Uncertainty in chemical analysis and validation of the analytical method: acid value determination in oils

Quantifying uncertainty in chemical analysis, according to EURACHEM document (1995), is based on known relationships between parameters of the analytical procedure and corresponding results of the analysis. This deterministic concept is different from the cybernetic approach to analytical method validation, where the whole analytical procedure is a "black box". In the latter case, analytical results only are the basis for statistical characterization of the method without any direct relationship with intermediate measurement results like weighings, volumes, instrument readings, or other parameters like molecular masses. This difference requires the harmonization of parameters to be validated and to be included in the uncertainty calculation. As an example, results of the uncertainty calculation and validation are discussed for a new method of acid value determination in oils by pH measurement without titration.     

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     

New advances in method validation and measurement uncertainty aimed at improving the quality of chemical data

The implementation of quality systems in analytical laboratories has now, in general, been achieved. While this requirement significantly modified the way that the laboratories were run, it has also improved the quality of the results. The key idea is to use analytical procedures which produce results that fulfil the users needs and actually help when making decisions. This paper presents the implications of quality systems on the conception and development of an analytical procedure. It introduces the concept of the lifecycle of a method as a model that can be used to organize the selection, development, validation and routine application of a method. It underlines the importance of method validation, and presents a recent approach based on the accuracy profile to illustrate how validation must be fully integrated into the basic design of the method. Thanks to the -expectation tolerance interval introduced by Mee (Technometrics (1984) 26(3):251–253), it is possible to unambiguously demonstrate the fitness for purpose of a new method. Remembering that it is also a requirement for accredited laboratories to express the measurement uncertainty, the authors show that uncertainty can be easily related to the trueness and precision of the data collected when building the method accuracy profile.     

Software support for the Nordtest method of measurement uncertainty evaluation

Software support for the Nordtest method of measurement uncertainty evaluation is described. According to the Nordtest approach, the combined measurement uncertainty is broken down into two main components??the within-laboratory reproducibility (intermediate precision) s _Rw and the uncertainty due to possible laboratory bias u(bias). Both of these can be conveniently estimated from validation and quality control data, thus significantly reducing the need for performing dedicated experiments for estimating detailed uncertainty contributions and thereby making uncertainty estimation easier for routine laboratories. An additional merit of this uncertainty estimation approach is that it reduces the danger of underestimating the uncertainty, which continues to be a problem at routine laboratories. The described software tool??MUkit (measurement uncertainty kit)??fully reflects the versatility of the Nordtest approach: it enables estimating the uncertainty components from different types of data, and the data can be imported using a variety of means such as different laboratory data systems and a dedicated web service as well as manual input. Prior to the development of the MUkit software, a laboratory survey was carried out to identify the needs of laboratories related to uncertainty estimation and other quality assurance procedures, as well as their needs for a practical tool for the calculation of measurement uncertainty.     

A comparison in the evaluation of measurement uncertainty in analytical chemistry testing between the use of quality control data and a regression analysis

The evaluation of measurement uncertainties has been widely applied to the calibration of measurement instruments, whereas its application to tests, despite increasing requirements, is a more recent phenomenon. The generalization of the evaluation of measurement uncertainties to tests has been a gradual process, in line with changes in the requirements of the normative framework that regulates the accreditation of tests laboratories and also as the perceived good practices have evolved. The sole identification of the relevant sources of uncertainty was followed by the requirement to provide a simplified estimate of the measurement uncertainty, and it is now an accepted requirement to properly evaluate the expanded measurement uncertainty associated with any tests. In this study, the evaluation of measurement uncertainty associated with the determination of sulfate in water will be attempted using a procedure that includes linear regression, with the regression parameters provided with associated uncertainties, and a Monte Carlo method applied as a validation tool of the conventional mainstream evaluation method, concerning the approximations in terms of linearization of the model and the assumed shape of the output distribution introduced by this approach.     

