Uncertainty profiles for the validation of analytical methods

This article aims to expose a new global strategy for the validation of analytical methods and the estimation of measurement uncertainty. Our purpose is to allow to researchers in the field of analytical chemistry get access to a powerful tool for the evaluation of quantitative analytical procedures. Indeed, the proposed strategy facilitates analytical validation by providing a decision tool based on the uncertainty profile and the β-content tolerance interval. Equally important, this approach allows a good estimate of measurement uncertainty by using data validation and without recourse to other additional experiments.In the example below, we confirmed the applicability of this new strategy for the validation of a chromatographic bioanalytical method and the good estimate of the measurement uncertainty without referring to any extra effort and additional experiments. A comparative study with the SFSTP approach [1] showed that both strategies have selected the same calibration functions.The holistic character of the measurement uncertainty compared to the total error was influenced by our choice of profile uncertainty. Nevertheless, we think that the adoption of the uncertainty in the validation stage controls the risk of using the analytical method in routine phase.     

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.     

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.     

Do we need to consider metrological meanings of different measurement uncertainty estimations?

Along the years, several approaches for measurement uncertainty estimation have been suggested. Emphasis has been put on the general metrological interpretation of measurement uncertainty, but not on its different meanings when it is associated to given conditions of measurement where analytical work is performed and errors are originated. Three different definitions for uncertainty are proposed for reproducibility and intermediate precision conditions of measurement. These definitions inherit features from the VIM 3 definition of measurement uncertainty. It is argued that if a high performance laboratory keeps errors under control with proper validation and quality assurance programs, measurement uncertainty from intermediate precision condition of measurement is justified as a suitable estimation of its capability to attribute values to a measurand. Alternatively, a laboratory that does not keep errors under control should use uncertainty from reproducibility condition of measurement as the cost of its imperfections. Selection of information sources for measurement uncertainty estimation should be in harmony with its metrological meaning.     

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.     

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.     

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     

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.     

Measurement uncertainty

Measurement uncertainty is a statistical parameter which describes the possible fluctuations of the result of a measurement. It is not a mere repeatability but it is at least as high as the intra-laboratory reproducibility. If it is an attribute of a general analytical test procedure it is at least as high as the inter-laboratory reproducibility. Measurement uncertainty can be determined by the addition of the variances of the individual steps of the test procedure or by an approach which starts with one of the above-mentioned reproducibilities. Any measurement uncertainty should be kept low but it is objectionable to state too low a value, e.g. by falsely reporting mere repeatability data instead of properly determined uncertainty data. Some good working principles can help to obtain low measurement uncertainties.     

The uncertainty in the calculation of the amount of blocked and reactive lysine in milk products,as determined by the furosine method

The measurement uncertainty in the calculation of the amount of blocked and reactive lysine (as determined by the furosine method) was evaluated according to the procedure described in the Eurachem/CITAC guide. The analytical method involves the chromatographic determination of lysine and furosine after acid hydrolysis. The calculation of blocked and reactive lysine in the initial protein is based on known conversion factors. The estimation of the uncertainty was performed in two steps: (1) determination of the uncertainty in the chromatographic determination of lysine and furosine, and (2) determination of the uncertainty in the calculation of blocked and reactive lysine. The individual contributions to the final uncertainty were identified, quantified, and combined in uncertainty budgets. The largest contribution to the calculation of blocked lysine came from estimating the conversion factor of blocked lysine into furosine during acid hydrolysis. For the calculation of reactive lysine, the main contribution came from the chromatographic determination of lysine. The uncertainty estimates were compared to available validation data (in-house and collaborative standard deviations of reproducibility).     

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.     

Calibration, handling repeatability, and the Maximum Permissible Error of single-volume glass instruments

The influence quantities for the uncertainty of a volumetric operation with glass instruments are calibration, repeatability and temperature. In the literature, measurement uncertainty budgets can be found, which count all three quantities separately although calibration and repeatability are merged in tabulated data to the Maximum Permissible Error. We propose that this error should be handled as a rectangular distribution in order to get a standard uncertainty. For the daily use in an analytical laboratory, the combined standard uncertainty of a volumetric operation is thus calculated from the Maximum Permissible Error plus the uncertainty of the temperature influence.     

Quantifying uncertainty in the measurement of arsenic in suspended particulate matter by Atomic Absorption Spectrometry with hydride generator

