Measurement of uncertainty in peptide molecular weight determination using size-exclusion chromatography with multi-angle laser light-scattering detection and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

The molecular weight of biopolymers such as peptides or proteins is vital information for understanding their physical/chemical properties. The matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) and size-exclusion chromotography-multi-angle laser light scattering (SEC-MALLS) techniques each with its advantages and limitations were used for molecular weight determination of the SPf66 peptide. The precision of each method was studied using a two-factor fully-nested design with all the analyses performed by the same operator on a single instrument. The overall precision corresponded to the time-different intermediate precision (i.e. time and repeatability conditions). In the case of SEC-MALLS, all potential uncertainty components were carefully evaluated in an Ishikawa diagram, then included and mathematically combined with the uncertainty arising from the accuracy assessment to provide the overall uncertainty. In this case, the refractive-index increment with solute concentration value (dn/dc) provided the most significant contribution to the combined uncertainty. A method for its quantitation is proposed. The accuracy of method B (SEC-MALLS) against reference method A (MALDI-TOF-MS) was assessed using the interval testing hypothesis to limit the risk of unacceptable bias. The results indicate that the bias of B is higher than the limit established at 5%, and is therefore not traceable to A under the studied conditions.     

塑料中镉的测定不确定度评定

建立了用实验室内精密度和偏差的数据来评定塑料中镉的测定不确定度的方法. 通过研究不同基体和不同含量水平的样品, 考察了方法的精密度和回收率, 分别计算并合并了两者的测量不确定度. 结果表明精密度和回收率的相对不确定度分量分别为0.026和0.068, 合成不确定度为0.072, 扩展不确定度为0.14. 此评定过程为实验室评定测量不确定度提供了一种新的方法, 简单、合理, 计算结果可靠.     

Bayesian Methods for Ion Selective Electrodes

With the increasing use of ion‐selective electrodes in environmental and health applications, it is important to know the precision of estimated concentrations. A Bayesian model for non‐linear calibration is introduced which provides estimates of measurement precision by incorporating uncertainty in calibration parameters and inherent random noise in emf response. The analysis of lead in 17 soil samples demonstrates that large gains in precision are possible when calibrations are extended to include multiple electrodes and standard addition data. The results highlight the need for improved calibration and routine use of standard addition as ion selective electrodes become increasingly popular for demanding, real world applications.     

An approach to detection capabilities estimation of analytical procedures based on measurement uncertainty

Detection capabilities are important performance characteristics of analytical procedures. There are several conceptual approaches on the subject, but in most of them a level of ambiguity is presented. It is not clear which conditions of measurements should be used, and there is a relative lack of definition concerning blanks. Moreover, there are no systematic experimental studies concerning the influence of uncertainty associated with bias evaluation. A new approach based on measurement uncertainty is presented for estimating quantities that characterize capabilities of detection. It can be applied to different conditions of measurement and it is not necessary to perform an additional experiment with blanks. Starting from a modelling process of the combined uncertainty of concentration, it is possible to include in the estimated quantities the effects due to random errors and the uncertainty associated to evaluation of bias. The detection capabilities are then compared with the results obtained using some other relevant approaches. Slightly higher values were obtained with the measurement uncertainty approach due to inclusion of uncertainty associated with bias.     

Measurement uncertainty in analytical methods in which trueness is assessed from recovery assays

We propose a new procedure for estimating the uncertainty in quantitative routine analysis. This procedure uses the information generated when the trueness of the analytical method is assessed from recovery assays. In this paper, we assess trueness by estimating proportional bias (in terms of recovery) and constant bias separately. The advantage of the procedure is that little extra work needs to be done to estimate the measurement uncertainty associated to routine samples. This uncertainty is considered to be correct whenever the samples used in the recovery assays are representative of the future routine samples (in terms of matrix and analyte concentration). Moreover, these samples should be analysed by varying all the factors that can affect the analytical method. If they are analysed in this fashion, the precision estimates generated in the recovery assays take into account the variability of the routine samples and also all the sources of variability of the analytical method. Other terms related to the sample heterogeneity, sample pretreatments or factors not representatively varied in the recovery assays should only be subsequently included when necessary. The ideas presented are applied to calculate the uncertainty of results obtained when analysing sulphides in wine by HS-SPME-GC.     

Estimation of Uncertainty for Measuring Codeine Phosphate Tablets Formulation Using UV-Vis Spectrophotometry

Analytical results represent a very important part in a quality control program. Uncertainty estimation is an important step in method validation. The objective of this paper is to study the uncertainty of measurement estimation in the quantitative determination of codeine phosphate from pharmaceutical formulations using UV-VIS spectrophotometry. The uncertainty estimation was performed using the Ishikawa diagram. The estimation of uncertainty components proved to be a good way for the experimental model to obtain low contribution of uncertainty to the analytical result.     