Empirical versus modelling approaches to the estimation of measurement uncertainty caused by primary sampling

Measurement uncertainty is a vital issue within analytical science. There are strong arguments that primary sampling should be considered the first and perhaps the most influential step in the measurement process. Increasingly, analytical laboratories are required to report measurement results to clients together with estimates of the uncertainty. Furthermore, these estimates can be used when pursuing regulation enforcement to decide whether a measured analyte concentration is above a threshold value. With its recognised importance in analytical measurement, the question arises of 'what is the most appropriate method to estimate the measurement uncertainty?'. Two broad methods for uncertainty estimation are identified, the modelling method and the empirical method. In modelling, the estimation of uncertainty involves the identification, quantification and summation (as variances) of each potential source of uncertainty. This approach has been applied to purely analytical systems, but becomes increasingly problematic in identifying all of such sources when it is applied to primary sampling. Applications of this methodology to sampling often utilise long-established theoretical models of sampling and adopt the assumption that a 'correct' sampling protocol will ensure a representative sample. The empirical approach to uncertainty estimation involves replicated measurements from either inter-organisational trials and/or internal method validation and quality control. A more simple method involves duplicating sampling and analysis, by one organisation, for a small proportion of the total number of samples. This has proven to be a suitable alternative to these often expensive and time-consuming trials, in routine surveillance and one-off surveys, especially where heterogeneity is the main source of uncertainty. A case study of aflatoxins in pistachio nuts is used to broadly demonstrate the strengths and weakness of the two methods of uncertainty estimation. The estimate of sampling uncertainty made using the modelling approach (136%, at 68% confidence) is six times larger than that found using the empirical approach (22.5%). The difficulty in establishing reliable estimates for the input variable for the modelling approach is thought to be the main cause of the discrepancy. The empirical approach to uncertainty estimation, with the automatic inclusion of sampling within the uncertainty statement, is recognised as generally the most practical procedure, providing the more reliable estimates. The modelling approach is also shown to have a useful role, especially in choosing strategies to change the sampling uncertainty, when required.     

Development of an ultra high performance liquid chromatography method for determining triamcinolone acetonide in hydrogels using the design of experiments/design space strategy in combination with process capability index

An ultra high performance liquid chromatography method was developed and validated for the quantitation of triamcinolone acetonide in an injectable ophthalmic hydrogel to determine the contribution of analytical method error in the content uniformity measurement. During the development phase, the design of experiments/design space strategy was used. For this, the free R‐program was used as a commercial software alternative, a fast efficient tool for data analysis. The process capability index was used to find the permitted level of variation for each factor and to define the design space. All these aspects were analyzed and discussed under different experimental conditions by the Monte Carlo simulation method. Second, a pre‐study validation procedure was performed in accordance with the International Conference on Harmonization guidelines. The validated method was applied for the determination of uniformity of dosage units and the reasons for variability (inhomogeneity and the analytical method error) were analyzed based on the overall uncertainty.     

Meeting the measurement uncertainty and traceability requirements of ISO/IEC standard 17025 in chemical analysis

The new laboratory accreditation standard, ISO/IEC 17025, reflects current thinking on good measurement practice by requiring more explicit and more demanding attention to a number of activities. These include client interactions, method validation, traceability, and measurement uncertainty. Since the publication of the standard in 1999 there has been extensive debate about its interpretation. It is the author's view that if good quality practices are already in place and if the new requirements are introduced in a manner that is fit for purpose, the additional work required to comply with the new requirements can be expected to be modest. The paper argues that the rigour required in addressing the issues should be driven by customer requirements and the factors that need to be considered in this regard are discussed. The issues addressed include the benefits, interim arrangements, specifying the analytical requirement, establishing traceability, evaluating the uncertainty and reporting the information.     

Measurement uncertainty evaluation and in-house method validation of the herbicide iodosulfuron-methyl-sodium in water samples by using HPLC analysis

