Variances and uncertainties of the sample laboratory-to-laboratory variance (S(L)2) and standard deviation (S(L)) associated with an interlaboratory study

The validation process for an analytical method usually employs an interlaboratory study conducted as a balanced completely randomized model involving a specified number of randomly chosen laboratories, each analyzing a specified number of randomly allocated replicates. For such studies, formulas to obtain approximate unbiased estimates of the variance and uncertainty of the sample laboratory-to-laboratory (lab-to-lab) STD (S(L)) have been developed primarily to account for the uncertainty of S(L) when there is a need to develop an uncertainty budget that includes the uncertainty of S(L). For the sake of completeness on this topic, formulas to estimate the variance and uncertainty of the sample lab-to-lab variance (S(L)2) were also developed. In some cases, it was necessary to derive the formulas based on an approximate distribution for S(L)2.     

LC method for the determination of R-timolol in S-timolol maleate: Validation of its ability to quantify and uncertainty assessment

This article presents the validation results of a chiral liquid chromatographic (LC) method previously developed for the quantitative determination of R-timolol in S-timolol maleate samples. A novel validation strategy based on the accuracy profiles was used to select the most appropriate regression model, to assess the method accuracy within well defined acceptance limits and to determine the limits of quantitation as well as the concentration range.The validation phase was completed by the investigation of the risk profiles of various acceptable regression models in order to ensure the risk of obtaining the future measurements outside the acceptance limits fixed a priori.On the other hand, the present paper also shows how data used in this validation approach can be used to estimate the measurement uncertainty. The uncertainty derived from β-expectation tolerance interval (), which is equal to the uncertainty of measurements as well as the expanded uncertainty (U_x) using a coverage factor k = 2 was estimated. The uncertainty estimates obtained from validation data were finally compared with those obtained from interlaboratory and robustness studies.     

Relationship between performance characteristics obtained from an interlaboratory study programme and combined measurement uncertainty: a case study

 In the interlaboratory study programme "ILS Coal Characterisation", eight interlaboratory studies were organised based on the ISO standards for coal analysis. The use of blind samples in each round allows comparability of measurement results between rounds to be assessed. Based on the results, it could be demonstrated that the vast majority of the measurement results of the laboratories were traceable to results obtained in previous rounds of this programme. The hypothesis has been formulated that the combined standard uncertainty obtained from an interlaboratory study is equal to the reproducibility standard deviation. Whether the reproducibility can be used as the basis for the certification depends on whether the interlaboratory study includes all effects to be taken into account for establishing an uncertainty statement. Received: 12 April 1998 · Accepted: 2 July 1998     

Estimating measurement uncertainty in an afternoon. A case study in the practical application of measurement uncertainty

The ISO/IEC 17025:1999 standard requires chemical testing laboratories to have an estimate of the uncertainty of their measurements. This is a new requirement for many laboratories and there is confusion as to how to estimate uncertainty. Concerns have been raised about the time and effort required to obtain uncertainty estimates.Uncertainty budgets were prepared for the measurement of benzene, toluene, ethyl benzene and xylenes (BTEX) in water using purge and trap coupled with GC/MS. A time limit of one working afternoon (2 pm–5.30 pm) was imposed for preparing the uncertainty estimate. Details of the uncertainty estimate for toluene are described.The method in question had been in routine use for several years and the laboratory held third party (NATA) accreditation for the test. Consequently a considerable amount of performance data was readily available. Relevant information was extracted from the documented test method, validation data, instrument calibration and from routine quality control. This data was combined according to the principles of the ISO Guide to the Expression of Uncertainty, as promulgated in the Eurachem document "Quantifying Uncertainty in Analytical Measurement."The uncertainty estimates were compared to estimates obtained from generalised empirical models (the Horwitz and Lowthian equations), and from interlaboratory studies of this analysis.A traceability chain from routine measurements to the SI units of metre, kilogram and mole is described.Realistic and useful uncertainty estimates were obtained with a few hours work using data extant in the laboratory.     

From GUM to alternative methods for measurement uncertainty evaluation

Since the advent of the Guide to the expression of Uncertainty in Measurement (GUM) in 1995 laying the principles of uncertainty evaluation numerous projects have been carried out to develop alternative practical methods that are easier to implement namely when it is impossible to model the measurement process for technical or economical aspects. In this paper, the author presents the recent evolution of measurement uncertainty evaluation methods. The evaluation of measurement uncertainty can be presented according to two axes based on intralaboratory and interlaboratory approaches. The intralaboratory approach includes “the modelling approach” (application of the procedure described in section 8 of the GUM, known as GUM uncertainty framework) and “the single laboratory validation approach”. The interlaboratory approaches are based on collaborative studies and they are respectively named “interlaboratory validation approach” and “proficiency testing approach”.     

