Optimised uncertainty at minimum overall cost to achieve fitness-for-purpose in food analysis.

An optimised uncertainty (OU) methodology is described, that balances the uncertainty of measurements on food against the cost of the measurements and the other expenditure that may arise as a consequence of the possible misclassification of the food. Measurement uncertainty from the sources of primary sampling and chemical analysis is estimated using an existing technique, which is based on the taking of duplicated samples and duplicated analyses. The input information required for the OU method is the actual costs of sampling and analysis, and the expected costs that could arise from either the 'false positive' or 'false negative' classification of batches of food. A loss function is then constructed that calculates the 'expectation of loss' which will arise for a given uncertainty of measurement. This function has a minimum value of cost at an optimal value of uncertainty, which can be estimated numerically. Application of this OU method to a case study on the determination of aflatoxin levels in pistachio nuts has demonstrated this minimum value. Below the optimum value of uncertainty, the costs increased due to higher measurement costs. Above the optimum value, the costs increased due to increasing probability of expenditure on consequences such as unnecessary rejection of the batch, potential litigation or loss of corporate reputation because of undetected contamination. A second stage of the OU method optimises the division of the expenditure on the measurement between that on sampling and that on analysis. The technique is demonstrated as a useful new approach for judging the fitness-for-purpose of chemical measurements in the food industry. Several areas for further development of the technique are identified. By matching the expenditure on the measurement against that caused by the misclassification of the food, the OU method has the potential to reduce overall expenditure whilst ensuring an appropriate reliability of measurement.     

Optimising uncertainty in physical sample preparation

Uncertainty associated with the result of a measurement can be dominated by the physical sample preparation stage of the measurement process. In view of this, the Optimised Uncertainty (OU) methodology has been further developed to allow the optimisation of the uncertainty from this source, in addition to that from the primary sampling and the subsequent chemical analysis. This new methodology for the optimisation of physical sample preparation uncertainty (u(prep), estimated as s(prep)) is applied for the first time, to a case study of myclobutanil in retail strawberries. An increase in expenditure (+7865%) on the preparatory process was advised in order to reduce the s(prep) by the 69% recommended. This reduction is desirable given the predicted overall saving, under optimised conditions, of 33,000 pounds Sterling per batch. This new methodology has been shown to provide guidance on the appropriate distribution of resources between the three principle stages of a measurement process, including physical sample preparation.     

Optimised uncertainty in food analysis: application and comparison between four contrasting 'analyte-commodity' combinations

The optimised uncertainty (OU) methodology is applied across a range of analyte-commodity combinations. The commodities and respective analytes under investigation were chosen to encompass a range of input factors: measurement costs (sampling and analytical), sampling uncertainties, analytical uncertainties and potential consequence costs which may be incurred as a result of misclassification. Two types of misclassification are identified-false compliance and false non-compliance. These terms can be used across a wide range of foodstuffs that have regulations requiring either minimum compositional requirements, maximum contaminant allowances or compositional specifications. The latter refers to foodstuffs with regulations that state an allowable tolerance around the compositional specification, i.e. the upper specification limit (USL) and the lower specification limit (LSL). The traditional OU methodology has been adapted so that it is applicable in these cases and has been successfully applied in practice. The Newton-Raphson method has been used to determine the optimal uncertainty value for the two case studies in which analyte concentration is assessed against a 'single threshold' regulatory requirement. This numerical method was shown to give a value of the optimal uncertainty that is practically identical to that given by the previously used method of visual inspection. The expectation of financial loss was reduced by an average of 65% over the four commodities by the application of the OU methodology, showing the benefit of the method.     

Multi-analyte optimisation of uncertainty in infant food analysis

The Optimised Uncertainty (OU) methodology has been developed to optimise multi-analyte situations. It has then been applied to a retail survey of infant food for trace elements, classifying the food as compliant or non-compliant with the regulatory thresholds or specification limits that are appropriate for each element. The large-scale survey of infant foods was successfully adapted to allow the estimation of uncertainties, from both primary sampling and chemical analysis, for elemental concentrations in infant formula (milk) and wet meals. The analytes included in this investigation comprised both contaminants (Pb and Cd) and elements essential for child development (Zn and Cu). Optimisation of the measurement process for a 'single analyte' demonstrated the potential financial benefits of optimising future surveys for a false compliance scenario. Uncertainty estimates for the measurement of elemental concentrations in infant formula were dominated by uncertainty from the analytical method. Large potential savings (up to pounds 575,000 per batch) are predicted for both Pb and Zn by increasing the expenditure on chemical analysis to the optimal level. In comparison the uncertainty estimates for elemental concentration in wet meals showed a dominance of sampling as a source of uncertainty for Cd and Cu due to the increased heterogeneity. The feasibility of 'multi-analyte' optimisation is demonstrated for the case study of infant milk. Single analyte optimisation of the four analytes for a false compliance scenario indicated a decrease in expectations of financial loss of between 99% and 8%. An overall decrease in the total expectation of financial loss of 99% is indicated following multi-analyte optimisation.     

