Uncertainty component

How can this situation arise It is because most certification bodies are not in a position to consider other uncertainty components than those associated with the certification process. 

Such a parameter may be, e.g., standard deviation, or a given multiple of it, or a one-sided confidence interval attributed to a fixed level of confidence. In general, uncertainty of measurement comprises many components. These uncertainty components are subdivided into... 

Occasionally, both these uncertainty components are denoted (i) as type A - and (ii) as type B uncertainties. 

The quantification should start with a rough estimation of the order of magnitude of each uncertainty contribution pi and pij. Insignificant one can be neglected because the uncertainty components are added according to a squared model. The significant values should be refined in subsequent stages and converted to parameters u(pf) which correspond to standard deviations. 

During validation, the relationship between response and concentration is established. Checks also are made to ensure that the linearity of the method does not make too large a contribution to the measurement uncertainty (the uncertainty due to the calibration should contribute less than about 20% of the largest uncertainty component). The calibration schedule required during routine operation of the method is also established. It is wise to carry out sufficient checks on some or all of the following performance parameters, in order to establish that their values meet any specified limits. 

One consequence of the equations for combining standard uncertainties is that the combined standard uncertainty will be dominated by the largest uncertainty components. This is illustrated in Figure 6.14. 

When estimating the uncertainty of measurement, all uncertainty components Ahich are of importance in the g/ven situation shall be taken into account using appropriate methods of analysis... 

When expressed as a standard deviation, an uncertainty component is known as a standard uncertainty u... 

From the positive square root of the total variance obtained bycombining all the uncertainty components, however evaluated... 

If we have a complete list of sources we try to group those that are covered by existing data (e.g. from repeatability experiments). The next step is the quantification of the grouped components. Usually some components will remain that have to be quantified separately. Step 3 is finalised with the conversion of all uncertainty components into standard uncertainties. 

Some of the uncertainty components may be evaluated from the statistical distribution of the results ot series of measurements (e.g. repeated eighings)... 

Conversion of the uncertainty of a parameter into an uncertainty component of the result... 

If we don t have such an ideal control sample, but only one with a matrix different from the routine sample (e.g. a standard solution) than we have to consider also the uncertainty component arising from changes in the matrix. For this purpose we use the (repeatability) standard deviation calculated from repeated measurements of our routine samples (performed e.g. for a range control chart). When we estimate the reproducibility within laboratory we now have to combine both contributions by calculating the square root of the sum of squares. 

It is possible only to estimate uncertainty components f om repeatability ia the range control chart... 

The Jong-term uncertainty component (f om batch to batch) has... 

Uncertainty component from the uncertainty of the certified value ... 

If we are lueky and we have several CRMs available, the uncertainty of the bias determination is covered by the results of the measurement of the different materials. From the biases of each CRM analysis we calculate the root of the mean of squares as shown in the slide. Finally we combine this value with an average of the uncertainty of the certified value and we get the final uncertainty component. 

For the calculation of the bias itself we again use the root of the mean of squares of all biases. In the example shown we have 6 PT results. We calculate the relative bias of these values and then the RMSbias- Finally we combine the RMSbias with the uncertainty of the assigned value and we get the uncertainty component for the bias. 

We also can take suitable data from a proficiency test (PT). In this case the laboratory must have participated in the PT successfully. We also have to consider, if the PT covered all relevant uncertainty components and steps of analysis. This includes e.g. if the matrix of the PT sample was similar to routine samples. If this is the case, we again calculate U from 2 Sr. 

If the comparison covers all relevant uncertainty components and steps (matrix )... 

Estimating the uncertainty components associated with all influences and references. 

Some examples include evaluation of uncertainty components associated with published values (i.e., the analyst did not measure them), uncertainties in a certificate of a certified reference material, manufacturer s statements about the accuracy of an instrument, or perhaps even personal experience. The latter could be viewed as an opportunity for anyone to just make up an uncertainty, but experience does count for something, and it is indeed usually better than nothing. Leaving out a component because of lack of exact knowledge immediately underestimates the uncertainty. 

