Statistically sound comparison of standardized and simulation methods for oil spill source identification in real spill scenarios.

The comparison of oil patterns of a spill (Sp) and suspected spill source (SS) samples is based on ratios between correlated GC-MS signals of oil-discriminating compounds, i.e., diagnostic ratios (DR). The Student's t statistics (S-t) and a maximum relative difference (SC), proposed in standard methods, have been used for DR comparison due to their simplicity. An alternative methodology based on Monte Carlo Method (MCM) simulations of correlated signals, capable of accurately defining DR comparison criteria, proved that S-t and SC assumptions regarding DR normality and precision are frequently not valid, affecting comparison reliability. The performance of the approaches was accurately compared from independent signals of the same oil sample from a perfect match between Sp and SS. The present study describes the comparison of the approaches in real oil spill scenarios reproduced in International Round Robin Tests. Since as the number of compared DR increases, also rises the probability of not all equivalent DR being actually considered equivalent, the decision of oil pattern equivalence was based on two comparisons of independent sets of Sp and SS signals. The risk of true oil standard equivalency claims is compared for the three oil spill scenarios studied, which are different considering oil types, DR sets and spill weathering. The ability of the approaches to distinguish the Sp sample from an oil sample known not to be the source of the spill was also assessed. The MCM based on two independent DR comparison trials was the only one consistently producing fingerprint comparison risks of correct equivalence claims larger than 98 %. MCM also performed better in distinguishing different oil patterns. It was concluded that comparing >22 DR does not change the risk of correct oil pattern equivalence assessment significantly. The complexity of the MCM approach is overcome by using user-friendly and validated software.

Determination of microplastic contamination levels and trends in vast oceanic sediment areas with uncertainty.

Small plastic particles, designated as microplastics, are known vehicles of several contaminants desorbed from their surface after being ingested by marine organisms. The monitoring of the levels and trends of microplastics in oceanic areas is essential to identify relevant threats and respective sources whose management should be improved to protect the environmental resources. However, the assessment of contamination trends in large oceanic areas is affected by contamination heterogeneity, sampling representativeness, and the uncertainty of collected sample analyses. Only contamination variations not justifiable by system heterogeneity and their characterisation uncertainty are meaningful and should be taken seriously by the authorities. This work describes a novel methodology for the objective identification of meaningful variation of microplastic contamination in vast oceanic areas by the Monte Carlo simulation of all uncertainty components. This tool was successfully applied to the monitoring of the levels and trends of microplastic contamination in sediments from a 700 km2 oceanic area from 3 km to 20 km offshore Sesimbra and Sines (Portugal). This work allowed concluding that contamination has not varied between 2018 and 2019 (difference of mean total microplastic contamination between -40 kg-1 and 34 kg-1) but that microparticles made of PET are the major type of studied microplastics (in 2019, mean contamination is between 36 kg-1 and 85 kg-1). All assessments were performed for a 99 % confidence level.

Metrologically sound comparison of trace-metal levels in sea cucumber tissues from different species and habitats.

Sea cucumbers are indicators of metal contamination in sea bottoms due to their low mobility and feeding behaviour. Comparing contaminations of specimens from different locations, habitats, and/or organs allows understanding of contamination processes and differences. However, the interpretation of these data is affected by the variability of contamination levels in specimens, the uncertainty of tissue analyses, and the complex correlation of mass fractions estimated by using the same calibration of the used instrumental method of analysis. This work presents a novel tool for the sound comparison of contamination levels of biota where all mentioned factors are considered to produce reliable and undisputable information on the studied system. The Monte Carlo simulation of uncertainty components, affecting the determination of mean contamination levels observed in selected types of tissues, allowed simulating mean contamination differences and determining if these are meaningful. This tool was used to assess the levels of Cd, Cu, Ni and Pb of animals collected in different locations of Sesimbra-Portugal. It was concluded that specimens that selectively consume macroalgae have larger contamination levels than animals feeding on sediment. The gut is the most contaminated organ suggesting intake from feeding is dominant. Three of the analysed animals have Pb mass fractions larger than a maximum admissible value for human consumption of 3 mg kg-1 with a probability larger than 2.5%.