A method for separation and quantitative determination of the iodosulfuron-methyl-sodium in water samples by high-performance liquid chromatography (HPLC) was developed and in-house validated in order to demonstrate its performance for monitoring of heterogeneous photocatalytic elimination of the herbicide iodosulfuron-methyl-sodium from water. Surface and ground water samples were used to demonstrate its selectivity, detection and quantification limits, linearity, trueness and precision. In addition, stability of iodosulfuron-methyl-sodium was studied in function of temperature and time. Method accuracy was quantified through measurement uncertainty estimate based on method validation data. The paper gives practical and easy to follow guidance on how uncertainty estimates can be obtained from method validation experiments. It shows that, if properly planned and executed, key precision and trueness studies undertaken for validation purposes can also provide much of the data needed to produce an estimate of measurement uncertainty. Our analytical protocol allowed us to quantify iodosulfuron-methyl-sodium in ground water and surface water in concentration level between 2.50–50.0 μmol L⁻¹ with satisfactory recoveries (99–104%) and repeatability lower or equal than 0.3% for all the matrices. We also estimated within-laboratory reproducibility over 3-month period, which was 0.7%. We proved that the method was selective for determination of iodosulfuron-methyl-sodium in the relevant matrices. Measurement uncertainty of results was evaluated to be 4.0% with 95% confidence level. After validation and measurement uncertainty evaluation steps, results obtained showed that the method can be applied to efficiently monitor heterogenous photocatalytic degradation of the herbicide iodosulfuron-methyl-sodium.     

Uncertainty in quantitative thin-layer chromatography

Globalization forces analysts to demand extended control of variability in analytical measurements. A calculation procedure named the "error budget model" following recommendations proposed more than 20 years ago by the Bureau International des Poids et Mesures is established as a rule for evaluating and expressing the measurement uncertainty across a broad spectrum of measurements. This metrological approach common in physical measurement is not applicable in separation techniques and cannot quantitate measurement uncertainty. Our experiments show that it can be used as a planning tool in the validation of thin-layer chromatographic (TLC) methods. A computer program that quantitates uncertainty components associated with potential sources of uncertainty in quantitative TLC is prepared and tested with experimental data. TLC plates with different qualities of stationary phases (TLC and high-performance TLC) spotted with different types of samples are measured. Application is performed manually and automatically. Plates are scanned with UV-vis scanners and a video documentation system in remission and transmission mode and fluorescence. Although the calculated values are close to the values obtained with validation procedures, the error budget approach cannot substitute validation. Calculated results can predict critical points in real quantitative TLC, but they cannot confirm the validity of a selected chromatographic procedure.     

A simplified approach to the estimation of analytical measurement uncertainty

The present study summarizes the measurement uncertainty estimations carried out in Nestlé Research Center since 2002. These estimations cover a wide range of analyses of commercial and regulatory interests. In a first part, this study shows that method validation data (repeatability, trueness and intermediate reproducibility) can be used to provide a good estimation of measurement uncertainty.In a second part, measurement uncertainty is compared to collaborative trials data. These data can be used for measurement uncertainty estimation as far as the in-house validation performances are comparable to the method validation performances obtained in the collaborative trial.Based on these two main observations, the aim of this study is to easily estimate the measurement uncertainty using validation data.     

A validation concept for purity determination and assay in the pharmaceutical industry using measurement uncertainty and statistical process control

 The analytical chemists in process development in the pharmaceutical industry have to solve the difficult problem of producing high quality methods for purity determination and assay within a short time without a clear definition of the substance to be analyzed. Therefore the quality management is very difficult. The ideal situation would be that every method is validated before use. This is not possible because this would delay the development process. A process-type quality development approach with an estimation type fast validation (measurement uncertainty) is therefore suggested. The quality management process consists of the estimation of measurement uncertainty for early project status. Statistical process control (SPC) is started directly after measurement uncertainty estimation and a classical validation for the end of the project. By this approach a process is defined that allows a fast and cost-efficient way of supporting the development process with the appropriate quality at the end of the process and provides the transparency needed in the development process. The procedure presented tries to solve the problem of the parallelism between the two development processes (chemical and analytical development) by speeding up the analytical development process initially. Received: 25 March 1997 · Accepted: 17 May 1997     

Speciation analysis of chromium in drinking water samples by ion-pair reversed-phase HPLC–ICP-MS: validation of the analytical method and evaluation of the uncertainty budget

