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

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. This so-called ‘spurious’ correlation is observed 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 test results and evaluation of risks of false decisions, due to measurement uncertainty, in conformity assessment of the substance or material. The objective of the present paper is the development of a technique for appropriate evaluation of the risks. A Bayesian multivariate approach to evaluate the conformance probability of materials or objects and relevant risks is discussed for different scenarios of the data modelling, taking into account all observed correlations. A Monte Carlo method, including the mass balance constraint, written in the R programming environment, is provided for the necessary calculations

Interlaboratory comparison of the intensity of drinking water odor and taste by two-way ordinal analysis of variation without replication

A case study of ordinal data from human organoleptic examination (sensory analysis) of drinking water obtained in an interlaboratory comparison of 49 ecological laboratories is described. The recently developed two-way ordinal analysis of variation (ORDANOVA) is applied for the first time for the treatment of responses on the intensity of chlorine and sulfurous odor of water at 20 and 60 degrees C, which is classified into the six categories from 'imperceptible' to 'very strong'. The one-way ORDANOVA is used for the analysis of the 'salty taste' intensity of the water. A decomposition of the total variation of the ordinal data and simulation of the multinomial distribution of the data-relative frequencies in different categories allowed the determination of the statistical significance of the difference between laboratories in classifying chlorine or sulfurous odor intensity by categories, while the effect of temperature was not significant. No statistical difference was found between laboratories on salty taste intensity. The capabilities of experts to identify different categories of the intensity of the odor and taste are also evaluated. A comparison of the results obtained with ORDANOVA and ANOVA showed that ORDANOVA is a more useful and reliable tool for understanding categorical data such as the intensity of drinking water odor and taste

Comparison of gravimetry and dynamic dilution for the generation of reference gas mixtures of CO2 at atmospheric amount fraction

Carbon dioxide (CO2) is the most important greenhouse gas generated by human activities. Its concentration has been growing in the atmosphere reaching a current annual average of 410 μmol mol−1. Reliable determinations of the atmospheric CO2 concentration are of great importance for the development of models used in climate change predictions. The production of reference mixtures of known composition is a key step for the achievement of reliable data for the monitoring of greenhouse gases in atmosphere.The present work deals with a comparison of two methods for gas mixtures preparation, the first based on the gravimetric preparation of gas mixtures in high pressure cylinders and the second based on dynamic dilution, for generating gas mixtures at the desired amount fraction online.Reference mixtures of CO2 can be used for the calibration of monitoring sensors, with various applications ranging from environmental monitoring to industrial process control

Risks of false decisions on conformity of a sausage with a mass balance constraint

A technique for evaluation of risks in a sausage conformity assessment is developed. Measurement uncertainty, correlation and mass balance constraint are considered. A multivariate Bayesian approach and a Monte Carlo method are applied. Risks in assessment of sausage "Braunschweigskaya" are evaluated as a case study. R code for the risk evaluation is provided as electronic supplementary material

Fit-for-purpose risks in conformity assessment of a substance or material – A case study of synthetic air

A technique is described for evaluation of the fit-for-purpose risks in conformity assessment of the chemical composition of a substance or material, based on a multivariate Bayesian approach. The approach takes into account measurement uncertainty, correlation and the mass balance constraint. Two datasets related to synthetic air (provided as electronic supplementary material to this paper) were studied. The first dataset was from an industrial factory producing routinely medicinal synthetic air according to the European Pharmacopoeia. The second dataset was from the National Metrology Institutes which participated in key comparison CCQM-K120 "Carbon dioxide at background and urban level". The fitness for purpose of the preparation of synthetic air was interpreted as total risks of false decisions on the conformity of the air composition to the tolerance limits of the contents of its main components. Calculations of these risks were performed with code written in the R programming environment

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

A tutorial and a user-friendly program for evaluating risks of false decisions in conformity assessment of a multicomponent material or object due to measurement uncertainty, based on a Bayesian approach, are presented. The developed program consists of two separate MS-Excel spreadsheets. It allows calculation of the consumer's and producer's risks concerning each component of the material whose concentration was tested (‘particular risks’) as well as concerning the material as a whole (‘total risks’). According to the Bayesian framework, probability density functions of the actual/‘true’ component concentrations (prior pdfs) and likelihood functions (likelihoods) of the corresponding test results are used to model the knowledge about the material or object. Both cases of independent and correlated variables (the actual concentrations and the test results) are treated in the present work. Spreadsheets provide an estimate of the joint posterior pdf for the actual component concentrations as the normalized product of the multivariate prior pdf and the likelihood, starting from normal or log-normal prior pdfs and normal likelihoods, using Markov chain Monte Carlo (MCMC) simulations by the Metropolis-Hastings algorithm. The principles of Bayesian inference and MCMC are described for users with basic knowledge in statistics, necessary for correct formulation of a task and interpretation of the calculation results. The spreadsheet program was validated by comparison of the obtained results with analytical results calculated in the R programming environment. The developed program allows estimation of risks greater than 0.003% with standard deviations of such estimates spreading from 0.001% to 1.5%, depending on the risk value. Such estimation characteristics are satisfactory, taking into account known variability in measurement uncertainty associated with the test results of multicomponent materials

Risk of a false decision on conformity of an environmental compartment due to measurement uncertainty of concentrations of two or more pollutants

Risks of false decisions in conformity assessment of an environmental compartment due to measurement uncertainty of concentrations of two or more pollutants are discussed. Even if the assessment of conformity for each pollutant in the compartment is successful, the total probability of a false decision concerning the compartment as a whole might still be significant. A model of the total probability of a false decision, formulated on the base of the law of total probability, is used, for example, for a study of test results of total suspended particulate matter (TSPM) concentration in ambient air near to three independent stone quarries located in Israel, as the sources of the air pollution. Total probabilities of underestimation of TSPM concentration (total risk of the inhabitants) and overestimation (total risk of the stone producers) are evaluated as a combination of the particular risks of air conformity assessment concerning TSPM concentration for each quarry. These probabilities characterize conformity of the TSPM concentration in the region of the quarries as a whole. Core code developed in R programming environment for the calculations is provided

How many shades of grey are in conformity assessment due to measurement uncertainty?

When a measured value of a property of a material or object differs from the upper or lower specification limit (actual or 'true' value) by the expanded measurement uncertainty or more, there is the clear decision on the material conformity or nonconformity - 'white' or 'black'. In the interval from the measured value to the specification limit, covered by the expanded measurement uncertainty ('grey zone'), risks of false decisions on conformity increase. Several kinds of the risks, named 'shades of grey', should be taken into account. For a multicomponent material there are four kinds of particular risks for each property value of the material (e.g. component concentration or content), and four kinds of total risks related to the material as a whole. Therefore, for n > 1 properties under control for the material conformity assessment one can distinguish 4(n +1) kinds of risks of false decisions - shades of grey