Uncertainty, of analytical results

Maroto, A., Riu, J., Boque, R., and Rius, F. X. (1999). Estimating uncertainties of analytical results using information from the validation process, Anal. Chim. Acta, 391, 173-185. 

Random error is an error resulting from typical fluctuations in the experimental field. The value decreases in the case of multiple designation of the same analyte in samples of the same material. It is not possible to calculate this error for a single result, nor to predict its value. In spite of their low value, these errors are the basis for calculating precision and are a component of the uncertainty of analytical results [2]. 

Initial QC is devoted to assuring that analytical methods and detection devices are suitable for the purpose of the program and includes estimating the uncertainty of analytical results. Subsequent methodological QC efforts during data processing evaluate the acceptability of the results and add information on the degree of reliability. 

In order to estimate the uncertainty of analytical results, the propagation of error cannot be considered alone for a single effect, for example, the reproducibility of the instrumental measurement, but all sources of uncertainty are to be taken into account for all steps of the analytical procedure. 

In our example, we will take this proposal for granted. Again, we focus attention on the expected uncertainty of analytical results to reach our objective in optimizing methods. 

Bi-functional radio-analytical scheme, based on exchange and extraction column chromatography, which provides the reliable information on molybdenum and uranium contents in biological materials has been elaborated. The contribution of uranium fission reaction has been strictly monitored. The uncertainty of the results of Mo determination by the presented method is very low. 

On most occasions CRMs are used as Quality Control materials, rather than as calibrations . As outlined above, this common application adds significantly to the user s uncertainty budget, since at a minimum it is necessary to consider at least two independent measurement events (Um). so increasing the combined uncertainty of the results. Again this process rapidly increases the combined uncertainty with increasing complexity of the analytical system and so the usefulness of a control analysis may be downgraded when a correct uncertainty budget is formulated. 

If users are to benefit from the implementation and/or verification of traceability in analytical chemistry the unbroken pathway of references must be kept short. The uncertainty of the references (CRMs) used may significantly widen the uncertainty a user must attach to the result of his measiuement when addressing accuracy and traceability through comparison with a CRM. These comparisons should be only considered in a first or second level step as to keep the uncertainties of the results within limits fit for the purpose. The producers of CRMs must keep their uncertainties sufficiently small to allow introduction of the CRM at different points in the analytical pathway, without limiting the usefiilness of results through unduly expanded uncertainties. 

Fundamentally, the uncertainties of measured values y estimated by calibration, e.g. according to Eq. (6.6), on the one hand and of analytical results x (analyte contents, concentrations) estimated by means of a calibration function, e.g. according to Eq. (6.17), on the other hand differ from one another as can be seen from Fig. 6.3B,C, and Fig. 6.7. Whereas the uncertainty of y values in calibration is characterized by the confidence interval cnf(y), the uncertainty of estimated x values is characterized by the prediction interval prd(x). 

Quantification Precision can be quantified by suitable dispersion characteristics. It is proposed to characterize precision by standard deviation, see Eqs. (4.12)-(4.14) and relative standard deviation, see Eq. (4.15) (Fleming et al. [1996b] Prichard et al. [2001]). Because of some uncertainty, the characterization of analytical proceedings in their hierarchy (see Fig. 7.1) and of analytical results, respectively, will be considered in detail. 

Formally, an analytical result x,- can be calculated from y, by means of the corresponding calibration function. When this result (from repeated measurements) should be reported, it must be taken into account that the relative uncertainty amounts minimally 100% (see Sect. 7.5, item (1) p. 201) and, therefore, it holds that (x x)- That means, that the uncertainty interval of analytical results calculated from measured values nearby the critical value covers a range of about 0... 2x. As additional information, the limit of quantification, xLq, should be given. 

The uncertainty of the results between the detection limit and the limit of quantification decreases continuously up to the precision set in advance by the precision factor k. In reaching and exceeding the quantification limit, analytical results can be reported as usual see Sect. 8.1. 

Evaluation and validation of analytical results and their uncertainty... 

Six 25 ml volumetric flasks are filled with 10 ml of the analyte and then 1, 2, 3, 4, 5 and 6 ml of a standard solution containing 6.5 x 10 3 moll-1 of the same analyte. 5.00 ml of color-developing reagent is added to each flask and enough distilled water is added to bring each flask to exactly 25.0 ml. The absorbances of the five solutions were 0.236, 0.339, 0.425, 0.548, 0.630 and 0.745, respectively. Use a spreadsheet to obtain a graph of the data and extrapolate the data to obtain the information needed to determine the initial concentration of the analyte. From the data, estimate the uncertainty of the result. 

Introduction Quality of Analytical Results Role of Method Validation in Traceability and MU Guidelines on Traceability and Uncertainty of Results Concept of Traceability Concept of MU... 

The process of providing an answer to a particular analytical problem is presented in Figure 2. The analytical system—which is a defined method protocol, applicable to a specified type of test material and to a defined concentration rate of the analyte —must be fit for a particular analytical purpose [4]. This analytical purpose reflects the achievement of analytical results with an acceptable standard of accuracy. Without a statement of uncertainty, a result cannot be interpreted and, as such, has no value [8]. A result must be expressed with its expanded uncertainty, which in general represents a 95% confidence interval around the result. The probability that the mean measurement value is included in the expanded uncertainty is 95%, provided that it is an unbiased value which is made traceable to an internationally recognized reference or standard. In this way, the establishment of trace-ability and the calculation of MU are linked to each other. Before MU is estimated, it must be demonstrated that the result is traceable to a reference or standard which is assumed to represent the truth [9,10]. 

