Exclusive statistics: simple treatment of the unavoidable correlations from key comparison reference values

Steele, A G; Wood, B.M.; Douglas, R J W

doi:10.1088/0026-1394/38/6/2

Cited by 22 publications

(31 citation statements)

References 8 publications

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“…We adopt exclusive statistics [4] to show that correlation between the CRV's and the results of NMISA is small as compared to the NMISA uncertainty.…”

Section: Considering Correlation Between Crv and Nmisa Resultsmentioning

confidence: 99%

NMISA, KEBS, BKSV tri-lateral vibration comparison results

Maina¹,

Veldman²,

Ploug³

2016

ACTA IMEKO

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National Metrology Institutes (NMIs) and calibration laboratories perform Inter Laboratory Comparisons (ILC) as part of their processes to validate their measurement capabilities (MCs). In the area of vibration (quantity acceleration) the Kenyan Bureau of Standards (KEBS) piloted an ILC, inclusive of two additional participating laboratories for this purpose. This technical review documents the calibration results and findings of the ILC.

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“…We adopt exclusive statistics [4] to show that correlation between the CRV's and the results of NMISA is small as compared to the NMISA uncertainty.…”

Section: Considering Correlation Between Crv and Nmisa Resultsmentioning

confidence: 99%

NMISA, KEBS, BKSV tri-lateral vibration comparison results

Maina¹,

Veldman²,

Ploug³

2016

ACTA IMEKO

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“…These N PDFs are to be pooled with a more general probability density function f (x) as the (N + 1)th PDF. From the perspective of the (N + 1)th NMI, we are considering the difference between likelihood distributions (equation (3)): the likelihood of unanimity of the (N + 1) NMIs and the likelihood of unanimity for N NMIs excluding the (N +1)th NMI-its exclusive likelihood distribution, which is also the distribution for the 'exclusive' inverse-variance weighted mean for the (N + 1)th NMI [6]. Taylor expanding the logarithm of f (x), g(x) = ln(f (x)), about x, and keeping terms to second order gives g( x) + g ( x)(x − x) + 1 2 g ( x)(x − x) 2 , based on g( x) and adding only the terms with the logarithmic slope [g (x) = ∂ ln(f (x))/∂x] and the logarithmic curvature [g (x) = ∂ 2 ln(f (x))/∂x 2 ] of the PDF at x.…”

Section: Insights From Graphical Methodsmentioning

confidence: 99%

Outlier rejection for the weighted-mean KCRV

Steele¹,

Wood²,

Douglas³

2005

Metrologia

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We propose new criteria to help select a subset of peer results for determining a weighted-mean Key Comparison Reference Value (KCRV) for describing Key Comparisons supporting the CIPM Mutual Recognition Arrangement (MRA). Often the results are all well behaved: their scatter is in the range expected from the Gaussian probability distributions associated with their stated standard uncertainties. In this case, the KCRV would usually be the inverse-variance weighted mean of all eligible results, the maximum likelihood estimate of independent Gaussian probability distributions. If most-but not all-of the results are well behaved, the comparison may be better described in terms of a KCRV computed with 'outliers' excluded from the weighted mean. An outlier's effects are quantified in terms of the logarithmic slope and logarithmic curvature of its associated probability density function in the vicinity of the consensus value. The outer tails of the probability distributions are generally not known with confidence, so two new criteria are suggested to help justify the identification of outliers: one based on uncertainty in the logarithmic slope, and the other based on uncertainty about whether the logarithmic curvature is negative definite.

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“…denotes the summation for i = 1, 2, …, k − 1, k + 1, …, n. This statistic is analogic to the concept of the "exclusive statistics" [13], [14]. When |E n ( k ) | ≤ 1 and > 1, the performances of Laboratory k are evaluated as "satisfactory" and "unsatisfactory", respectively.…”

Section: The Statistical Modelmentioning

confidence: 99%

Proficiency tests with uncertainty information: analysis using the maximum likelihood method

Shirono¹,

Shiro²,

Tanaka³

et al. 2016

ACTA IMEKO

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In this study, we report the application of the maximum likelihood method to the analysis of proficiency test data when uncertainty information is given and a reference laboratory does not exist. There are two causes that could impair the quality of analysis using the maximum likelihood method: the existence of an unknown random effect, and outliers. The conditions under which performance evaluations can be appropriately conducted are discussed in this study. To avoid serious impacts from these two causes, the maximum permissible standard uncertainty of an unknown random effect and the minimum permissible standard uncertainty of the values reported by a participating laboratory are quantified. Through simulations, the maximum and the minimum permissible standard uncertainties are found to be 0.3 and 0.5 times the intermediate magnitude of the standard uncertainty that the participants are expected to report. We believe that our proposed procedure based on these criteria is sufficiently simple to be employed in actual proficiency tests.

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Exclusive statistics: simple treatment of the unavoidable correlations from key comparison reference values

Cited by 22 publications

References 8 publications

NMISA, KEBS, BKSV tri-lateral vibration comparison results

NMISA, KEBS, BKSV tri-lateral vibration comparison results

Outlier rejection for the weighted-mean KCRV

Proficiency tests with uncertainty information: analysis using the maximum likelihood method

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