The approach presented in this article refers to the modification of a method for the detection and quantitative determination of chromium species in water by high-performance liquid chromatography inductively coupled plasma mass spectrometry. The main aim of this work was to establish a detailed validation of the analytical procedure and an estimation of the budget of measurement uncertainty which was helpful in recognizing the critical points of the presented method. As a result of the method validation experiment, the obtained limit of quantification, repeatability and intermediate precision were satisfied for the quantification Cr(III) and Cr(VI) in water matrices. The trueness of the method was verified via an estimation of the recovery of the spiked real samples. The recovery rate of both determined analytes was found to be between 93 and 115 %. Considering that the validation of the method and the evaluation of measurement uncertainty are crucial for quantitative analysis, the above-mentioned assessment of the uncertainty budget was performed in two different ways: a modelling approach and a single-laboratory validation approach. The measurement uncertainties of the results were found to be 4.4 and 7.8 % for Cr(III), 4.2 and 7.9 % for Cr(VI) using the classical concept and method validation data, respectively. This paper is the first publication to presenting all the steps needed to evaluate the measurement uncertainty for the speciation analysis of chromium species. In summary, the obtained results demonstrate that the method can be applied effectively for its intended use.     

Production of certified reference materials for mycotoxins: IRMM’s view on the assessment of uncertainties

Analytical difficulty and the economic importance of controlling mycotoxin levels in food and feed led the Community Bureau of Reference (BCR) to prepare a series of certified reference materials (CRM) for various mycotoxins. Because of the wide acceptance of these CRM and the need to ensure the comparability and traceability of measurements in the future it is necessary to prepare and certify new batches of mycotoxin reference materials (RM). In the following text two different approaches for evaluation of the characterisation uncertainty of CRM will be compared using the certification of aflatoxin M₁ (AfM₁) in milk powder as an example. The conventional approach is based on evaluation of characterisation exercise data; the alternative approach is based on measurement uncertainties of the employed analytical methods. Because laboratories are using totally different approaches to estimate the measurement uncertainties, combination of the uncertainties obtained from the participating laboratories was not recommended. Therefore, a new integrated approach for assessment of the measurement uncertainties of the analytical methods on the basis of additional data collected during the characterisation exercise will be described. The conventional approach was found to be the most appropriate and economical approach to evaluate the characterisation uncertainty as a characterisation exercise must be performed anyway to establish the property values of candidate (C)RM, irrespective of whether or not reliable measurement uncertainties can be provided by the laboratories. An integrated approach for assessment of measurement uncertainties based on additional characterisation data as applied here to enable use of an uncertainty-based approach provides more information but is too time-consuming and cost-intensive to become common practice.     

Method validation and measurement uncertainty evaluation for measurement of mass concentration of organic acids in fermentation broths by using ion chromatography

In the present paper, a methodology for method validation and measurement uncertainty evaluation for the measurement of mass concentration of organic acids in fermentation broths was developed. Acetic acid was selected as a representative of organic acids. A detailed procedure for in-house method validation based on simple experimental design and consistent statistics is presented. In addition, a step-by-step illustration of ??Bottom-Up?? approach for measurement uncertainty evaluation of acetic acid in fermentation broths is also provided. The major sources of uncertainty of the result of measurement were identified and the combined uncertainty was calculated. Our analytical protocol allowed us to quantify acetic acid in fermentation broths in mass concentrations up to 75?g?L^?1 with satisfactory recovery (102.3%) and repeatability lower than 2%. We also estimated within-laboratory reproducibility over 3-month period, which was 2.3%. We proved that the method was selective for the measurement of mass concentration of acetic acid in fermentation broths. Measurement uncertainty of results was evaluated to be 6.2% with 95% confidence level. After validation and measurement uncertainty evaluation steps, results obtained showed that the method can be applied to efficiently monitor fermentation processes.     

