Tutorial and spreadsheets for Bayesian evaluation of risks of false decisions on conformity of a multicomponent material or object due to measurement uncertainty

Silva, Ricardo J.N.B. da; Pennecchi, Francesca; Hibbert, David Brynn; Kuselman, Ilya

doi:10.1016/j.chemolab.2018.09.004

Cited by 22 publications

(12 citation statements)

References 7 publications

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“…( 34) and descending risk values were performed in the R programming environment described in Annex A, Examples 3 and 4. Simulation of the posterior distribution is also possible by Markov Chain Monte Carlo (MCMC) method, using the Metropolis-Hastings algorithm with MS Excel [54]. The analytical solution (34) for parameters of the posterior pdf and corresponding specific risk values is more accurate by definition than the MCMC solution, even when obtained by a large number of trials.…”

Section: Computational Detailsmentioning

confidence: 99%

IUPAC/CITAC Guide: Evaluation of risks of false decisions in conformity assessment of a multicomponent material or object due to measurement uncertainty (IUPAC Technical Report)

2021

Chemistry International

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Risks of a false decision on conformity of the chemical composition of a multicomponent material or object due to measurement uncertainty are defined using the Bayesian approach. Even if the conformity assessment for each particular component of a material is successful, the total probability of a false decision (total consumer's risk or producer's risk) concerning the material as a whole might still be significant. This is related to the specific batch, lot, sample, environmental compartment, or other item of material or object (specific consumer's and producer's risks), or to a population of these items (global consumer's and producer's risks). A model of the total probability of such false decisions for cases of independent actual ('true') concentrations or contents of the components and the corresponding measurement results is formulated based on the law of total probability. It is shown that the total risk can be evaluated as a combination of the particular risks in the conformity assessment of components of the item. For a more complicated task, i.e. for a larger number of components under control, the total risk is greater. When the actual values of the components' concentrations or contents, as well as the measurement results, are correlated, they are modelled by multivariate distributions. Then, a total global risk of a false decision on the material conformity is evaluated by the calculation of integrals of corresponding joint probability density function. A total specific risk can be evaluated as the joint posterior cumulative function of actual property values of a specific item lying outside the multivariate specification (tolerance) domain when the vector of measured values obtained for the item is inside this domain. The effect of correlation on the risk is not easily predictable. Examples of the evaluation of risks are provided for conformity assessment of denatured alcohols, total suspended particulate matter in ambient air, a cold/flu medication, and a PtRh alloy.

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Section: Computational Detailsmentioning

confidence: 99%

IUPAC/CITAC Guide: Evaluation of risks of false decisions in conformity assessment of a multicomponent material or object due to measurement uncertainty (IUPAC Technical Report)

2021

Chemistry International

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“…A multivariate Bayesian model was recently elaborated for evaluation of risks of false decisions in conformity assessment of multicomponent materials or objects, also taking into account possible correlations between measured concentrations or contents of an item's components [13,14,[44][45][46][47]. This "conventional" approach applies integration of the relevant posterior multivariate probability density function on the tolerance/specification multi-domain of the material (or object) compositions in order to obtain total specific risks, or integration of the joint probability density function of true and measured values to give total global risks.…”

Section: Fig 2 22mentioning

confidence: 99%

Correlation of test results and influence of a mass balance constraint on risks in conformity assessment of a substance or material

et al. 2020

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When components of a substance or material are subject to a mass balance constraint, test results of the components' contents are intrinsically correlated because of the constraint. That is in addition to possible metrologically-related correlation of test results, and natural and/or technological correlation of the components' contents. Such correlations may influence understanding of compositional data and evaluation of risks in conformity assessment of the substance or material due to measurement uncertainty. A Bayesian multivariate approach to evaluate the conformance probability of multicomponent materials or objects and corresponding risks of false decisions, able to take into account all observed correlations including spurious, is discussed for different scenarios of compositional data. A Monte Carlo method, which includes the mass balance constraint, written in the R programming environment is provided for the necessary calculations. A technique for separation of spurious correlations from experimental (natural and/or technological) correlations is proposed.

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“…(34) and descending risk values were performed in the R programming environment described in Annex A, Examples 3 and 4. Simulation of the posterior distribution is also possible by Markov Chain Monte Carlo (MCMC) method, using the Metropolis-Hastings algorithm with MS Excel [54]. The analytical solution (34) for parameters of the posterior pdf and corresponding specific risk values is more accurate by definition than the MCMC solution, even when obtained by a large number of trials.…”

Section: Computational Detailsmentioning

confidence: 99%

“…The core of the R codes [57], developed for calculations of the risks for uncorrelated and correlated data, are published in papers [41] and [43], respectively. User-friendly MS Excel spreadsheet programs for the same purposes are described in papers [54,55]. Both the R codes and Excel spreadsheet programs can be sent by the corresponding author upon request.…”

Section: Computational Detailsmentioning

confidence: 99%

IUPAC/CITAC Guide: Evaluation of risks of false decisions in conformity assessment of a multicomponent material or object due to measurement uncertainty (IUPAC Technical Report)

Kuselman

Pennecchi

Silva

et al. 2020

Pure and Applied Chemistry

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Risks of a false decision on conformity of the chemical composition of a multicomponent material or object due to measurement uncertainty are defined using the Bayesian approach. Even if the conformity assessment for each particular component of a material is successful, the total probability of a false decision (total consumer’s risk or producer’s risk) concerning the material as a whole might still be significant. This is related to the specific batch, lot, sample, environmental compartment, or other item of material or object (specific consumer’s and producer’s risks), or to a population of these items (global consumer’s and producer’s risks). A model of the total probability of such false decisions for cases of independent actual (‘true’) concentrations or contents of the components and the corresponding measurement results is formulated based on the law of total probability. It is shown that the total risk can be evaluated as a combination of the particular risks in the conformity assessment of components of the item. For a more complicated task, i.e. for a larger number of components under control, the total risk is greater. When the actual values of the components’ concentrations or contents, as well as the measurement results, are correlated, they are modelled by multivariate distributions. Then, a total global risk of a false decision on the material conformity is evaluated by the calculation of integrals of corresponding joint probability density function. A total specific risk can be evaluated as the joint posterior cumulative function of actual property values of a specific item lying outside the multivariate specification (tolerance) domain when the vector of measured values obtained for the item is inside this domain. The effect of correlation on the risk is not easily predictable. Examples of the evaluation of risks are provided for conformity assessment of denatured alcohols, total suspended particulate matter in ambient air, a cold/flu medication, and a PtRh alloy.

show abstract

Tutorial and spreadsheets for Bayesian evaluation of risks of false decisions on conformity of a multicomponent material or object due to measurement uncertainty

Cited by 22 publications

References 7 publications

IUPAC/CITAC Guide: Evaluation of risks of false decisions in conformity assessment of a multicomponent material or object due to measurement uncertainty (IUPAC Technical Report)

IUPAC/CITAC Guide: Evaluation of risks of false decisions in conformity assessment of a multicomponent material or object due to measurement uncertainty (IUPAC Technical Report)

Correlation of test results and influence of a mass balance constraint on risks in conformity assessment of a substance or material

IUPAC/CITAC Guide: Evaluation of risks of false decisions in conformity assessment of a multicomponent material or object due to measurement uncertainty (IUPAC Technical Report)

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