Adequacy in the metrology of chemical analysis and other complicated measurements

The adequacy of specimens to each other, and of reference material to routine specimens, is an important idea in the metrology of chemical analysis. However, the literature gives no strict definition for this notion. In this paper, a determination of adequacy based on the measure of adequacy is proposed. For the case of two specimens, the measure of adequacy is the absolute value of the difference between the systematic errors in the results from analysis of the specimens; it depends on the differences in the composition and properties of the specimens. The measure of adequacy of a certified reference material to a population of routine specimens is the maximum distance between the systematic error of the reference material and one of the quantiles of the systematic error distribution of the routine specimens Q(0.025); Q(0.975); the errors in this case are due to the composition and the properties of the routine specimens and other complicated measurements. When the measure of adequacy can be neglected compared to the permissible error of the analysis, the specimens are considered adequate. Using the determination of total cholesterol in the blood serum of human beings as an example, it was shown that the certified reference material used in the analysis of specimens of complex composition is often inadequate when compared to routine specimens.

Variable isotopic composition of lead as a source of systematic error in proton activation analysis

This paper considers the variable isotopic composition of lead as a possible source of systematic errors in proton activation analysis. The importance of this source of error was evaluated for environmental and geological samples. As proton activation analysis is frequently used for the certification of lead, the error was determined for three sediment reference materials. Inductively coupled plasma-mass spectrometry was used for the determination of the isotopic composition of lead. The systematic error amounted for the sediments to approximately 1%.     

The impact of uncertainty in the elemental composition of the certified reference material on gamma spectrometry

In this paper the impact of the uncertainty in the elemental composition of the certified reference material (CRM) used for absolute efficiency calculations in gamma spectrometry is investigated. The method involved the use of semi-empirical modeling using solid angle concepts. The samples involved were a standard Jamaican soil, four bauxite reference samples from NIST and a standard ICRU reference material configuration simulating the calibrating CRM. The results indicate that at gamma energies below 60 keV, the impact on the bauxite reference samples and local soil samples resulted in errors up to 43 and 70 % respectively when the elemental composition of the efficiency calibrating reference sample was ignored. A set of equations for correcting the errors introduced were developed. The modeling of a theoretical soil type validated the process of ashing soils for low energy gamma spectrometry due to the extremely high errors introduced by the element carbon.     

Automatic NAA: Saturation activities

A system for Automatic NAA is based on a list of specific saturation activities determined for one irradiation position at a given neutron flux and a single detector geometry. Originally compiled from measurements of standard reference materials, the list may be extended also by the calculation of saturation activities from k ₀ and Q ₀ factors, and f and a values of the irradiation position. A systematic improvement of the SRM approach is currently being performed by pseudo-cyclic activation analysis, to reduce counting errors. From these measurements, the list of saturation activities is recalculated in an automatic procedure.     

Reliability of measurements of pesticide residues in food

This paper accounts for the major sources of errors associated with pesticide residue analysis and illustrates their magnitude based on the currently available information. The sampling, sample processing and analysis may significantly influence the uncertainty and accuracy of analytical data. Their combined effects should be considered in deciding on the reliability of the results. In the case of plant material, the average random sampling (coefficient of variation, CV=28–40%) and sample processing (CV up to 100%) errors are significant components of the combined uncertainty of the results. The average relative uncertainty of the analytical phase alone is about 17–25% in the usual 0.01–10 mg/kg concentration range. The major contributor to this error can be the gas-liquid chromatography (GLC) or high-performance liquid chromatography (HPLC) analysis especially close to the lowest calibrated level. The expectable minimum of the combined relative standard uncertainty of the pesticide residue analytical results is in the range of 33–49% depending on the sample size.The gross and systematic errors may be much larger than the random error. Special attention is required to obtain representative random samples and to eliminate the loss of residues during sample preparation and processing.     

<Emphasis Type="Italic">Perna perna</Emphasis> mussel reference material: short term stability assessment

Instrumental neutron activation analysis was used at a 2-month long isochronous short term stability test performed on a Perna perna mussel candidate reference material. The assessment of the analysis of variance test, as well as, the normalized results to the control temperature showed no systematic changes in the concentration of Ag, As, Br, Co, Cr, Cs, Fe, Eu, La, Na, Rb, Se, Sc, Th and Zn during the test period. The result showed that the candidate reference material may be transported under normal transport conditions without significant changes in composition for the determined elements.     