Quantitation of 35S promoter in maize DNA extracts from genetically modified organisms using real-time polymerase chain reaction, part 2: interlaboratory study

The European Committee for Standardization (CEN) and the European Network of GMO Working Laboratories have proposed development of a modular strategy for stepwise validation of complex analytical techniques. When applied to the quantitation of genetically modified organisms (GMOs) in food products, the instrumental quantitation step of the technique is separately validated from the DNA extraction step to better control the sources of uncertainty and facilitate the validation of GMO-specific polymerase chain reaction (PCR) tests. This paper presents the results of an interlaboratory study on the quantitation step of the method standardized by CEN for the detection of a regulatory element commonly inserted in GMO maize-based foods. This is focused on the quantitation of P35S promoter through using the quantitative real-time PCR (QRT-PCR). Fifteen French laboratories participated in the interlaboratory study of the P35S quantitation operating procedure on DNA extract samples using either the thermal cycler ABI Prism 7700 (Applied Biosystems, Foster City, CA) or Light Cycler (Roche Diagnostics, Indianapolis, IN). Attention was focused on DNA extract samples used to calibrate the method and unknown extract samples. Data were processed according to the recommendations of ISO 5725 standard. Performance criteria, obtained using the robust algorithm, were compared to the classic data processing after rejection of outliers by the Cochran and Grubbs tests. Two laboratories were detected as outliers by the Grubbs test. The robust precision criteria gave values between the classical values estimated before and after rejection of the outliers. Using the robust method, the relative expanded uncertainty by the quantitation method is about 20% for a 1% Bt176 content, whereas it can reach 40% for a 0.1% Bt176. The performances of the quantitation assay are relevant to the application of the European regulation, which has an accepted tolerance interval of about +/-50%. These data were fitted to a power model (r2 = 0.96). Thanks to this model, it is possible to propose an estimation of uncertainty of the QRT-PCR quantitation step and an uncertainty budget depending on the analytical conditions.     

Measurement of near zero concentration: recording and reporting results that fall close to or below the detection limit

Issues relating to the recording and reporting of analytical data obtained where the concentration of analyte is around or below the detection limit are discussed. The following recommendations are proposed. Analytical results should be recorded by the analyst exactly as they occur, including any negative results, and such records retained for an appropriate length of time. For the purposes of quality assurance in the laboratory (including method validation, internal quality control, and proficiency testing), negative results should be used as they stand. Analytical results reported to a customer should be accompanied by a statement of uncertainty including, in the present context, uncertainty at low concentrations of analyte. The method of editing of reported results must be a contractual matter between the analyst and the customer, but a statement of the procedure used should accompany the results and should be explicit. Normally such editing should be restricted to setting negative results to zero. The customer should be encouraged to pass on the statement to all end users. Data intended for the public domain should be accompanied by a statement detailing the uncertainty, the method of editing, and the location of the unedited data. Most types of statistical processing of datasets containing low concentrations of analyte should be undertaken on the unedited data.     

Determination of niacin in infant formula by solid-phase extraction/liquid chromatography: peer-verified method performance-interlaboratory validation

This paper reports the results of the interlaboratory peer validation study of AOAC Peer-Verified Method (PVM) 1:2,000 for the determination of niacin in infant formula by solid-phase extraction/liquid chromatography. We have used a Data Quality Objectives (DQO) approach to address not only method variability and robustness but also accuracy of data through the use of an appropriate reference material in conjunction with the interlaboratory validation study. Our DQO included the following: (1) statistical agreement of analytical results and quantitative recovery between 2 collaborating laboratories; (2) the repeatability relative standard deviation (RSDr) values and the HORRAT (Horwitz ratio) obtained (1.07), which satisfied the criteria of the Horwitz "limits of acceptability" at the analyte level present; (3) validation of lack of interference; and (4) accuracy agreement within assigned values for a certified reference material. National Institute of Standards and Technology Standard Reference Material (NIST SRM) 1846 Infant Formula, with a certified value of 63.3 +/- 7.6 microg/g for niacin content, was used as a test material for collaborative study and accuracy assessment. Niacin values obtained by the originating laboratory were 59.7 +/- 4.0 microg/g (95% confidence interval [CI] = 1.4 microg/g with a relative standard deviation [RSD] of 6.7%) and by the peer laboratory were 56.6 +/- 6.6 microg/g (95% CI = 4.1 microg/g, with an RSD of 11.7%). Statistical evaluation using the means equivalence test showed that nicotinic acid values obtained by the peer laboratory were equivalent to those values obtained by the originating laboratory. Linear calibration curves and quantitative recovery were obtained. Integration of the PVM process with a readily available certified reference material gives the user confidence in the accuracy of the data generated by the method through traceability to the reference material used.     