Bottom-up uncertainty evaluation of complex measurements from correlated performance data: Determination of total Cr in yeast by ICP-MS after acid digestion.

The objective interpretation of a measurement result requires knowing the associated uncertainty. The cost-effective collection of measurement performance data on the same day produces correlated values that can affect measurement uncertainty evaluation. This work describes a novel methodology for the bottom-up evaluation of measurements based on complex sample pretreatment and the instrumental quantification of the prepared sample applicable to correlated inputs. The numerical Kragten method is used to combine the uncertainty components shared in various analyte recovery determinations. The developed methodology was applied to the determination of total chromium in yeast samples by ICP-MS after microwave-assisted acid digestion. The developed analysis of yeast samples is fit for monitoring the contamination of this product since it is associated with a relative expanded uncertainty, U', lower than 20%, ranging from 8.4% to 10.0% in determinations of Cr between 0.125 mg/kg and 305.5 mg/kg. Duplicate analyses are adequate for reference materials production (U' < 7%).

Evaluation of temporal trends and correlations of physical-chemical parameters in vast oceanic areas robust to information uncertainty.

The physical-chemical monitoring of vast oceanic areas aims at assessing the status and evolution of the environmental resource for its exploration, protection and/or better understanding. However, the interpretation of monitoring data is affected by ocean seasonality and heterogeneity, and by the quality of sampling and characterization tools used to study the environment. All these factors contribute to the uncertainty of collected information that should be expressed in determined parameter values or trends. A trend of a studied parameter quantified by values difference is significant if the observed absolute value of the difference is larger than their expanded uncertainty. The correlation of studied parameters, useful for their interpretation, is equality affected by the mentioned sources of uncertainty. This work describes the metrologically sound evaluation of trends and correlations of physicochemical parameters of vast oceanic areas where all uncertainty sources affecting the information are considered by simulating their complex impact by the Monte Carlo Method. The described methodology was successfully used to study the impact of summer upwelling in an 800 km2 coastal area offshore two large cities in Portugal. Nutrients, conductivity, salinity and temperature trends and correlations are distinguished from system heterogeneity, sampling and sample analysis uncertainty for a 99% confidence level.

Optimisation of the uncertainty of oil spill identification from replicate comparative analyses: Comparison of standardised and novel identification methods.

Oil spill identifications involve the comparison of oil fingerprints between the oil spill and suspected oil sources, defined by ratios between the abundances of oil-discriminating compounds, Diagnostic Ratios (DR). The normalised Nordtest and EN 15522-2 methodologies use Student's t statistic (S-t) or a maximum relative difference (SC) to compare mean DR from replicate sample analysis. While the S-t method assumes the normality of DR distribution, the SC method is based on controlled DR dispersion. However, when false, the assumptions and approximations adopted can lead to low true identification rates. This work presents a novel computational tool for the statistically sound oil spill identification that allows following requirements defined by EN 15522-2, the comparison of replicate DR determinations, and the use of different DR sets and formats. The tool uses the Monte Carlo Method (MCM) to describe the probability distribution of the difference of mean DR, allowing estimating the probability of the true acceptance of fingerprints equivalence. The studied methods were applied to the comparison of signals from the same oil and to a real scenario reproduced in an International Round Robin Test. The methods were compared considering the probabilities of true acceptance of oil patterns equivalence based on a single, γ, or various, δ, DR. The MCM method performs identifications with γ equivalent to the defined confidence level for the comparison, P. Since the various DR studied are not perfectly correlated, the δ is below P. The number of replicate analyses performed and the DR considered in the comparison affect identification performance. The S-t produces comparison criteria with a γ lower than P. The SC criteria for duplicate analysis is associated with a δ lower than the obtained by the MCM. A user-friendly MS-Excel spreadsheet is available to perform oil pattern comparisons using various methods and conditions.

Bottom-Up Evaluation of the Uncertainty of the Quantification of Microplastics Contamination in Sediment Samples.