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.     

X射线荧光光谱法同时测定矿石中铀和钍

建立了X射线荧光光谱法测定矿石样品中铀、钍含量的快速分析方法。采用高压粉末制样法,对不同含量的放射性样品的压片压力、粒径、含水率、用量等处理条件到进行单因素实验。在400 MPa压力下压制,克服了低压制样的弊端,制备的样片表面光滑、致密,大幅改善了制样重现性,有效地减少了部分基体效应,铀校准曲线的标准偏差从0.053%降到0.0071%,钍校准曲线的标准偏差从0.062%降到0.0057%。经国家一级标准物质验证,表明方法准确、可靠,能满足样品中铀、钍含量日常分析要求。     

Soil sampling uncertainty on arable fields estimated from reference sampling and a collaborative trial

On three fields of arable land of (3–6)×10⁴ m², simple reference sampling was performed by taking up to 195 soil increments from each field applying a systematic sampling strategy. From the analytical data reference values for 15 elements were established, which should represent the average analyte mass fraction of the areas. A “point selection standard deviation” was estimated, from which a prediction of the sampling uncertainty was calculated for the application of a standard sampling protocol (X-path across the field, totally 20 increments for a composite sample). Predicted mass fractions and associated uncertainties are compared with the results of a collaborative trial of 18 experienced samplers, who had applied the standard sampling protocol on these fields. In some cases, bias between reference and collaborative values is found. Most of these biases can be explained by analyte heterogeneity across the area, in particular on one field, which was found to be highly heterogeneous for most nutrient elements. The sampling uncertainties estimated from the reference sampling were often somewhat smaller compared to those from the collaborative trial. It is suspected that the influence of sample preparation and the variation due to sampler were responsible for these differences. For the applied sampling protocol, the uncertainty contribution from sampling generally is in the same range as the uncertainty contribution from analysis. From these findings, some conclusions were drawn, especially about the consequences for a sampling protocol, if in routine sampling a demanded “certainty of trueness” for the measurement result should be met.     

On the measurement of the moisture content in different matrix materials

Twelve different samples were analyzed for their water content by the classical oven-drying method and a commercial moisture analyzer. Nominal values have been set by Karl Fischer titration and gravimetry. The decomposition during the drying process of samples containing organic compounds was checked by thermogravimetry coupled with Fourier transform infrared spectrometric and mass spectrometric detection. Summarizing all measurement results, the commercial moisture analyzer demonstrated an average bias for the determination of water contents, which is much smaller than the stated uncertainty and thus is negligible. Compared to the classical oven-drying method, the commercial moisture analyzer shows a smaller bias, more ease in handling and less time consumption per analysis. When validated by a reference procedure like Karl Fischer titration the commercial moisture analyzer is the method of choice for routine analysis.     

Non-enzymatic electrochemical detection of glycerol on boron-doped diamond electrode

A non-enzymatic direct electrochemical glycerol detection method at a commercial boron-doped diamond (BDD) electrode in 0.1 M NaOH supporting electrolyte was developed. All the used electrochemical techniques proved useful features for the oxidation and direct amperometric determination of glycerol at a BDD electrode in 0.1 M NaOH aqueous solution. It was found that the direct electrooxidation of glycerol on the BDD electrode requires both adsorbed glycerol and hydroxyls at the electrode surface. Also, the sp(2) carbon did not allow enhancement of the glycerol oxidation process. The electronalytical sensitivity for the determination of glycerol at the BDD electrode ranged from 0.040 to 0.226 μA mM(-1) as a function of the technique used. The highest electroanalytical sensitivity for the determination of glycerol at the BDD electrode was reached in batch system amperometric quantification under stirring conditions. Performed recovery studies indicated that it is possible to determine glycerol in real samples, and the proposed batch system analysis-based methodology can be a valuable tool for practical glycerol analysis.     