Calibration lines passing through the origin with errors in both axes

Linear regression of calibration lines passing through the origin was investigated for three models of y-direction random errors: normally distributed errors with an invariable standard deviation (SD) and log normally and normally distributed errors with an invariable relative standard deviation (RSD). The weighted (weighting factor is x ² _i ), geometric and arithmetic means of the ratios y _i /x _i estimate the calibration slope for these models, respectively. Regression of the calibration lines with errors in both directions was also studied. The x-direction errors were assumed to be normally distributed random errors with either an invariable SD or invariable RSD, both combined with a constant relative systematic error. The random errors disperse the true, unknown x-values about the plotted, demanded x-values, which are shifted by the constant relative systematic error. The systematic error biases the slope estimate while the random errors do not. They only increase automatically the slope estimate uncertainty, in which the uncertainty component reflecting the range of the possible values of the systematic error must be additionally included. Received: 9 May 2000 Accepted: 7 March 2001     

Long-term stability study on a Perna perna mussel candidate reference material

The long-term stability study, one of the steps in the characterization of new reference materials, is performed on freeze-dried biological reference materials to verify if they may be stored at room temperature without modification of the property values of interest. In this study, instrumental neutron activation analysis was used in a 12-month long isochronous long-term stability study performed on a Perna perna mussel candidate reference material. No trend in the results was observed in respect to measurement order and exposition period to room temperature. The assessment of the analysis of variance test as well as the normalized results to the control temperature showed no systematic changes in the mass fractions of Ag, As, Br, Co, Cr, Cs, Fe, Eu, La, Na, Rb, Sc, Se, Th and Zn during the test period. The result showed that the candidate reference material may be stored at room temperature without significant changes in composition for the determined elements.     

The degree of efficiency, the degree of reproducibility and the equivalence probability in statistical comparisons of analytical methods for the determination of tin in tin ores

Summary In most cases investigations concerning the reproducibility of different analytical methods for the determination of tin in tin ores consist only in comparisons of means, i.e. detection of systematic errors. The fact that the methods use different calibrating procedures, on the one hand, and that their accuracy varies, on the other hand, makes it necessary, to look for more sensitive criteria. For this purpose, the degree of efficiency regarding the determination of the true mean of a reference method, the degree of (mutual) reproducibility, and the equivalence probability are defined and their meaning is statistically interpreted. The degree of efficiency ɛ of any two methods is defined as the ratio of their mean square errors in determining the true mean of a reference method. This quantity can be described by the ratio of the upper bounds for the probabilities of an error by the two methods. The degree of reproducibility P* of different analytical methods we understand as minimal probability of comparable measuring results. The equivalence probability P_e is defined as a-posteriori probability of the hypothesis that the two distribution functions considered are identical. The criteria ɛ, P* and P_e seem to be more suitable for statistical comparisons as compared to known statistical standard procedures, such as the t-test criterion. The applicability of these quantities was checked by the example of 6 different methods for the determination of tin in tin ores. For this purpose, it was necessary to evaluate objectively the efficiency of sample division in order to get reproducible final samples for analysis using the hierarchical two-way classification of variance analysis. General knowledge concerning the analytical methods used could be completed.     

A new algorithm to evaluate bielectronic integrals with 1s Slater‐type orbitals obtained by the integral transforms

This article presents a variation of the integral transform method to evaluate multicenter bielectronic integrals (12|34), with 1s Slater‐type orbitals. It is proved that it is possible to define, out of the expression of (12|34) given by the integral transform method, a function F(q) that has the property of having a unique Q, such that F(Q) = (12|34). Therefore, F(q) may be used to calculate (12|34). It is shown that the evaluation of F(Q) turns out to be simpler than the three‐dimensional integral involved in the calculation of (12|34), and an algorithm is presented to calculate Q. The results show that relative errors on the order of 10^?3 or lower are obtained very efficiently. In addition, it is shown that the proposed algorithm is very stable. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Peculiarities in the Behavior of Rare-Earth Elements in Their Determination in Black Shales by Inductively Coupled Plasma Mass Spectrometry