The quantification and comparison of microplastic contamination of sediments are affected by sample heterogeneity and the systematic and random effects affecting sample analysis. The quantification and combination of these components in the measurement uncertainty allows the objective interpretation of analysis results. This work presents the first detailed evaluation of the uncertainty of microplastic contamination quantification in sediments. The random and systematic effects affecting microplastic counts are modeled by the Poisson-lognormal distribution with inputs estimated from duplicate sediment analysis and the analysis of sediments spiked with microparticles. The uncertainty from particle counting was combined with the uncertainty from the determination of the dry mass of the analytical portion by the Monte Carlo method. The developed methodology was implemented in a user-friendly spreadsheet made available as the Supporting Information. The contamination of sediment samples collected in various inland Portuguese waters was determined, ranging from [0; 160] to [361; 2932] kg-1 for a 99% confidence level, and compared by assessing if the difference between contamination levels is equivalent to zero for the same confidence level. Several samples proved to have metrologically different microplastic contamination. This work represents a contribution to the objectivity of the assessment of environmental contamination with microplastics.

Microplastics contamination in sediments from Portuguese inland waters: Physical-chemical characterisation and distribution.

Plastics are the major constituent of waste accumulated in inland waters and subsequently transferred to the ocean. The smaller plastic particles, typically obtained from the fragmentation of larger pieces, are vehicles for food chain accumulation of plastic components and contaminants sorbed to these particles through their ingestion by small organisms. The monitoring of the level and trends of the contamination by microplastics is essential to determine the relevance and potential sources of this contamination necessary to define strategies to reduce this threat. This work presents microplastic contamination levels and trends of sediments of four Portuguese inland waters, namely Ria de Aveiro, Ria Formosa, Mira river, and Mondego river, between 02/2019 and 09/2020. The contamination is classified considering the type of polymer and size, shape, and colour of particles. Polymers are identified by micro-ATR-FTIR with true and false identification rates larger and lower than 95% and 5%, respectively. Duplicate analysis results are used to quantify contamination heterogeneity subsequently applied to assess if a specific contamination trend is not meaningful for a 99% confidence level. The analytical procedure is described in detail to clarify the scope of the analysis. Tests' quality is controlled by following strict quality control measures. Results from sixty-three sediment samples proved the ubiquitous presence of microplastic (MP) in these inland waters with contamination levels ranging between 20 MP kg-1 and 1090 MP kg-1, excluding six samples not contaminated with these particles. Overall, more than 86% of the microplastics were fragments lower than 1000 µm, and 33% were identified as polyethylene or polypropylene. A large diversity of microplastic colours was observed. For the Mondego River and Ria de Aveiro locations monitored for consecutive years, no significant variations of microplastic contamination were observed for a 99% confidence level.

Development and validation of statistically sound criteria for the match of unweathered GC-MS fingerprints in oil spill forensics.

The investigation of an oil spill's origin frequently relies on determining the equivalence of oil component patterns in samples from the contaminated environment and suspected oil source. This comparison benefits if based on the ratio of the abundance of unweathered characteristic components of the oil product, Diagnostic Ratios, DR. Replicate determinations of DR from one sample are used to set limits for the second sample's DR. The composition equivalence of oil patterns in both samples is indicated if all compared DR are statistically equivalent with a high confidence level. Some studies define DR limits assuming their normality and using Student's t statistics (S-t). However, since the ratio of correlated abundances can be not normally distributed, this criterion can drive to more false comparisons than predicted by the test confidence level. This work developed a computational tool for the reliable description of the non-normal distribution of the DR based on the Monte Carlo Method (MCM), aiming to allow the accurate control of the confidence of DR comparison. This work concluded that S-t defines 95% or 98% confidence limits with probabilities of falsely rejecting samples equivalence, φ, that can be up to 4.3% higher than predicted by the confidence level of the S-t test (i.e., 5% and 2%). The fragilities of the S-t limits significantly reduce the probability (1-θ) of two samples with the same oil producing equivalent values of all compared DR. For the studied 69 DR from unweathered components, the (1-θ) for 98% confidence level limits, set by the MCM and S-t from triplicate injections of one sample, are 94.8% and 91.7%, respectively. These values are below the confidence level (P) defined for each DR because DR are correlated with a correlation coefficient lower than 1. The (1-θ) can be increased to above P by using MCM limits and accepting composition equivalence if at least one of two sample extract injections produces values within limits set from the other sample's replicate injection. The validated user-friendly MS-Excel file used to set and access comparison criteria is made available as Supplementary Material and was checked experimentally. However, it is not feasible to estimate model confidence exclusively from experimentation because it would require too much independent analysis.