The modular analytical procedure and validation approach and the units of measurement for genetically modified materials in foods and feeds

Food and feed analysts are confronted with a number of common problems, irrespective of the analytical target. The analytical procedure can be described as a series of successive steps: sampling, sample processing, analyte extraction, and ending, finally, in interpretation of an analytical result produced with, e.g., real-time polymerase chain reaction. The final analytical result is dependent on proper method selection and execution and is only valid if valid methods (modules) are used throughout the analytical procedure. The final step is easy to validate-the measurement uncertainty added from this step is relatively limited and can be estimated with a high degree of precision. In contrast, the front-end sampling and processing steps have not evolved much, and the corresponding methods are rarely or never experimentally validated according to internationally harmonized protocols. In this paper, we outlined a strategy for modular validation of the entire analytical procedure, using an upstream validation approach, illustrated with methods for genetically modified materials that may partially apply also to other areas of food and feed analyses. We have also discussed some implications and consequences of this approach in relation to reference materials, measurement units, and thresholds for labelling and enforcement, and for application of the validated methods (modules) in routine food and feed analysis.     

Comparison of different approaches to estimate the uncertainty of a liquid chromatographic assay

A measurement result cannot be properly interpreted without knowledge about its uncertainty. Several concepts to estimate the uncertainty of a measurement result have been developed. Here, four different approaches for uncertainty estimation are compared on the example of the RP-high-performance liquid chromatography (HPLC) assay for tylosin for veterinary use: the guide to the expression of uncertainty in measurement (GUM) approach, which derives the uncertainty of a measurement result by combining the uncertainties related to the uncertainty sources of the measurement process; the top-down approach, which uses the reproducibility estimate from an inter-laboratory study as uncertainty estimate; an approach recently presented by Barwick and Ellison, which combines precision, trueness and robustness data to obtain an uncertainty estimate of the measurement result and finally a further approach, which directly estimates the measurement uncertainty from a robustness test. The comparison shows that the different approaches lead to comparable uncertainty estimates.     

Assessment of permissible ranges for results of pH-metric acid number determinations using uncertainty calculation

 An approach to assess the permissible ranges for results of replicate determinations using uncertainty calculation is discussed. The approach is based on the known range distribution for normalized "range/standard deviation" values, which is equivalent to the distribution of the range for normalized results of replicate determinations having an average of 0 and a standard deviation of 1. It is shown that the permissible ranges can be assessed using tabulated percentiles of this distribution and calculated values of the determination (analysis) standard uncertainty. When the standard uncertainty calculation is performed before the analytical method validation, the permissible ranges can be predicted. As an example, the range is predicted for a new pH-metric method for acid number determination without titration in petroleum oils (basic, white and transformer). The results of the prediction are in good conformity with the experimental data. Received: 23 May 1999 · Accepted: 14 November 1999     

The evaluation of measurement uncertainty from method validation studies

 A protocol has been developed illustrating the link between validation experiments, such as precision, trueness and ruggedness testing, and measurement uncertainty evaluation. By planning validation experiments with uncertainty estimation in mind, uncertainty budgets can be obtained from validation data with little additional effort. The main stages in the uncertainty estimation process are described, and the use of trueness and ruggedness studies is discussed in detail. The practical application of the protocol will be illustrated in Part 2, with reference to a method for the determination of three markers (CI solvent red 24, quinizarin and CI solvent yellow 124) in fuel oil samples. Received: 10 April 1999 / Accepted: 24 September 1999     

A Monte Carlo approach for estimating measurement uncertainty using standard spreadsheet software

Despite the importance of stating the measurement uncertainty in chemical analysis, concepts are still not widely applied by the broader scientific community. The Guide to the expression of uncertainty in measurement approves the use of both the partial derivative approach and the Monte Carlo approach. There are two limitations to the partial derivative approach. Firstly, it involves the computation of first-order derivatives of each component of the output quantity. This requires some mathematical skills and can be tedious if the mathematical model is complex. Secondly, it is not able to predict the probability distribution of the output quantity accurately if the input quantities are not normally distributed. Knowledge of the probability distribution is essential to determine the coverage interval. The Monte Carlo approach performs random sampling from probability distributions of the input quantities; hence, there is no need to compute first-order derivatives. In addition, it gives the probability density function of the output quantity as the end result, from which the coverage interval can be determined. Here we demonstrate how the Monte Carlo approach can be easily implemented to estimate measurement uncertainty using a standard spreadsheet software program such as Microsoft Excel. It is our aim to provide the analytical community with a tool to estimate measurement uncertainty using software that is already widely available and that is so simple to apply that it can even be used by students with basic computer skills and minimal mathematical knowledge.