Interlaboratory studies usually provide the test material in a homogeneous form that can be subsampled without additional uncertainty. In the field, if the result is attributed to a bulk material from which the sample was drawn, then sampling uncertainty needs to be estimated. Again, proper definition of the measurand is important in understanding where to start adding in uncertainty components. 

It is important not to assume that this or that effect always has negligible uncertainty each factor must be assessed for a particular result. For example, in the quantitative NMR work in my laboratory, we could just see the effect of the uncertainty of molar masses. As a rule of thumb, if the uncertainty component is less than one-fifth of the total, then that component can be omitted. This works for two reasons. First, there are usually clear major components, and so the dangers of ignoring peripheral effects is not great, and second, components are combined as squares, so one that is about 20% of the total actually contributes only 4% of the overall uncertainty. There is a sort of chicken-and-egg dilemma here. How do you know that a component is one-fifth of the total without estimating it and without estimating the total And if you estimate the contribution of a factor to uncertainty,... 

Weighing on an appropriate balance is usually a very accurate procedure, and therefore is often a candidate for the insignificance test. Uncertainty components of weighing on a modern electronic balance are given in table 6.1. 

Measurement Uncertainty 179 Table 6.2. Uncertainty components of volume measurements... 

It is worthwhile to discuss the components of the standard uncertainty of a volume measurement here. The repeatability may be independently assessed by a series of fill-and-weigh experiments with water at a controlled temperature (and therefore density) using a balance so that the uncertainty of weighing is small compared with the variation in volume. Although this may be instructive, if the whole analysis is repeated, say, ten times, then the repeatability of the use of the pipette, or any other volume measurement is part of the repeatability of the overall measurement. This shows the benefit, in terms of reaching the final estimate of measurement uncertainty more quickly, of lumping together uncertainty components. 

Systematic effects are estimated by repeated measurements of a CRM, suitably matrix matched. Any difference between the CRM and a routine sample for which the measurement uncertainty is being estimated should be considered and an appropriate uncertainty component added. Suppose a concentration measurement is routinely made in a laboratory that includes measurement of a CRM in the same run as calibration standards and unknowns. The bias (6) is given by... 

Once the uncertainty components have been identified and quantified as standard uncertainties, the remainder of the procedure to estimate uncertainty is a somewhat complicated but mostly straightforward. Most software products on the market will perform this task. Otherwise, some spreadsheet manipulation or mathematics must be done to reach the uncertainty. The combined standard uncertainty of a result is obtained by mathematical manipulation of the standard uncertainties as part of the uncertainty budget. These standard uncertainties may also be combinations of other uncertainties, and so on, as the branches and sub-branches of the cause-and-effect diagram are worked through. A combined standard uncertainty of a quantity is written uc(y). 

The GUM approach described here has the advantage that each uncertainty component is designed to have the properties of a standard deviation, and so the rules for combining standard deviations of the normal distribution can be followed. The complete equation will be given, but it may be simplified to useable equations for the majority of applications. 

If the algebraic manipulations required by equation 6.21 are becoming too complicated, there is a spreadsheet method that gives the answer directly from the uncertainty components and the function for y. It relies on the fact that uncertainties are usually only a small fraction of the quantities (a few percent at most), and so the simplifying assumption may be made that, for... 

For more than one contributing uncertainty component, the u(y) calculated one x at a time can be squared and summed to give the square of the combined uncertainty. 

The simple equations used to combine uncertainty rely on the independence of the values of the components. Consider a titration volume calculated from the difference between initial and final readings of a burette and the three uncertainty components identified for volume in table 6.2. Repeatability should be genuinely random, and so the combined uncertainty of a difference measurement with repeatability u(r) is... 

Thus, if it is believed that the estimate of an uncertainty component is within 10% of the appropriate value (i.e., Au/u = 0.1) then there are 50 degrees of freedom. Degrees of freedom are exhausted when the uncertainty in the estimate reaches about 50%. For many Type estimates there is no uncertainty in the estimate and ve(( is infinite. Having determined the degrees of freedom of each uncertainty component, the effective degrees of freedom for the combined uncertainty is calculated from the Welch-Satterthwaite formula (Satterthwaite 1941), taking the integer value rounded down from... 

Figure 6.9. Bar charts of the uncertainty components in the quantitative NMR example.

---