Validated spreadsheet for the identification of PE, PET, PP and PS microplastics by micro-ATR-FTIR spectra with known uncertainty.

The monitoring of microplastics in the environment is crucial to determine the relevance and trends of this contamination necessary to plan environmental protection policies. Monitoring data reliability is essential for this purpose. This work describes a methodology for the reliable identification of the most abundant polymer types in aquatic sediments (polyethylene, PE, polypropylene, PP, polyethylene terephthalate, PET, and polystyrene, PS) by micro-ATR-FTIR. Identifications with true and false result rates greater than 95% and lower than 5% are performed, respectively. The analysis is based on defining spectra requirements regarding characteristic and interfering bands intensity and selecting optimal assessed wavenumber range, signal processing, and algorithm to quantify the match/agreement between particle and reference spectra. It is also defined the minimum match value, P5¼P, for reliable identifications. Examinations are performed in two stages where in the first stage PE and PP, PE&PP, are distinguished from other microplastics by taking the [4000-500] cm-1 spectra and various Match Methods and P5¼P depending on the polymer type. PE and PP are distinguished by quantifying weighted or unweighted Pearson correlation coefficients against a reference spectrum in the [3000-2800] cm-1 range. The defined P5¼P are above the 0.6 value considered in many references that do not quantify identification uncertainty. The MS-Excel files used in method development and validation are made available as Supplementary Material being applicable to other spectral techniques and analytical fields.

Monte Carlo bottom-up evaluation of the uncertainty of complex sample preparation: Elemental determination in sediments.

Many chemical analyses involve a complex sample preparation, and some, based on an instrumental method of analysis such as spectrometric or chromatographic methods, are affected by matrix effects. The objective interpretation of the results of these analyses performed in the framework of a research or a conformity assessment requires quantifying the measurement uncertainty. This work presents a novel methodology for the bottom-up modelling of the performance of complex analytical operations, such as sample digestion or extraction, by the Monte Carlo simulation of their performance independently of the performance of the other analytical steps. The simulation of between-days precision of complex sample preparation and mean measurement error observed from the analysis of various reference materials and their combination with models of instrumental quantification performance allow the detailed modelling of the measurement uncertainty. The developed methodology adapts to the complex distribution of observed measurement performance data avoiding the under evaluation of the measurement uncertainty by assuming the normal distribution of systematic and random effects. The developed methodology was successfully applied to the determination of total or acid-extractable As (following OSPAR or EPA 3051A methods, respectively) in sediments where measurement trueness was assessed from the analysis of one Certified Reference Material and two spiked samples. The evaluated uncertainty is fit for environmental monitoring considering performance criteria defined for Quasimeme proficiency tests. The developed measurement models were successfully cross-validated by randomly extracting data from the validation set subsequently used to check the compatibility between estimated and reference values for 95% or 99% confidence level. The observed success rate of these assessments is compatible with the confidence level of the tests.

Tutorial and spreadsheet for the evaluation of instrumental quantification uncertainty by the linear weighted regression model: Determination of elemental impurities in a nasal spray by ICP-MS.