The duplicate method of uncertainty estimation: are eight targets enough?

This paper presents methods for calculating confidence intervals for estimates of sampling uncertainty (s(samp)) and analytical uncertainty (s(anal)) using the chi-squared distribution. These uncertainty estimates are derived from application of the duplicate method, which recommends a minimum of eight duplicate samples. The methods are applied to two case studies--moisture in butter and nitrate in lettuce. Use of the recommended minimum of eight duplicate samples is justified for both case studies as the confidence intervals calculated using greater than eight duplicates did not show any appreciable reduction in width. It is considered that eight duplicates provide estimates of uncertainty that are both acceptably accurate and cost effective.     

粮食水分的测量和电子水分仪测量不确定度的评定

介绍粮食中水分的两种测量方法：烘干称重法和电测法。同一台水分仪测量不同品种的粮食可能有不同的不确定度,一台水分仪要存入多条工作曲线用以测量不同品种粮食的含水量。介绍了电子水分仪测量不确定度的评定方法。     

A case study in the practical estimation of measurement uncertainty

This case study is written for analytical laboratories, in order to give support to the implementation of the concept of measurement uncertainty for routine measurements. The aim is to provide a practical, understandable and common way of performing measurement uncertainty calculations, based mainly on pre-existing quality control and validation data. Practical examples taken directly from environmental laboratory monitoring are presented and explained. However, the approach is very general and should be applicable to most testing laboratories in the chemical field. Following the protocol of evaluation illustrated in the case study, it is possible to ensure that most relevant uncertainty components associated with the method are covered. Contributions associated with sampling, homogenisation, sub-sampling, and so on, are, however, excluded.     

Application of 1,10-phenanthroline for preconcentration of selected heavy metals on silica gel

Stripping voltammetry analysis using a hemispheroidal mercury microelectrode has been previously assessed theoretically as a possible candidate ‘primary method’ for amount of substance measurement. It was shown that the measurement methodology can be described completely by a set of measurement equations when a novel quantification process is employed to measure the steady-state diffusion-limited deposition current over an optimum sampling time, instead of employing an analyte stripping step. The corollary is that, for solutions of known composition, the method may be used for highly accurate determination of diffusion coefficients. This investigation uses experimental data from steady-state diffusion-limited current measurements with sampling periods optimised using Allan deviation techniques, together with a full uncertainty analysis to estimate feasibility and likely accuracy of this method.     

Uncertainty in analytical results from solid materials with electrothermal atomic absorption spectrometry: a comparison of methods

The combined uncertainty in the analytical results of solid materials for two methods (ET-AAS, analysis after prior sample digestion and direct solid sampling) are derived by applying the Guide to the Expression of Uncertainty in Measurement from the International Standards Organization. For the analysis of solid materials, generally, three uncertainty components must be considered: (i) those in the calibration, (ii) those in the unknown sample measurement and (iii) those in the analytical quality control (AQC) process. The expanded uncertainty limits for the content of cadmium and lead from analytical data of biological samples are calculated with the derived statistical estimates. For both methods the expanded uncertainty intervals are generally of similar width, if all sources of uncertainty are included. The relative uncertainty limits for the determination of cadmium range from 6% to 10%, and for the determination of lead they range from 8% to 16%. However, the different uncertainty components contribute to different degrees. Though with the calibration based on reference solutions (digestion method) the respective contribution may be negligible (precision < 3%), the uncertainty from a calibration based directly on a certified reference material (CRM) (solid sampling) may contribute significantly (precision about 10%). In contrast to that, the required AQC measurement (if the calibration is based on reference solutions) contributes an additional uncertainty component, though for the CRM calibration the AQC is “built-in”. For both methods, the uncertainty in the certified content of the CRM, which is used for AQC, must be considered. The estimation of the uncertainty components is shown to be a suitable tool for the experimental design in order to obtain a small uncertainty in the analytical result.     