The accuracy of the results of analysis by inductively coupled plasma mass spectrometry (ICP-MS) was studied for the determination of rare-earth elements in black shales rich with a carbonaceous organic substance of a different nature: biogenic (samples SChS-1 and SLg-1, which were put through certification studies at the Institute of Geochemistry, Siberian Division, Russian Academy of Sciences) and bituminous (SDO-1 and SGR-1, reference samples of the US Geological Survey). Based on the comparison of the results obtained by ICP MS with the reference data for SChS-1 and SLg-1 shales, it was found that the systematic error depends on the procedure of sample decomposition: in open systems (A), in autoclaves (B), and by fusion with lithium metaborate (C). In decomposition procedures A and B, the underestimation of results was observed for heavy rare-earth elements (Gd–Lu): up to 60–80% in the open decomposition of samples and up to 30–40% in the decomposition in an autoclave; these errors cannot be eliminated by preliminary calcination of samples, and only the use of procedure C provides the smallest deviations between the found and reference concentrations. The behavior of rare-earth elements in the analysis of SDO-1 and SGR-1 shales differs from their behavior in the analysis of SChS-1 and CLg-1: systematic errors were not revealed when the above decomposition procedures were used.     

Systematische Fehler in der Analyse

Zusammenfassung Der systematische Fehler einer analytischen Messung ist um so gravierender, je mehr von den Entscheidungen auf Grund der Analysendaten abhängt. Die heute so wichtig gewordene Spurenanalytik ist besonders anfällig gegen systematische Fehler, weil sich da der systematische Probennahmefehler und der Fehler auf Grund einer nicht vollständig erfaßbaren und mit Testgemischen nicht simulierbaren Matrix verstärkt auswirkt. Ein hoher Informationsgehalt und eine gute Wiederholbarkeit bzw. Vergleichbarkeit sind zwar notwendige, aber nicht hinreichende Bedingungen für eine fehlerarme Analytik. Zwei Methoden zur Erkennung und Beseitigung systematischer Fehler werden diskutiert: 1. Das Gütekriterium. Es ist dies die Veränderbarkeit des Meßwertes am echten Analysenprodukt, nicht am Testgemisch, als Funktion der Veränderung der Meßparameter, und 2. Der Bilanztest. Hier wird bei Proben aus statischen Quellen die Menge des Stoffesi in der Ursprungsprobe und in durch physikalische Disproportionierung ohne Produktverlust gewonnenen Probenanteilen, deren relative qualitative Zusammensetzung geändert wurde, gemessen und bilanziert. Bei Proben aus dynamischen Quellen (Beispiel: kontinuierliche Destillation) wird der Produktfluß voni in Masse pro Zeiteinheit bilanziert. Dieses Verfahren kann zum Nachweis von systematischen Probennahmefehlern dienen.

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Tests for systematic errors in analysis

The systematic error of an analysis is as important as the decision made on behalf the analytical dates. Most important are systematic errors in trace analysis, as here the sampling error and the error caused by limited knowledge about the total sample composition is dominant. To get correct results a high yield of analytical information and a good repeatability is necessary, but not sufficient. Two methods to detect systematic errors are discussed: 1. Gütekriterium (criterion on quality of the analytical procedure) by testing the change of the result versus change of measurement parameters. 2. Test balance. The sample is quantitatively disingrated in parts with differing concentrations of the compoundi to be measured. The absolute amount ofi is measured in all parts and balanced with the amount in the prime sample. With samples from a process, not the masses ofi, but the flow ofi is balanced. This test procedure can detect systematic sampling errors too.

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Auszüge aus einem Vortrag zur Analytiker-Tagung in Basel am 17. November 1970.

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Auf den Ergebnissen der Interpretation von Einzelwerten eines Bilanztestes baut man die analytische Fehlersuche auf.     

Mass spectrometry determination of the isotopic composition of uranium hexafluoride

An absolute method for the determination of isotopic composition of substances in multiple collector mass spectrometers was proposed. The detailed analysi of terms used in the method for the determination of the isotopic composition of uranium hexafluoride was given. Parabolic nature of occurring constant measurement error, obtained in theory, was proved by test data for ²³⁵U within a wide range of its concentrations. In order to use the method of measurements in practice, the registration of constant error, through linear discriminatory relations Δc _i (c _i ), preliminary determined using uranium hexafluoride with standard isotopic composition, was proposed. The advantages of the developed method in comparison with the traditional analysis procedures, applied at present, were considered.     