Arsenic is the toxic element, which creates several problems in human being specially when inhaled through air. So the accurate and precise measurement of arsenic in suspended particulate matter (SPM) is of prime importance as it gives information about the level of toxicity in the environment, and preventive measures could be taken in the effective areas. Quality assurance is equally important in the measurement of arsenic in SPM samples before making any decision. The quality and reliability of the data of such volatile elements depends upon the measurement of uncertainty of each step involved from sampling to analysis. The analytical results quantifying uncertainty gives a measure of the confidence level of the concerned laboratory. So the main objective of this study was to determine arsenic content in SPM samples with uncertainty budget and to find out various potential sources of uncertainty, which affects the results. Keeping these facts, we have selected seven diverse sites of Delhi (National Capital of India) for quantification of arsenic content in SPM samples with uncertainty budget following sampling by HVS to analysis by Atomic Absorption Spectrometer-Hydride Generator (AAS-HG). In the measurement of arsenic in SPM samples so many steps are involved from sampling to final result and we have considered various potential sources of uncertainties. The calculation of uncertainty is based on ISO/IEC17025: 2005 document and EURACHEM guideline. It has been found that the final results mostly depend on the uncertainty in measurement mainly due to repeatability, final volume prepared for analysis, weighing balance and sampling by HVS. After the analysis of data of seven diverse sites of Delhi, it has been concluded that during the period from 31^st Jan. 2008 to 7^th Feb. 2008 the arsenic concentration varies from 1.44 ± 0.25 to 5.58 ± 0.55 ng/m³ with 95% confidence level (k = 2).     

Using target measurement uncertainty to determine fitness for purpose

The methods an analytical laboratory uses must be validated to be fit for purpose. The fitness for purpose of a quantitative method used to determine the concentration of a substance when assessing compliance to requirements can be described by the maximum measurement uncertainty. This is called the target measurement uncertainty. Acceptance criteria for precision and bias in the method validation are then established in terms of the target measurement uncertainty. The target measurement uncertainty can be decided by following a process which involves determining the required concentration range of the measurand; determining the acceptable level of risks of incorrect decisions of compliance; developing a suitable decision rule, with guard bands if appropriate; using the probability of making an incorrect decision of compliance based on the decision rule; and assessing the impact of bias. A key participant in this process is the end user of the data, the laboratory customer. This paper presents the concepts concerning target measurement uncertainty introduced in recently published international guidelines to the practicing analytical chemist who is not generally familiar with these concepts. Three examples are used to illustrate the process.     

Uncertainty sources in UV-Vis spectrophotometric measurement

An overview is given of the most important uncertainty sources that affect analytical UV-Vis spectrophotometric measurements. Altogether, eight uncertainty sources are discussed that are expected to have influence in chemical analysis. It is demonstrated that the well-known intrinsic (or “physical”) sources of uncertainty that originate from the instrument itself (repeatability of spectrophotometer reading, spectrophotometer drift, stray light, etc.) often have significantly lower contributions to the combined uncertainty of the result than the “chemical” sources of uncertainty that originate from the object under study (interference from the constituents of the matrix, decomposition of the photometric complex, etc.). Although selectivity of a photometric procedure is often considered more a validation topic than an uncertainty topic, it is very often important to include it also in the uncertainty budget.Usually the most difficult part of uncertainty estimation of a chemical measurement result is to evaluate the magnitude of the actual uncertainty components, especially the chemical ones. For most of the uncertainty sources discussed in this paper, approaches for their evaluation are given. A generic uncertainty budget for absorbance is presented. Electronic Supplementary Material Supplementary material is available for this article at     

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.     

Method validation approach on the basis of a quadratic regression model

A method validation approach that bases on a quadratic regression model in which two types of error are incorporated is presented and applied to an experimental data set. The validation approach enables the determination of analytical performance characteristics referred to in Commission Decision 2002/657/EC (i.e., repeatability, within-laboratory reproducibility, decision limit, detection capability).     

A global approach to method validation and measurement uncertainty

The enforcement of legal limits for food safety raises the question of decision-making in the context of uncertain measurements. It also puts the question of demonstrating that measurement technique that is used is fit for the purpose of controlling legal limits. A recent European Commision (EC) decision gives some indications how to deal with this question. In the meantime, the implementation of quality systems in analytical laboratories is now a reality. While these requirements deeply modified the organization of the laboratories, it has also improved the quality of the results. The goal of this communication is to describe how two fundamental requirements of ISO 17025 standard, i.e. validation of the methods and estimation of the uncertainty of measurements, can give a way to check whether an analytical method is correctly fit for the purpose of controlling legal limits. Both these requirements are not independent and it will be shown how they can be combined. A recent approach based on the “accuracy profile” of a method was applied to the determination of acrylamide and illustrates how uncertainty can be simply derived from the data collected for validating the method. Moreover, by basing on the β-expectation tolerance interval introduced by Mee [Technometrics (1984) 26(3): 251–253], it is possible to unambiguously demonstrate the fitness for purpose of a method. Remembering that the expression of uncertainty of the measurement is also a requirement for accredited laboratories, it is shown that the uncertainty can be easily related to the trueness and precision issuing from the data collected to build the method accuracy profile. The example presented here consists in validating a method for the determination of acrylamide in pig plasma by liquid chromatography–mass spectromery (LC–MS). Concentrations are expressed as mg/l and instrumental response is peak surface. The calibration experimental design included 5×5×2 measurements and namely consisted in preparing duplicate standard solutions at five concentration levels ranging from 10 to about 5000 mg/l. This was repeated for 5 days. The validation experimental design was similar.     

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.