Measurement uncertainty from physical sample preparation: estimation including systematic error

A methodology is proposed, which employs duplicated primary sampling and subsequent duplicated physical preparation coupled with duplicated chemical analyses. Sample preparation duplicates should be prepared under conditions that represent normal variability in routine laboratory practice. The proposed methodology requires duplicated chemical analysis on a minimum of two of the sample preparation duplicates. Data produced from the hierarchical design is treated with robust analysis of variance (ANOVA) to generate uncertainty estimates, as standard uncertainties ('u' expressed as standard deviation), for primary sampling (ssamp), physical sample preparation (sprep) and chemical analysis (sanal). The ANOVA results allow the contribution of the sample preparation process to the overall uncertainty to be assessed. This methodology has been applied for the first time to a case study of pesticide residues in retail strawberry samples. Duplicated sample preparation was performed under ambient conditions on two consecutive days. Multi-residue analysis (quantification by GC-MS) was undertaken for a range of incurred pesticide residues including those suspected of being susceptible to loss during sample preparation procedures. Sampling and analytical uncertainties dominated at low analyte concentrations. The sample preparation process contributed up to 20% to the total variability and had a relative uncertainty (Uprep%) of up to 66% (for bupirimate at 95% confidence). Estimates of systematic errors during physical sample preparation were also made using spike recovery experiments. Four options for the estimation of measurement uncertainty are discussed, which both include and exclude systematic error arising from sample preparation and chemical analysis. A holistic approach to the combination and subsequent expression of uncertainty is advised.     

A pilot study of routine quality control of sampling by the SAD method, applied to packaged and bulk foods

A recently proposed method of looking at sampling uncertainty has been tested by its application to the sampling and analysis of several types of food and an animal feedstuff. In this 'SAD' method, increments comprising the conventional sample (that is, collected in the fashion prescribed by the standard sampling protocol) are allocated to either of two equal sized 'splits', which are prepared and analysed separately. The absolute difference between the analytical results for the two splits (the split absolute difference, or SAD) is plotted on a one-sided control chart. A non-compliance indicates that the combined uncertainty of sampling or analysis is larger than expected and the result of the measurement (the mean of the two split results) is possibly not fit for purpose. In addition, the SAD results give rise to a rugged estimate the uncertainty associated with the sampling protocol, often a major part of the total measurement uncertainty.     

Modifying uncertainty from sampling to achieve fitness for purpose: a case study on nitrate in lettuce

Existing methods have been applied to estimate the uncertainty of measurement, caused by both sampling and analysis, and fitness-for-purpose of these measurements. A new approach has been taken to modify the measurement uncertainty by changing the contribution made by the sampling process. A case study on nitrate in lettuce has been used to demonstrate the applicability of this new generic approach. The sampling theory of Gy was used to predict the alterations in the sampling protocol required to achieve the necessary change in sampling uncertainty. An experimental application of this altered sampling protocol demonstrated that the predicted change in sampling uncertainty was achieved in practice. For the lettuce case study, this approach showed that composite samples containing 40 heads, rather than the usual ten heads, produced measurements of nitrate that where more fit-for-purpose.     

Multidetermination of PCBs and pesticides by use of a dual GC column-dual detector system

Summary A new gas chromatographic method involving the use of two capillary columns, a switching valvue and electron capture-nitrogen-phosphorus detection, and allowing up to four retention characteristics per component to be obtained is reported.The proposed method was applied to the analysis for 123 compounds (13 PCBs and 110 pesticides), the determination limits and optimal measuring ranges of which are reported.The performance of the method was checked by analysis of certified standards and spiked samples, and was applied to the determination of the analytes in various water samples.     

A decision theory approach to fitness for purpose in analytical measurement

The choice of an analytical procedure and the determination of an appropriate sampling strategy are here treated as a decision theory problem in which sampling and analytical costs are balanced against possible end-user losses due to measurement error. Measurement error is taken here to include both sampling and analytical variances, but systematic errors are not considered. The theory is developed in detail for the case exemplified by a simple accept or reject decision following an analytical measurement on a batch of material, and useful approximate formulae are given for this case. Two worked examples are given, one involving a batch production process and the other a land reclamation site.     

Flow injection analysis : Part II. Ultrafast determination of phosphorus in plant material by continuous flow spectrophotometry

The effect of sample volume, tube length, tube diameter, peak height and sampling rate on the determination of phosphorus in acidic plant digests was investigated, and optimal conditions for the flow injection method are described. Sampling rates of 420 samples per hour were achieved without incurring problems from carryover of samples, and evidence was obtained that rates as high as 700 samples per hour are possible. The flow injection method was proved to be suitable for routine analyses and has obvious advantages over other automated or manual methods in sampling rate, simplicity of design and cost.