Evaluation of “method uncertainty” in the calibration of piston pipettes (micropipettes) using the gravimetric method in accordance with the procedure of ISO 8655-6

The gravimetric method specified by ISO 8655-6 is a standard method for calibrating piston pipettes (micropipettes). The quality of the calibration can be assessed by uncertainty evaluation, the procedure for which is described in ISO/Technical Report (TR) 20461. However, the existence of “method uncertainty” due to ambiguity in the calibration operation, which is not described in the TR, has been found in various experiments, such as the interlaboratory comparison of CCM.FF-K4.2.2011. In this report, the “method standard uncertainty” is quantified as exp(?4.51 + 0.36 ln(V ^nom/μL) + 0.05{ln(V ^nom/μL)}²) μL for a nominal volume, V ^nom, in the range from 2 μL to 10000 μL. Furthermore, the reported values in an interlaboratory comparison are confirmed to be consistent using the quantified method standard uncertainty.     

Estimation of measurement uncertainty in the determination of orthophosphates in seawater by continuous flow analysis (CFA)

Phosphorus is the second most important limiting nutrient for the growth of autotrophic organisms in coastal and oceanic environments and is present in a wide range of chemical forms both dissolved and particulate. Within the dissolved inorganic fraction of phosphorus, orthophosphates are the so-called soluble reactive phosphorus. This nutrient, as a central element in coastal and oceanic biogeochemical cycles, is one of the compounds measured for the physico-chemical quality indices established by the Water Framework Directive 2000/60/EC and one of the characteristics to be measured in the Marine Strategy Framework Directive 2008/56/EC. In this work, an estimation of the measurement uncertainty in the determination of orthophosphates in seawater by continuous flow analysis, based on ISO 15681-2:2003, in the range of 10–150 μg/L as P was carried out by means of a global model of uncertainty quantification from validation data. The results were coherent with previous interlaboratory comparisons of orthophosphates in seawater. Expanded uncertainty did not exceed 6.5 % in the entire range.     

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.     

Measurement uncertainty of food carotenoid determination

For consistent interpretation of an analytical method result it is necessary to evaluate the confidence that can be placed in it, in the form of a measurement uncertainty estimate. The Guide to the expression of Uncertainty in Measurement issued by ISO establishes rules for evaluating and expressing uncertainty. Carotenoid determination in food is a complex analytical process involving several mass transfer steps (extraction, evaporation, saponification, etc.), making difficult the application of these guidelines. The ISO guide was interpreted for analytical chemistry by EURACHEM, which includes the possibility of using intra- and interlaboratory information. Measurement uncertainty was estimated based on laboratory validation data, including precision and method performance studies, and also, based on laboratory participation in proficiency tests. These methods of uncertainty estimation were applied to analytical results of different food matrices of fruits and vegetables. Measurement uncertainty of food carotenoid determination was 10–30% of the composition value in the great majority of cases. Higher values were found for measurements near instrumental quantification limits (e.g. 75% for β-cryptoxanthin, and 99% for lutein, in pear) or when sample chromatograms presented interferences with the analyte peak (e.g. 44% for α-carotene in orange). Lower relative expanded measurement uncertainty values (3–13%) were obtained for food matrices/analytes not requiring the saponification step. Based on these results, the saponification step should be avoided if food carotenoids are not present in the ester form. Food carotenoid content should be expressed taking into account the measurement uncertainty; therefore the maximum number of significant figures of a result should be 2.     

A practical procedure for assigning a reference value and uncertainty in the frame of an interlaboratory comparison

A method is suggested for the calculation of a reference value and its uncertainty to be used in the frame of an interlaboratory comparison (ILC). It is assumed that the reference value of the measurand is determined independently from the ILC round. It is derived from a limited set of measurement results obtained from one or several expert laboratories. The procedure involves three stages: (1) check of the experimental data and possible corrections; (2) check of the consistency of data, and possibly increase of the uncertainties in order to attain internal consistency; (3) choice between fully, partially or un-weighted mean.     

