Step 2: Identifying Uncertainty Sources

6.1. A comprehensive list of relevant sources of uncertainty should be assembled. At this stage, it is not necessary to be concerned about the quantification of individual components; the aim is to be completely clear about what should be considered. In step 3, the best way of treating each source will be considered.

6.2. In forming the required list of uncertainty sources it is usually convenient to start with the basic expression used to calculate the measurand from intermediate values. All the parameters in this expression may have an uncertainty associated with their value and are therefore potential uncertainty sources. In addition there may be other parameters that do not appear explicitly in the expression used to calculate the value of the measurand, but which nevertheless affect the measurement results, e.g. extraction time or temperature. These are also potential sources of uncertainty. All these different sources should be included.

6.3. The cause and effect diagram described in appendix d is a very convenient way of listing the uncertainty sources, showing how they relate to each other and indicating their influence on the uncertainty of the result. It also helps to avoid double counting of sources. Although the list of uncertainty sources can be prepared in other ways, the cause and effect diagram is used in the following chapters and in all of the examples in appendix a. Additional information is given in appendix c (Structure of Analytical Procedures) and in appendix d (Analysing uncertainty sources).

6.4. Once the list of uncertainty sources is assembled, their effects on the result can, in principle, be represented by a formal measurement model, in which each effect is associated with a parameter or variable in an equation. The equation then forms a complete model of the measurement process in terms of all the individual factors affecting the result. This function may be very complicated and it may not be possible to write it down explicitly. Where possible, however, this should be done, as the form of the expression will generally determine the method of combining individual uncertainty contributions.

6.5. It may additionally be useful to consider a measurement procedure as a series of discrete operations (sometimes termed unit operations), each of which may be assessed separately to obtain estimates of uncertainty associated with them. This is a particularly useful approach where similar measurement procedures share common unit operations. The separate uncertainties for each operation then form contributions to the overall uncertainty.

6.6. In practice, it is more usual in analytical measurement to consider uncertainties associated with elements of overall method performance, such as observable precision and bias measured with respect to appropriate reference materials. These contributions generally form the dominant contributions to the uncertainty estimate, and are best modelled as separate effects on the result. It is then necessary to evaluate other possible contributions only to check their significance, quantifying only those that are significant. Further guidance on this approach, which applies particularly to the use of method validation data, is given in section 7.2.1.

6.7. Typical sources of uncertainty are

  • Sampling
    Where in-house or field sampling form part of the specified procedure, effects such as random variations between different samples and any potential for bias in the sampling procedure form components of uncertainty affecting the final result.
  • Storage Conditions
    Where test items are stored for any period prior to analysis, the storage conditions may affect the results. The duration of storage as well as conditions during storage should therefore be considered as uncertainty sources.
  • Instrument effects
    Instrument effects may include, for example,the limits of accuracy on the calibration of an analytical balance; a temperature controller that may maintain a mean temperature which differs (within specification) from its indicated set-point; an auto-analyser that could be subject to carry-over effects.
  • Reagent purity
    The molarity of a volumetric solution will not be known exactly even if the parent material has been assayed, since some uncertainty related to the assaying procedure remains. Many organic dyestuffs, for instance, are not 100% pure and can contain isomers and inorganic salts. The purity of such substances is usually stated by manufacturers as being not less than a specified level. Any assumptions about the degree of purity will introduce an element of uncertainty.
  • Assumed stoichiometry
    Where an analytical process is assumed to follow a particular reaction stoichiometry, it may be necessary to allow for departures from the expected stoichiometry, or for incomplete reaction or side reactions.
  • Measurement conditions
    For example, volumetric glassware may be used at an ambient temperature different from that at which it was calibrated. Gross temperature effects should be corrected for, but any uncertainty in the temperature of liquid and glass should be considered. Similarly, humidity may be important where materials are sensitive to possible changes in humidity.
  • Sample effects
    The recovery of an analyte from a complex matrix, or an instrument response, may be affected by composition of the matrix. Analyte speciation may further compound this effect.
    The stability of a sample/analyte may change during analysis because of a changing thermal regime or photolytic effect.
    When a 'spike' is used to estimate recovery, the recovery of the analyte from the sample may differ from the recovery of the spike, introducing an uncertainty which needs to be evaluated.
  • Computational effects
    Selection of the calibration model, e.g. using a straight line calibration on a curved response, leads to poorer fit and higher uncertainty.
    Truncation and round off can lead to inaccuracies in the final result. Since these are rarely predictable, an uncertainty allowance may be necessary.
  • Blank Correction
    There will be an uncertainty on both the value and the appropriateness of the blank correction. This is particularly important in trace analysis.
  • Operator effects
    Possibility of reading a meter or scale consistently high or low.
    Possibility of making a slightly different interpretation of the method.
  • Random effects
    Random effects contribute to the uncertainty in all determinations. This entry should be included in the list as a matter of course.

NOTE: These sources are not necessarily independent.