Potentialities of Quantitative Analysis by High-Performance Liquid Chromatography without Reference Standards of Analytes: Use of Reference Data on UV Spectra for Calculating Calibration Coefficients

It was shown by the examples of simple organic compounds and some medicinal substances that, in the quantitative analysis by the internal standard method in high-performance liquid chromatography (HPLC) with UV detection, one can use calibration coefficients calculated from reference data on UV spectra. Determinations should be performed at several constant wavelengths (for example, 220, 254, 280, and 320 nm) using at least two internal standards (a set of eight samples was proposed) rather than one standard. As can be judged from the estimates obtained, the systematic component of the determination error under these conditions does not exceed the contributions of random errors. The developed approach opens up new opportunities for quantitative determinations by HPLC without reference samples of analytes, instead of which reference data on molar absorptivities are used.     

Collimated scanning LS-INAA for testing trace elements homogeneity in Brazilian coffee beans

The degree of homogeneity is normally assessed by the variability of the results of independent analyses of several (e.g., 15) normal-scale replicates. Large sample instrumental neutron activation analysis (LS-INAA) with a collimated Ge detector allows inspecting the degree of homogeneity of the initial batch material, using a kilogram-size sample. The test is based on the spatial distributions of induced radioactivity. Such test was applied to samples of Brazilian whole (green) coffee beans (Coffea arabica and Coffea canephora) of approximately 1 kg in the frame of development of a coffee reference material. Results indicated that the material do not contain significant element composition inhomogeneities between batches of approximately 30–50 g, masses typically forming the starting base of a reference material.     

Correcting measurement errors using reference materials in method validation

Quality assurance and method validation are needed to reduce false decisions due to measurement errors. In this context accuracy and standard uncertainty for the analytical method need to be considered to ensure that the performance characteristics of the method are understood. Therefore, analytical methods ought to be validated before implementation and controlled on a regular basis during usage. For this purpose reference materials (RMs) are useful to determine the performance characteristics of methods under development. These performance parameters may be documented in the light of a method evaluation study and the documentation related to international standards and guidelines. In a method evaluation study of Pb in blood using reference samples from the Laboratoire Toxicologie du Quèbec, Canada, a difference between the systematic errors was observed using a Perkin-Elmer Model 5100 atomic absorption spectrometer and a Perkin-Elmer Model 4100 atomic absorption spectrometer, both with Zeeman background correction. For measurement of blood samples, the performance parameters obtained in the method evaluation studies, i.e. slopes and intercepts of the method evaluation function (MEF), were intended to be used for correcting the systematic errors. However, the number of MEF samples was insufficient to produce an acceptable SD for the MEF slopes to be used for correction. In a method evaluation study on valproate in plasma using the SYVA's EMIT assay on COBAS MIRA S a significant systematic error above the concentration 300 mmol dm^–3 was demonstrated (slope 0.9541) and consequently the slope was used for correction of results. For analytes, where certified RMs (CRMs) exist, a systematic error of measurements can be reduced by correcting errors by assessment of the trueness as recommended in international guidelines issued by ISO or the National Institute of Standards and Technology (NIST). When possible, the analysis of several RMs, covering the concentration range of interest, is the most useful way to investigate measurement bias. Unfortunately, until recently only few RMs existed and only few had been produced and certified by specialized organizations such as NIST or the Standards, Measurements and Testing (SMT, previously BCR) programme. Due to the lack of such RMs, network organizations are nowadays established with the aim of supporting the correct use and production of high-quality CRMs.     