A tutorial and spreadsheet for the validation and bottom-up uncertainty evaluation of quantifications performed by instrumental methods of analysis based on linear weighted calibrations is presented. The developed tool automatically assesses if calibrator values uncertainty is negligible given instrumental signal precision, assesses signal homoscedasticity by the Levene's test, guides the selection of weighting factors and evaluates the fitness of the regression model to define the calibration curve. The spreadsheet allows the use of the linear weighted regression model without the need for collecting many replicate signals of calibrators and sample by taking previously developed detailed models of signal precision variation in the calibration interval after adjustments to the daily precision conditions. This tool was successfully applied to the determination of the mass concentration of Cd, Pb, As, Hg, Co, V and Ni in a nasal spray by ICP-MS after samples dilution and acidification. The developed uncertainty models were checked through the analysis of nasal sprays after spiking with known analyte concentration levels. The metrological compatibility between estimated and reference analyte levels for 95% or 99% confidence level supports uncertainty model adequacy. The spiked samples were quantified from many replicate signals but uncertainty evaluation from duplicate calibrator and sample signals was assessed by randomly selecting calibrators and sample signals and by numerically defining a minimum acceptable success rate of the compatibility tests. The developed model was proven adequate to quantify the uncertainty of the studied measurements.

Evaluation of seawater composition in a vast area from the Monte Carlo simulation of georeferenced information in a Bayesian framework.

The detection of composition or pollution trends of vast environmental water areas, from a river, lake or sea, requires the determination of the mean concentration of the studied component in the studied area at defined depth in, at least, two occasions. Mean concentration estimates of a large area are robust to system heterogeneity and, if expressed with uncertainty, allow assessing if observed trends are meaningful or can be attributed to the measurement process. Mean concentration values and respective uncertainty are more accurately determined if various samples are collected from the studied area and if samples coordinates are considered. The spatial representation of concentration variation and the subsequent randomization of this model, given coordinates and samples analysis uncertainty, allows an improved characterization of studied area and the optimization of the sampling process. Recently, this evaluation methodology was described and implemented in a user-friendly MS-Excel file. This tool was upgraded to allow determinations close to zero concentration and "bottom-up" uncertainty evaluations of collected samples analysis. Since concentrations cannot be negative, this prior knowledge is merged with the original measurements in a Bayesian uncertainty evaluation that improves studied area description and sampling modelling. The Bayesian assessment avoids the underestimation of concentrations distribution by assuming that negative concentrations are impossible. This tool was successfully applied to the determination of reactive phosphate concentration in a vast ocean area of the Portuguese coast. The new version of the developed tool is made available as Supplementary Material.

Microplastics identification by infrared spectroscopy - Evaluation of identification criteria and uncertainty by the Bootstrap method.

The assessment of microplastic contamination in an environmental compartment involves identifying and counting microplastics in a representative fraction of the compartment. Microplastics can be identified by µFTIR spectroscopy where spectra are manually examined for characteristic polymer bands or by an automatic comparison of particle spectrum with reference spectra of polymers. The automatic spectra comparison can involve calculating a correlation coefficient, CC, between particle and reference spectra where a minimum correlation above which identification is adequately reliable should be defined. Correlation can be calculated from original or transformed signals, such as taking the first derivative, and by using unweighted or weighted CC. Weighted CC can highlight the spectral features more relevant to distinguish polymers. This work describes a methodology for setting the minimum CC, P5¼P, associated with a true positive result rate, TP, of 95% and for checking if this threshold allows identifications with a false positive result rate, FP, not greater than 5%. This methodology was successfully applied to the use of various CC determined from original or transformed spectra for the identification of polyethylene, PE, and polypropylene, PP, microplastics in river sediments by µFTIR. The analytical portions of sediments were digested with H2O2 and microplastics separated from the remaining particles by density using a saturated NaCl solution. Pearson's, Spearman's and Alternative unweighted and weighted correlation coefficients were studied. The P5¼P was estimated by the Bootstrap method that resamples spectra CC between a reference material and microparticle of the same polymer collected from the environment. This resampling allows simulating CC distribution required to estimate its 5th percentile (i.e. P5¼P). The FP was estimated from the probability of a particle not from the same polymer type of the reference material producing a CC greater than P5¼P. Some unweighted and weighted CC determined from original or transformed spectra were successfully used to identify PE or PP particles in river sediments. More particle spectra need to be collected to ensure performance is assessed from a representative diversity of aged polymers with different additives. The spreadsheets used for CC calculations and Bootstrap simulations are made available and can be used for the validation of the identification of other polymer types by µFTIR or ATR-FTIR spectroscopy.