Element analysis of inhomogeneous samples by laser ablation ICP mass spectrometry

Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) has been used for the determination of selected elements in heterogeneous powdered soils. The precision of the method essentially depends on the homogeneity of the samples. Therefore the influence of sample inhomogeneity on the precision of analytical results has been checked. The statistical evaluation was carried out using a correlation function. In the context of the described experiments, it is necessary to analyze a volume of about 20 mm³ in order to obtain reliable information on the bulk composition of the heterogeneous samples. This corresponds to about 50 craters, each with a depth of 1 mm. The results can be used to calculate certain analytical parameters, particularly the sample homogeneity, depending on the necessary analytical volume and the representative mass for the quantitative analysis under previously defined conditions. In addition to these calculations, analytical experiments have been carried out which confirm the applicability of this approach.     

Estimation of uncertainty in size-exclusion chromatography with a double detection system (light-scattering and refractive index)

Size-exclusion chromatography (SEC) coupled with online laser light-scattering (LS) and refractive index (RI) detection provides an excellent approach to determine the molecular weights (Mw) of proteins by the “two-detector” approach. Mw is determined only at the maximum of a peak, using either peak heights or area ratio from the two detectors. However, proper calibration of the SEC/LS/RI system is critical to obtain high precision.Today, an essential part of any analysis is to evaluate the uncertainty associated with the method. Basically, it is possible to distinguish between factors related to signal nature, precision and those due to signal processing. Given the signal of interest is the peak height or area ratio from two detectors, the signal ratio uncertainty was calculated using the random propagation of error formula. In this case, the effect of signal correlation was evaluated to avoid the uncertainty overestimation. In the second case, the sources of uncertainty affecting analytical measurement were estimated with the information from the precision assessment. For this, two designs with two-factor fully nested were followed for each method. Finally, the contributions from various uncertainty sources related with calibration are also analysed in detail. There are in fact only three main sources of measurement uncertainty: intermediate precision, calibration and repeatability. Of these, method precision is always the greatest, regardless of approach.For all proteins and peptides studied, the Mw calculated using both methods are close to the theoretical results, independently of the design, but the contributions of individual terms to combined uncertainty depend on both the design and method used. For example, the combined uncertainty varied between 223 and 813.2 Da for carbonic anhydrase, although higher values were found for human insulin and ovalbumin dimer. Other considerations that can have a significant impact on the results are discussed.The reproducibility of the two methods versus that based on ASTRA software used as reference method was performed using the concordance correlation coefficient. The methods’ reproducibility depends on the permitted losses in precision and accuracy.     

Assessment of the determination of water-soluble ionic composition of atmospheric aerosols from the analysis of crossed halves of filters

The water-soluble ionic composition of atmospheric aerosols is a key parameter for estimating its anthropogenic or natural origin. This evaluation depends on the reliability of the performed measurements. The differential approach for the evaluation of the measurement uncertainty was used for estimating, separately, the uncertainty associated with the extraction step, by difference from the observed intermediate precision and the combination of all the other uncertainty components affecting the estimated intermediate precision. The intermediate precision was estimated from the difference of results of the analysis, in different days, of several pairs of filters resulting from cross-changing of their halves. The precision associated with the symmetry of filters division, affecting the homogeneity of studied combined pairs of filters, was subtracted from the observed dispersion of results. The resulting detailed model of measurement performance allowed defining strategies for cost of analysis or magnitude of measurement uncertainty reduction. Measurements are fit for the analysis of urban aerosols since the expanded relative measurement uncertainty is smaller than a target value of 30 %.     

Uncertainty and traceability in an assay method (ascorbic acid in juices)

We discus two of the most important aspects for ensuring the quality of the measurements in an assay method. These parameters are: measurement uncertainty and traceability of the measuring method. To be able to exemplify these parameters, we took as an example the measuring of ascorbic acid in commercial juices to clearly understand all the implicit metrological requirements in an assay method. To do this, it was necessary to meticulously analyze every step of the ascorbic acid measuring process via implementation of the practical application of the AOAC 967.21 Official Method for determining ascorbic acid, which is a titrimetric method based on the ISO 10012 norm. The uncertainty and traceability were studied and applied to control the process variability on the assay method. All this allows us to show the importance of implementing a measurement control system on an assay method, thus guaranteeing repeatable and traceable measurements, and ensuring that the measurements have been done accurately.     