Determination of butoxyacetic acid (biomarker of ethylene glycol monobutyl ether exposure) in human urine candidate reference material

Ethylene glycol monobutyl ether (EGBE), an industrial solvent, is absorbed by the body not only by inhalation but also by dermal absorption (liquid or vapour). EGBE is metabolized to butoxyacetic acid (BAA). Pooled freeze-dried urine candidate reference material (RM) was prepared from urine obtained from persons occupationally exposed to EGBE. This material has the advantage of containing butoxyacetic acid in both the free and conjugated (glutamine and glycine) forms, as found in native urine. In all GC method modifications used, acid hydrolysis was used to release BAA from its conjugated form. The amount of butoxyacetic acid in homogeneity and stability testing was measured by GC after derivatisation with N-tert-butyldimethylsilyl-N-methyltrifluoroacetamide. Detection was by MS in EI mode, in the authors’ laboratory. For interlaboratory comparison of the reference material GC methods with MS, FID, and ECD were used. Different extraction solvents (dichloromethane–isopropanol 2:1, ethyl acetate, or dichloromethane) and derivatisation reagents (trimethylsilyldiazomethane, N-tert-butyldimethylsilyl-N-methyltrifluoroacetamide) were used. Using ANOVA (at the statistical level α = 0.05) no changes were found in the concentration of butoxyacetic acid during fifteen month isochronous stability testing, or in homogeneity testing. The uncertainty contributions were u _h = 8.8 mg L⁻¹ and u _s = 6.5 mg L⁻¹. The concentration of butoxyacetic acid in freeze-dried urine RM was evaluated from the results of eight laboratory data sets within an interlaboratory comparison by use of the interactive statistical software IPECA. The contribution to total uncertainty derived from interlaboratory comparison was u _i = 12.7 mg L⁻¹. The reference value (c = 273 ± 33 mg L⁻¹) is an unweighted arithmetic average of accepted results. The value is traceable to the pure butoxyacetic acid (98% w/w; Acros Organic #257760010) used as calibrant. The uncertainty given is combined expanded uncertainty derived from the results from interlaboratory comparison, and from homogeneity and stability tests (k = 2). The reference material will be used to verify method performance in the biological monitoring of occupational exposure to EGBE.     

Reference values of urinary 3,5,6-trichloro-2-pyridinol in the Italian population--validation of analytical method and preliminary results (multicentric study)

The interlaboratory validation of analytical procedures for the assay of urinary 3,5,6-trichloro-2-pyridinol (TCP) in the general Italian population is reported. The determinations were performed by high-resolution gas chromatography (HRGS) with electron capture detection and HRGS with mass spectrometry (MS) in 2 laboratories. The urine samples were from 42 participants from 3 regions of Italy. The results were evaluated by interlaboratory quality control. Urinary TCP concentrations were above the detection limit (1.2 micrograms/L) in 88% of the population, with a mean detectable concentration [GM (GSD)] of 2.8 (1.9) micrograms/g creatinine (creat). (GM, geometric mean; GSD, geometric standard deviation.) The Mann-Whitney U test showed that wine consumption was a statistically significant variable (p < 0.05) for urinary concentrations of TCP. Analysis of variance of the logarithm of urinary TCP versus wine consumption and diet showed a statistically significant fit. The model used explained 30% of the total variance: wine consumption and diet accounted for 37 and 17% respectively of the explained variance.     

ELISA kit for mustard protein determination: interlaboratory study

An interlaboratory study in 12 laboratories was performed to prove the validation of the ELISA method developed for the quantitative determination of mustard protein in foods. The ELISA kit used for this study is based on rabbit polyclonal antibody. This kit did not produce any false-positive results or cross-reactivity with in-house validation for a broad range of food matrixes with no detectable mustard protein. All participants obtained the Mustard ELISA kit with standard operational procedures, a list of samples, samples, and a protocol for recording test results. The study included 15 food samples and two spiked samples. Seven food matrix samples of zero mustard content and four samples with mustard declared as an ingredient showed mustard protein content lower than that of the first standard (0.42 mg/kg). Four samples with mustard declared as an ingredient revealed mustard protein content above 12.5 mg/kg (the highest standard). The statistical tests (Cochran, Dixon, and Mandel) and analysis of variance were used to evaluate the interlaboratory study results. Repeatability and reproducibility limits, as well as an LOQ (1.8 mg mustard proteins/kg) and LOD (0.5 mg mustard proteins/kg), for the kit were calculated.     

Analysis of interlaboratory performance in the determination of total selenium in water

This study explored the performance of experienced laboratories in the analysis for total selenium in water by a variety of analytical methods. The goal of the study was to examine intra- and interlaboratory variability. Replicates (n = 7) of 7 sample types that included a reference material of known Se concentration, natural waters, and treated wastewaters were submitted to 7 laboratories with prequalified Se analytical experience. Results of the study indicated wide ranges in minimum and maximum results, distinct differences in laboratory precision, and routine reporting of numerical results below statistical limits of quantitation. Hydride generation as a sample introduction technique demonstrated superior performance. In general, the study supports a caution advisory about using low-level Se data, especially results lower than about 10 micrograms Se/L, without quantitating the statistical uncertainty of the data. Because this study used data from samples that were submitted in bulk to participating laboratories prequalified for Se analytical expertise and experience, it can be considered a best-case demonstration of performance.