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 °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.

Total risk of a false decision on conformity of an alloy due to measurement uncertainty and correlation of test results.

Total risk (probability) of a false decision on conformity of an alloy due to measurement uncertainty and correlation of test results is quantified. As an example, a dataset of test results of a PtRh alloy is studied when contents of four components of the alloy composition are under control. There are specification limits for contents of 1) Pt and 2) Rh; 3) three precious impurities - Au, Ir and Pd, and 4) eight impurities, both precious Au, Ir, Pd, and non-precious Fe, Pb, Si, Sn, Zn. Test results of 100 batches of the alloy produced at the same plant, obtained by X-ray fluorescence and optical atomic emission spectrometry methods at the plant laboratory, were in the dataset. The Pt content was tested based on the mass balance. Measurement uncertainties of the test results are estimated summarizing data of validation reports of the measurement procedures for different elements/analytes. These test results are correlated because of the natural chemical origin of the raw materials used in the alloy production and mass balance constraints. Correlations between test results for two pairs of the components (Pt vs. Rh, and the three vs. the eight impurities) were strong. To assess the correlation effects on the total risk, the study was performed for two scenarios considering 1) correlated test results for all four components, and 2) practically uncorrelated test results for two components only - Rh and the eight impurities. A multiparameter Bayesian approach was applied for total risk evaluation, where the observed correlations are taken into account within the experimental correlation matrix. This matrix influenced all subsequent multivariate calculation results. It was shown that simplification of the testing by reducing the number of components under control leads to a significant increase of the probability of a false decision on conformity of an alloy batch randomly drawn from a statistical population of such batches. Core of the developed R code, used for the risk calculations, is presented.

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.

Risk of false decision on conformity of a multicomponent material when test results of the components' content are correlated.

The probability of a false decision on conformity of a multicomponent material due to measurement uncertainty is discussed when test results are correlated. Specification limits of the components' content of such a material generate a multivariate specification interval/domain. When true values of components' content and corresponding test results are modelled by multivariate distributions (e.g. by multivariate normal distributions), a total global risk of a false decision on the material conformity can be evaluated based on calculation of integrals of their joint probability density function. No transformation of the raw data is required for that. A total specific risk can be evaluated as the joint posterior cumulative function of true values of a specific batch or lot lying outside the multivariate specification domain, when the vector of test results, obtained for the lot, is inside this domain. It was shown, using a case study of four components under control in a drug, that the correlation influence on the risk value is not easily predictable. To assess this influence, the evaluated total risk values were compared with those calculated for independent test results and also with those assuming much stronger correlation than that observed. While the observed statistically significant correlation did not lead to a visible difference in the total risk values in comparison to the independent test results, the stronger correlation among the variables caused either the total risk decreasing or its increasing, depending on the actual values of the test results.