Optimal estimator for uncertainty-based measurement quality control

Huang, Hening

doi:10.1007/s00769-015-1111-x

Cited by 8 publications

(10 citation statements)

References 11 publications

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“…They could be derived, for example, from z-based and, t-based uncertainty estimators or an unbiased uncertainty estimator (z/c 4 ), as has been recommended by Huang even for small samples [16]. However, choice of threshold is not the subject of this article.…”

Section: Resultsmentioning

confidence: 99%

Is the assessment of interlaboratory comparison results for a small number of tests and limited number of participants reliable and rational?

Szewczak

Bondarzewski

2016

Accred Qual Assur

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Tests and/or test items can sometimes be expensive, unique, or only performed in a few laboratories. There can be cases where assigned values are unknown, there is no information, or only poor information on the probability density function attributed to the test result. Sometimes there are neither reference materials nor the ability to establish consensus values due to a lack of experts. It can be impossible to repeat a test on the same item because it is destroyed during the test itself, or the homogeneity of tested items is unknown and no criteria can be established. Specified technical requirements concerning proficiency testing and interlaboratory comparison schemes are generally not applicable in this situation. However, interlaboratory comparison could allow laboratories to have more confidence in their results. The present paper discusses three statistical methods of assessing interlaboratory comparison results obtained in such conditions. Two methods are based on an assigned value determined from participant results through robust analysis. The third is based on the compatibility of results assessed using the f parameter. This paper focuses on an interlaboratory comparison for two laboratories, each testing three samples. The use of statistical methods turns out to be high risk, particularly in terms of falsely accepting results. Additionally, is shown that methods dedicated to small samples are also not efficient in detecting discrepancies of test results.

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Section: Resultsmentioning

confidence: 99%

Is the assessment of interlaboratory comparison results for a small number of tests and limited number of participants reliable and rational?

Szewczak

Bondarzewski

2016

Accred Qual Assur

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show abstract

“…The transformation distortion can be quantitatively measured by the RBE of the t-based uncertainty with respect to the z-based uncertainty. That is (Huang 2015),…”

Section: Transformation Distortion: the T-and Z-intervals In The S-t ...mentioning

confidence: 98%

“…The results suggest that the measurement quality control based on the t-based uncertainty is overly conservative and misleading when the sample size is very small; therefore, the t-based uncertainty is inappropriate for measurement quality control for small samples. The author (Huang 2015) evaluated the performance of eight uncertainty estimators in terms of false acceptance/rejection probability, mean absolute percentage error (MAPE), mean squared percent age error (MSPE), relative bias error (RBE), and relative precision error (RPE). The results show that, among the eight estimators, the t-based uncertainty yields the highest false rejection probability and highest MAPE, MSPE, RBE, and RPE.…”

Section: Measurement Science and Technologymentioning

confidence: 99%

Uncertainty estimation with a small number of measurements, part I: new insights on thet-interval method and its limitations

Huang¹

2017

Meas. Sci. Technol.

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The conventional approach to estimating measurement uncertainty employs the t-interval when the population standard deviation is unknown and the sample size is small (<30). This is because the t-interval, or t-based uncertainty, is considered to be the ‘exact’ solution to estimating measurement uncertainty for small samples. However, three paradoxes have been found to be attributable to the t-interval. This paper is the first one (Part I) in a series of two papers (Part I and Part II). It presents some new insights on the t-interval and explores its true underlying meaning. This paper reveals that the t-interval is a result from a distorted statistical inference in the transformed sample space. The transformation distortion is the root cause of extremely high t-scores when the sample size is very small (<5), resulting in unrealistic estimates of uncertainty. This is the fundamental limitation of the t-interval method for uncertainty estimation. Part II will propose a redefinition of uncertainty and a modification of the conventional approach to estimating measurement uncertainty.

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“…Apparently, a sample-based uncertainty estimator U, equation (3), is an approximate answer to this question. How good is the approximation or the performance of the estimator U can be evaluated in terms of false acceptance/rejection probability, mean absolute percentage error (MAPE), mean squared percentage error (MSPE), relative bias error (RBE), and relative precision error (RPE), as discussed in Huang (2015).…”

Section: Misuse Of the T-interval In Uncertainty Estimationmentioning

confidence: 99%

“…For example, Bernardo (2006) presented an intrinsic estimator of σ based on an objective Bayesian decision-theoretic solution to minimizing the expected value of the intrinsic loss function. This intrinsic estimator turns out to be an approximate median-unbiased estimator developed by Huang (2015) based on the frequentist acceptance probability approach with the risk balance criterion. However, the confidence interval approach should not be used because it does not yield an inference about the true value of the population parameters (e.g.…”

Section: Case Ii: σ Is Unknownmentioning

confidence: 99%

Uncertainty estimation with a small number of measurements, part II: a redefinition of uncertainty and an estimator method

Huang¹

2017

Meas. Sci. Technol.

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This paper is the second (Part II) in a series of two papers (Part I and Part II). Part I has quantitatively discussed the fundamental limitations of the t-interval method for uncertainty estimation with a small number of measurements. This paper (Part II) reveals that the t-interval is an ‘exact’ answer to a wrong question; it is actually misused in uncertainty estimation. This paper proposes a redefinition of uncertainty, based on the classical theory of errors and the theory of point estimation, and a modification of the conventional approach to estimating measurement uncertainty. It also presents an asymptotic procedure for estimating the z-interval. The proposed modification is to replace the t-based uncertainty with an uncertainty estimator (mean- or median-unbiased). The uncertainty estimator method is an approximate answer to the right question to uncertainty estimation. The modified approach provides realistic estimates of uncertainty, regardless of whether the population standard deviation is known or unknown, or if the sample size is small or large. As an application example of the modified approach, this paper presents a resolution to the Du–Yang paradox (i.e. Paradox 2), one of the three paradoxes caused by the misuse of the t-interval in uncertainty estimation.

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Optimal estimator for uncertainty-based measurement quality control

Cited by 8 publications

References 11 publications

Is the assessment of interlaboratory comparison results for a small number of tests and limited number of participants reliable and rational?

Is the assessment of interlaboratory comparison results for a small number of tests and limited number of participants reliable and rational?

Uncertainty estimation with a small number of measurements, part I: new insights on thet-interval method and its limitations

Uncertainty estimation with a small number of measurements, part II: a redefinition of uncertainty and an estimator method

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