1 to SPRT2 (R SPRT1/R SPRT2) are measured with the two SPRTs placed at different positions and immersion depths in the bath. This paper describes the derivation of the temperature difference from the SPRT resistance ratio using the ITS-90 reference equations and the estimation of the measurement uncertainties. The potential of reducing the uncertainties of measured temperature gradient by leveraging the correlation of the two SPRTs calibrated at the same set of temperature fixed points is discussed. The paper also compares the calibration results obtained by the instantaneous comparisons method and the sequential method.

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“…The following example has also been treated in [6]. It shows how complex-valued quantities are handled.…”

Section: Equivalent Source Matchmentioning

confidence: 99%

“…Only a few of the packages support complex-valued quantities, see e.g. [5,6], and are available as libraries with a license model that allows unrestricted free use. To our knowledge none of them would have fulfilled our performance requirements.…”

Section: Introductionmentioning

confidence: 99%

Metas.UncLib—a measurement uncertainty calculator for advanced problems

Zeier¹,

Hoffmann²,

Wollensack³

2012

Metrologia

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Software Tools for Evaluation of Measurement Models for Complex-valued Quantities in Accordance with Supplement 2 to the GUM

Cited by 7 publications

References 3 publications

Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results

Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results

Implementation of instantaneous comparison methods in temperature gradient evaluation of stirred liquid temperature baths

Metas.UncLib—a measurement uncertainty calculator for advanced problems

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