Interlaboratory assessment of measurement precision and bias in the coulometric Karl Fischer determination of water

The precision and bias of the coulometric Karl Fischer ASTM method D1533-00 have been assessed in a collaborative ASTM round robin program for a group of 34 laboratories. The test materials used in this study included water saturated 1-octanol (WSO), water saturated 1-butanol (WSB), and a series of new and used transformer oil samples. Fundamental systematic biases have been demonstrated in the accuracy of the measurement of water in the WSO, WSB, and transformer oil samples. The systematic bias in the measurement of the WSO and WSB standards indicates that for some laboratories either the instruments were not accurate or the quantity of the standard was not measured accurately. A second type of systematic bias consisted of measurement errors associated with the selection of the Karl Fischer solvent that was used with each instrument, and this was superimposed upon the error in the measurement of the water in the standards. Using the statistical calculation method ASTM D 6300 the repeatability and reproducibility for water in transformer oil were found to be 7 mg/kg and 14 mg/kg respectively. The method detection limit of water was 8 mg/kg oil. The method bias was estimated based on the National Institute of Standards and Technology (NIST) Standard Reference Material (SRM) 2890, WSO, since no suitable reference material for water in transformer oil was available for this study.     

Addition of internal standards to particulate sample matrices for routine trace analyses of semivolatile organic compounds: A source of systematical and random errors

This article is a criticism of the strategy of adding (isotope labelled) internal standards of semi volatile hydrophobic organic compounds directly on the surface of particulate samples matrix such as sediment, soil and fly ash, etc. in a small aliquot (mL) of solvent, before trace level analysis. The use of the internal standard is intended to compensate for incomplete extractions, clean-up losses, dilution errors and instrument variations. However, direct addition of internal standards to sample matrices creates two possibilities for inaccurate results by processes only affecting the internal standard: First, evaporation losses of standard from the sample matrix during evaporation of the carrier solvent. Second, the native analyte and internal standard sorb to the sample matrix with differing force. Both processes can introduce systematic and random error to the result. A systematic error of 74% due to evaporation losses of tetra chlorinated dibenzo-p-dioxins is observed, while the corresponding error for octa chlorinated dioxin is 0%. The associated random error is 45% for tetra down to 1–4% relative standard deviations for hepta and octa chlorinated dioxins. For laboratory staff the evaporation losses of standard (and native) compounds causes, besides dust, an additional risk of inhalation exposure. The internal standard should instead be added to the extraction solvent after the extraction. Smaller systematical errors (10–20%) and associated random errors due to irreversible sorption are discussed. Received: 4 September 1997 / Revised: 26 January 1998 / Accepted: 31 January 1998     

Quality control in activation analysis

Analytical quality control is needed to ascertain the reliability of results from all types of analysis, including activation analysis. Thea priori precision has to be combined with the statistics of counting in order to reach a state of statistical control. The Analysis of Precision is used to verify the absence of unknown sources of variability and to ascertain the absence of systematic biases or calibration errors by analyzing samples or reference materials with accurately known content or actual samples by an independent method.     

Multi-residue determination of 130 multiclass pesticides in fruits and vegetables by gas chromatography coupled to triple quadrupole tandem mass spectrometry

A multi-residue method has been developed and validated for the simultaneous quantification and confirmation of around 130 multiclass pesticides in orange, nectarine and spinach samples by GC-MS/MS with a triple quadrupole analyzer. Compounds have been selected from different chemical families including insecticides, herbicides, fungicides and acaricides. Three isotopically labeled standards have been used as surrogates in order to improve accurate quantitation. Samples were extracted by using accelerated solvent extraction (ASE) with ethyl acetate. In the case of spinach, an additional clean-up step by gel permeation chromatography was applied. Determination was performed by GC-MS/MS in electron ionization mode acquiring two MS/MS transitions for each analyte. The intensity ratio between quantitation transition (Q) and identification transition (q) was used as confirmatory parameter (Q/q ratio). Accuracy and precision were evaluated by means of recovery experiments in orange, nectarine, and spinach samples spiked at two concentration levels (0.01 and 0.05 mg/kg). Recoveries were, in most cases, between 70% and 120% and RSD were below 20%. The limits of quantification objective for which the method was satisfactorily validated in the three samples matrices were for most pesticides 0.01 mg/kg. Matrix effects over the GC-MS/MS determination were tested by comparison of reference standards in pure solvent with matrix-matched standards of each matrix. Data obtained showed enhancement of signal for the majority of analytes in the three matrices investigated. Consequently, in order to reduce the systematic error due to this effect, quantification was performed using matrix-matched standard calibration curves. The matrix effect study was extended to other food matrices such as raisin, paprika, cabbage, pear, rice, legume, and gherkin, showing in all cases a similar signal enhancement effect.