Measurement uncertainty evaluation from correlated validation data: Determination of elemental impurities in pharmaceutical products by ICP-MS.

Pharmaceutical products as well as active pharmaceutical ingredients (APIs) are checked for levels of elemental contaminants to guarantee medicines administration will not involve the consumption of level of contaminants greater than their maximum admissible intake. However, the conformity decision is affected by the measurement uncertainty function of analytical steps performance, used standards quality and how measurement performance is assessed during method validation. When an ingredient is considered conform, since the measured concentration is lower than the maximum limit, the risk of a false acceptance depends on how close the measured concentration is from the limit and on the measurement uncertainty. The analytical methods used for pharmaceutical analysis should be validated by ICH and USP recommendations, in order to prove measurements are fit for purpose. The validation must also be economically feasible and have an acceptable duration. This work discusses how to evaluate the uncertainty of elemental analysis in pharmaceutical ingredients from data collected during the validation of the analytical method by following ICH guidelines and USP chapters. A top-down uncertainty evaluation based on results from the analysis of a model API intermediate, with the native analyte after spiking at three concentration levels, where analyses are performed by two analysts in two different days, is presented. The impact of the correlation of some uncertainty components of collected results on the uncertainty evaluation is discussed and considered in the calculations. The developed measurement model was checked by a cross-validation procedure where some validation data was randomly removed and used for an independent model control. The developed uncertainty evaluation methodology was successfully applied to the analysis of Pd in a model API intermediate by ICP-MS after a micro-wave assisted acid digestion, where the risk of a false acceptance of the pharmaceuticals is determined. The measurement performance data and used spreadsheet are made available as Supplementary Material.

Determination of river water composition trends with uncertainty: Seasonal variation of nutrients concentration in Tagus river estuary in the dry 2017 year.

The assessment of long-term trends in river water composition is hampered by river composition heterogeneity, and sampling and sample analysis uncertainty. This work describes a novel methodology for the reliable detection of small river composition trends by taking all relevant uncertainty components into account. The methodology was applied to study the variation of nutrients concentration of Tagus river estuary in the extremely dry 2017 year. Mean nutrient concentrations were determined with an uncertainty that combines sampling and sample analysis uncertainty by the Monte Carlo Method. The nutrient concentration variation observed in two occasions is meaningful if the difference of mean concentrations is metrologically different from zero for a 95% confidence level. The observed meaningful NO2 increase, and SiO2 and NOx variations is justified by dissolved oxygen reduction, decreased freshwater input and algal productivity variations. The developed tool can be applied to the assessment of other composition trends in rivers.

Monte Carlo bottom-up evaluation of global instrumental quantification uncertainty: Flexible and user-friendly computational tool.

Many instrumental methods of analysis require the daily collection of calibrator signals to calibrate their response. The quality of quantifications based on these calibrations depends on calibrators quality, instrumental signal performance and regression model fitness. Linear Ordinary Least Squares (LOLS), Linear Weighted Least Squares (LWLS) or Linear Bivariate Least Squares (LBLS) regression models can be used to calibrate and evaluate the uncertainty from instrumental quantifications, but require the fulfilment of some assumptions, namely, constant signal variance (LOLS), high calibrators quality (LOLS and LWLS) and linear variation of instrumental signal with calibrator values. The LBLS is flexible regarding calibrator values uncertainty and correlation but requires the determination of calibrator values and signals covariances. This work developed a computational tool for the bottom-up evaluation of global instrumental quantifications uncertainty which simulates calibrator values correlations from entered calibrators preparation procedure and simulates calibrators and samples signals precision from prior precision data, allowing accurate uncertainty evaluation from a few replicate signals of the daily calibration. The used signal precision models were built from previously observed repeatability variation throughout the calibration interval adjusted to daily precision condition from a residual standard deviation adjustment factor. This approach was implemented in a user-friendly MS-Excel file and was successfully applied to the analysis of As, Cd, Ni and Pb in marine sediment extracts by Absorption Spectroscopy. Evaluations were tested by the metrological compatibility of estimated and reference values of control standards for confidence levels of 95% and 99%. The success rates of the compatibility tests were statistically equivalent to the confidence level (p-value>0.01).