Experimental comparisons of statistical uncertainties in analysis of nuclear spectra with the Cambio software application

Cambio is a software application well-suited for analysis of high-resolution nuclear spectral data in which the critical information resides in well-masked peaks or in which the data are sparse and good statistics cannot be obtained. The statistical uncertainty in the results is reported in terms of standard deviations. In the practical use of any analysis application, it is important to have a good understanding of the accuracy of the reported statistical uncertainties in the results. The authors report the results of an experiment that provides a quantitative measure of the accuracy of the reported uncertainties in analyses using Cambio. Ten calibration sources ranging in activity from 25 to 450 kBq were placed 20.5 m from a bare, 100 % relative-efficient high-purity germanium detector. Peaks in these sources occur from 20 to 2,800 keV. Data were accumulated for 128 h to create a parent spectrum from which 1024 8-hour statistically-equivalent daughter spectra were created by random sampling of the parent spectrum data. The parent spectrum was analyzed by fitting parameters which included an underlying continuum, a background of natural peaks adjusted by detector efficiency and material attenuation, and a foreground of the ten sources adjusted by detector efficiency only. Each of the daughter spectra were then analyzed starting with the parameters of the fit to the parent spectrum and then minimizing Chi-square with respect to changes in these parameters. The standard deviations of the estimated activities of the sources from all 1024 spectra were then calculated and compared to the reported statistical uncertainty in the activities and peak areas of the sources.     

Determination of standard sample purity using the high-precision 1H-NMR process

This paper discusses the technique for high-precision quantification using ¹H-NMR to determine the purity of analytical standard samples. The procedure described is based on the use of internal reference samples in an ¹H NMR experiment in our laboratories. The sample preparation and all relevant NMR parameters were optimized for minimum uncertainty. The validation of accuracy and precision was performed by comparing different certified reference materials. It was shown that the high-precision measurement is applicable even for relatively small sample amounts down to 2.5 mg. The relative combined uncertainty of measurement was found to be 0.15%. Two different approaches for uncertainty calculation were compared; a complete uncertainty budget was calculated.     

Response surface modelling and kinetic studies for the experimental estimation of measurement uncertainty in derivatisation

Response surface modelling is proposed as an approach to the estimation of uncertainties associated with derivatisation, and is compared with a kinetic study. Fatty acid methyl ester formation is used to illustrate the approach, and kinetic data for acid-catalysed methylation and base-catalysed transesterification are presented. Kinetic effects did not lead to significant uncertainty contributions under normal conditions for base-catalysed transesterification of triglycerides. Uncertainties for acid-catalysed methylation with BF3 approach significance, but could be reduced by extending reaction times from 3 to 5 min. Non-linearity is a common feature of response surface models for derivatisation and compromised first-order estimates of uncertainty; it was necessary to include higher order differential terms in the uncertainty estimate. Simulations were used to examine the general applicability of the approach and to study the effects of poor precision and of change of response surface model. It is concluded that reliable uncertainty estimates are available only when the model is statistically significant, robust, representative of the underlying behaviour of the system, and forms a good fit to the data; arbitrary models are not generally suitable for uncertainty estimation. Where statistically insignificant effects were included in models, they gave negligible uncertainty contributions.     

Systematic errors in the measurement of adsorption isotherms by frontal analysis Impact of the choice of column hold-up volume, range and density of the data points

Besides the accuracy and the precision of the measurements of the data points, several important parameters affect the accuracy of the adsorption isotherms that are derived from the data acquired by frontal analysis (FA). The influence of these parameters is discussed. First, the effects of the width of the concentration range within which the adsorption data are measured and of the distribution of the data points in this range are investigated. Systematic elimination of parts of the data points before the calculation of the nonlinear regression of the data to the model illustrates the importance of the numbers of data points (1) within the linear range and (2) at high concentrations. The influence of the inaccuracy of the estimate of the column hold-up volume on each adsorption data point, on the selection of the isotherm model, and on the best estimates of the adsorption isotherm parameters is also stressed. Depending on the method used to measure it, the hold-up time can vary by more than 10%. The high concentration part of the adsorption isotherm is particularly sensitive to errors made on t(0,exp) and as a result, when the isotherm follows bi-Langmuir isotherm behavior, the equilibrium constant of the low-energy sites may change by a factor 2. This study shows that the agreement between calculated and experimental overloaded band profiles is a necessary condition to validate the choice of an adsorption model and the calculation of its numerical parameters but that this condition is not sufficient.     