The purpose of an analytical method is the deliverance of a qualitative and/or quantitative result with an acceptable uncertainty level. Therefore, theoretically, validation boils down to measuring uncertainty . In practice, method validation is done by evaluating a series of method performance characteristics, such as precision, trueness, selectivity/specificity, linearity, operating range, recovery, LOD, limit of quantification (LOQ), sensitivity, ruggedness/robustness, and applicability. Calibration and traceability have been mentioned also as performance characteristics of a method [2, 4]. To these performance parameters, MU can be added, although MU is a key indicator for both fitness for purpose of a method and constant reliability of analytical results achieved in a laboratory (IQC). MU is a comprehensive parameter covering all sources of error and thus more than method validation alone. 

CX/MAS 02/13 (2002), Codex Alimentarius Commission, Codex Committee on Methods of Analysis and Sampling (FAO/WHO),The use of analytical results Sampling, relationship between the analytical results, the measurement uncertainty, recovery factors and the provisions in Codex standards, agenda item 9 of the 24th session, Budapest, Hungary, Nov. 18-22, 2002. 

This consideration of the principles of diffusive sampling identifies a range of factors which may influence the performance of a diffusive sampler for monitoring VOC concentrations in indoor air. These factors will potentially be a source of error in such measurements and add to the overall uncertainty of the result given by the measurement procedure. In addition the amount of uncertainty will be influenced by other factors including amount and consistency of background contamination of sorbents, repeatability of analytical determination, formation of artifacts, stability of analyte on the sorbent, recovery of analyte during analyses and presence of interferents. 

Abstract For ensuring the traceability and uniformity of measurement results, the main objectives of national metrology programmes in chemistry are to calibrate and verify measuring instruments, to evaluate the uncertainty of measurement results and to intercompare the analytical results, etc. The concept of traceability has developed recently in chemical measurements, thus, an attempt to implement the principles of metrological traceability especially by appropriateness calibration using composition certified reference materials (CRMs) is underlined. Interlaboratory comparisons are also a useful response to the need for comparable results. The paper presents some aspects and practices in the field of spec-... 

Abstract Establishment of the traceability and the evaluation of the uncertainty of the result of a measurement are essential in order to establish its comparability and fitness for purpose. There are both similarities and differences in the way that the concepts of traceability and uncertainty have been utilised in physical and chemical measurement. The International Committee of Weights and Measures (CIPM) have only in the last decade set up programmes in chemical metrology similar to those that have been in existence for physical metrology for over a century. However, analytical chemists over that same period have also developed techniques, based on the concepts of traceability and uncertainty, to ensure that their results are comparable and fit for purpose. This paper contrasts these developments in physical and chemical metrology and identifies areas where these two disciplines can learn from each other. 

RM certification is the whole process of obtaining the property values and their uncertainties, which includes homogeneity testing, stability testing, and RM characterization [5]. ISO Guide 35 [1] requires one to show that the value of such a certified property does not exhibit a systematic error specific to a method or to a laboratory. By widespread opinion, correctness of analytical results is an obvious prerequisite for the RM characterization in contrast to stability and homogeneity studies in which analytical bias is acceptable [5]. 

Keywords Traceability Measurement uncertainty Reference materials Quality of analytical results... 

Traceability and uncertainty of measurement results are basic technical elements of quality systems in analytical laboratories whose competence is recognized by accreditation according to ISO/IEC 17025 [24]. However, GLP and GMP standards widely used since the 1960s for the... 

The need to carry out both QA and QC in order to achieve the expected quality of analytical results immediately generates the requirement for clearly defined performance criteria. These criteria enable comparability to be achieved via the traceability of analytical results to national or international standards along an unbroken chain of comparisons. Validation is the central task in the development of any analytical method whose capabilities in specific applications can be assessed with the aid of measurement uncertainty. Finally, proficiency testing (PT) serves to demonstrate comparability in terms of the scatter of the results.3... 

Worldwide acceptance of analytical results requires reliable, traceable, and comparable measurements. A key property of a reliable result is its traceability to a stated reference. Traceability basically means that a laboratory knows what is being measured and how accurately it is measured. It is also an important parameter where comparability of results is concerned and is usually achieved by linking the individual result of chemical measurements to a commonly accepted reference or standard. The result can therefore be compared through its relation to that reference or standard. Every link in the traceability chain must be based on the comparison of an unknown value with a known value. The stated reference might be an International System of unit (SI) or a conventional reference scale such as the pH scale, the delta scale for isotopic measurements, or the octane number scale for petroleum fuel. In order to be able to state the uncertainty of the measurement result, the uncertainty of the value assigned to that standard must be known. Therefore a traceability chain should be designed and then demonstrated using the value of the respective standard with its uncertainty.11... 

Quality of Analytical Results Classifiying Errors and Estimating Measurement Uncertainty... 

Values are means standard errors for 2 years of data. Numbers of observations range from 15 (HNO3) to 26 (particles) to 128 (precipitation) to 730(802). In comparing these deposition rates it must be recalled that any such estimates are subject to considerable uncertainty. The standard errors given provide only a measure of uncertainty in the calculated sample means relative to the population means hence additional uncertainties in analytical results, hydrologic measurements, scaling factors, and deposition velocities must be included. The overall uncertainty for wet deposition fluxes is about 20% and that for dry deposition fluxes is approximately 50% for SOj", Ca ", K", and approximately 75% for NOj" and... 

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