Development and validation of an advanced electrochemical sensor for the fast and cheap determination of hydrochlorothiazide in urine samples using the Monte-Carlo method for uncertainty evaluation.

This work describes the development, optimization, and validation of an electrochemical method for the determination of hydrochlorothiazide (HCTZ) in urine. The method allows fast, cheap and reliable determinations of recent administrations of this diuretic that can be used in doping control in sport. The response of the sensor was determined by differential pulse voltammetry (DPV). The glassy carbon electrode was modified with multiwall carbon nanotubes (MWCNT) and gold nanoparticles. The sensor is calibrated in the analysed sample matrix by the cumulative standard addition method. The method validation was based on the bottom-up evaluation of the measurement uncertainty were components were combined using the Monte Carlo Method (MCM) applicable with no restrictions regarding components uncertainty value and measurement function linearity. The developed metrological models were implemented in MS-Excel spreadsheets. The adequacy of the electrochemical measurements was assessed by comparing their relative standard uncertainty with a target value of 20% and by evaluating the compatibility of measurements with determinations performed by a reference procedure. The tools developed for the construction and optimization of working electrodes are applicable to measurements of other analytes and matrices. The used cumulative standard addition method and respective measurement uncertainty models are applicable to any kind of non-destructive chemical measurement of a solution.

Standard addition method with cumulative additions: Monte Carlo uncertainty evaluation.

The cumulative standard addition method allows the calibration of an instrument affected by matrix effects when a small sample volume is available. Recently, it was developed and validated a metrologically sound procedure to estimate the uncertainty of these measurements based on the modelling of the uncertainty of the extrapolation of the calibration curve by the linear least squares regression model. However, this procedure is only applicable when the uncertainty of cumulative sample dilutions and analyte mass additions are negligible given the uncertainty of the total solution volume (v) times the instrumental signal (I) (i.e. v∙I). This work developed a measurement uncertainty model, not limited by this assumption of the quality of calibrators preparation, based on Monte Carlo simulations. This method was successfully applied to the voltammetric measurements of uric acid in human serum, using a working nanocarbon electrode modified with Cu-nanocarbon-lignin, since the uncertainty model adapts to the uncertainty of cumulative volume additions. The validated procedure was checked through the analysis of spiked physiological serum samples and human serum samples, by assessing the metrological compatibility between estimated and reference values. The measurements are reported with an expanded uncertainty not larger than a target value of 0.56 mg dL-1. The used spreadsheet is made available as supplementary material.

Risk of false conformity decisions of multicomponent items controlled by correlated measurement results due to the sharing of analytical steps.

The assessment of the conformity of some items, such as medicines, food products or drinking waters, with limits set for several of their components, involves the determination of these components using multi-analyte measurement procedures. Since these determinations involve the sharing of relevant analytical steps, such as the sample preparation and analytical instrument run, the measurement results of the various components become correlated (i.e. 'between components metrologically correlated'). The closeness of the values of the components to the respective tolerance limits, the measurements uncertainty and the correlation of the measurements results affects the risk of false conformity decisions of the analysed item. This correlation can either increase or decrease the risk of false conformity decision and is relevant to decide if the item should be considered conform or not conform with the regulation. This work presents a methodology to estimate the 'between components metrological correlation' of results of the analysis of an item subsequently used to assess the impact of this correlation on the risk of false conformity decisions. The methodology was successfully applied to the assessment of the conformity of pharmaceutical tablets against tolerance limits for lamivudine (3TC) and zidovudine (AZT) determined from the analysis of the same analytical portion in the same HPLC-UV/Vis run. The correlation of measurement results was determined from Monte Carlo simulations of shared analytical operation (linear correlation coefficient of 0.53) being their impact on conformity decisions relevant. For instance, for measurement results of 3TC and AZT equal to the upper limit and lower limit, respectively, the risk of a wrong acceptance of the medicines is 84% while if it is assumed that measurement results are independent this risk would be wrongly considered as 75%. The Excel® spreadsheet used for this assessment is made available as supplementary material.