Micro-Winkler titration method for dissolved oxygen concentration measurement

In this report a gravimetric micro-Winkler titration method for determination of dissolved oxygen concentration in water is presented. Mathematical model of the method taking into account all influence factors is derived and an uncertainty analysis is carried out to determine the uncertainty contributions of all influence factors. The method is highly accurate: the relative expanded uncertainties (k = 2) are around 1% in the case of small (9-10 g) water samples. The uncertainty analysis carried out in characterizing the uncertainty of the method is the most comprehensive published for a micro-Winkler method, resulting in experimentally obtained estimates for all uncertainty sources of practical significance (around 20 uncertainty sources altogether).     

Quantifying the measurement uncertainty of results from environmental analytical methods

The Eurachem–CITAC Guide Quantifying Uncertainty in Analytical Measurement was put into practice in a public laboratory devoted to environmental analytical measurements. In doing so due regard was given to the provisions of ISO 17025 and an attempt was made to base the entire estimation of measurement uncertainty on available data from the literature or from previously performed validation studies. Most environmental analytical procedures laid down in national or international standards are the result of cooperative efforts and put into effect as part of a compromise between all parties involved, public and private, that also encompasses environmental standards and statutory limits. Central to many procedures is the focus on the measurement of environmental effects rather than on individual chemical species. In this situation it is particularly important to understand the measurement process well enough to produce a realistic uncertainty statement. Environmental analytical methods will be examined as far as necessary, but reference will also be made to analytical methods in general and to physical measurement methods where appropriate. This paper describes ways and means of quantifying uncertainty for frequently practised methods of environmental analysis. It will be shown that operationally defined measurands are no obstacle to the estimation process as described in the Eurachem/CITAC Guide if it is accepted that the dominating component of uncertainty comes from the actual practice of the method as a reproducibility standard deviation.     

Uncertainty budget for final assay of a pharmaceutical product based on RP–HPLC

Compliance with specified limits for the content of active substance in a pharmaceutical drug requires knowledge of the uncertainty of the final assay. The uncertainty of measurement is based on the ISO recommendation as expressed in the Guide to the Expression of Uncertainty in Measurement (GUM). The reported example illustrates the estimation of uncertainty for the final determination of a protein concentration by HPLC using UV detection, using the approach described by EURACHEM/CITAC. The combined standard uncertainty for a protein concentration of 2400 µmol/L was estimated to be 14 µmol/L.. All known and potential uncertainty components are presented in Ishikawa diagrams and were carefully evaluated using Type A or Type B estimates. Special efforts were made to avoid duplication or omission of significant contributions to the combined uncertainty. Hence, before accepting the uncertainty budget, the estimated combined standard uncertainty was verified using the variation observed in a number of quality control samples.     

An Expert System for EPMA

 Experimental parameters for an electron microprobe are numerous and their choice influence the quality and accuracy of the analysis results. The expert system intends to optimise the choice of every parameter as well as to automate the stages of a quantitative analysis for all kinds of materials. In short, the expert system aims to master the accuracy of results and to control the time of analysis. The starting point of the expert system is an interactive questionnaire about the sample and about the expectations of the analysis (the accuracy of the result and/or the duration of the analysis). Then, the expert system makes a semi-quantitative analysis on the sample. It gives the sample composition in a first approximation. This is necessary for the expert system to optimise all the parameters for an accurate quantitative analysis. Each parameter is modelled by a specific algorithm. The expert system selects the parameters by minimising, at every stage, the statistical error generated by the algorithm. In this way, it operates in a sufficiently independent way to create a quantitative analysis configuration adapted to an unknown sample. The expert system employs the usual methods of quantification but the results are obtained in half the time. Moreover, the accuracy of the result is guaranted by the statistical error calculation as the expert system is running.     

The application of the measurement uncertainty concept to in-process control in pharmaceutical development

 Any analytical data is used to provide information about a sample. The "possible error" of the measurement can be of extreme importance in order to have complete information. The measurement uncertainty concept is a way to achieve quantitative information about this "possible error" using an estimation procedure. On the basis of the analytical result, the chemist makes a decision on the next step of the development process. If the uncertainty is unknown, the information is not complete; therefore this decision might be impossible. The major problem for the in-process control (IPC) procedure is that not only the repeatability but also the intermediate precision (which expresses the variations within laboratories related to different days, different analysts, different equipment, etc.) has to be good enough to make a decision. Unfortunately, the statistical information achieved from one single analytical run only gives information about the repeatability. This paper shows that the estimation of the measurement uncertainty for IPC is a way to solve the problem and gives the necessary information about the quality of the procedure. An example demonstrates that an estimate of uncertainty based on the standard deviations of an analytical method gives a value similar to one based on the standard deviations obtained from a control chart. Therefore, the estimation is both a very useful and also a very cost-effective tool. Though measurement uncertainty cannot replace validation in general, it is a viable alternative to validation for all methods that will never be used routinely. Received: 24 May 1996 Accepted: 10 August 1996