Total sampling error

Thus the TOS introduces both the correct and incorrect sampling errors, CSE and ISE. At all particnlar sampling stages, these combine to the total samphng error (TSE)  

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Process Analytical Technology 3.2.10 Total sampling error... 

K.H. Esbensen, H.H. Eriis-Petersen, L. Petersen, J.B. Hohn-Nielsen and P.P. Mortensen, Representative process sampling - in practice variographic analysis and estimation of Total Sampling Errors (TSE). Proceedings 5 th Winter Symposium of Chemometrics (WSC-5), Samara 2006. Chemom. Intell. Lab. Syst, Special Issue, 88(1), 41—19 (2007). 

Estimations based on statistics can be made for total accuracy, precision, and reproducibility of results related to the sampling procedure being applied. Statistical error is expressed in terms of variance. Total sampling error is the sum of error variance from each step of the process. However, discussions herein will take into consideration only step (1)—mechanical extraction of samples. Mechanical-extraction accuracy is dependent on design reflecting mechanical and statistical factors in carrying out efficient and practical collection of representative samples S from a bulk quantity B. 

The total sampling error is made up of errors due to the primary sampling, subsequent sample dividing and errors in the analysis itself Sampling is said to be accurate when it is free from bias, that is, the error of sampling is a random variable about the true mean. Sampling is precise when the error variation is small irrespective of whether the mean is the true mean or not. The ultimate that may be obtained by representative sampling may be called the perfect sample the difference between this sample and the bulk may be ascribed wholly to the expected difference on a statistical basis. Errors in particle size analysis may be due to ... 

Delimitation and extraction errors contribute to both bias and variation, and bias is very difficult to detect unless a special effort is made. As a result, the magnitude of these errors is often unknown and frequently underestimated. It would be extremely unfortunate to learn of a bias via a lawsuit. To avoid bias, a proper tool must be chosen and used correctly. Even if the right equipment is available, additional error is added to the total sampling error if the equipment is not used correctly. 

Intuitively, we can think of the total sampling error as the discrepancy between the sample value and the true but unknown lot value. Gy parses it into component parts, allowing us to reduce this total error by eliminating one or more of the components or moderating their effects. In some cases the word error means mistake in other cases it... 

The second error, the grouping and segregation error (GE), is also related to the material variation, in this case the distribution heterogeneity. At the level of the small scale where we actually take a sample, particles may segregate by particle size or shape. If we cannot select material totally at random, then our sample will be biased. In addition, we sample groups of particles, not one at a time as in SRS. So in addition to the unavoidable FE, we have an additional component in bulk sampling that contributes to our total sampling error. The GE is not present in classical SRS. 

Finally, a plan for reducing the total sampling error can be started in a straightforward way. Using the information in this chapter, you can audit sampling procedures. 

With the AMS technique only 0.25 liter of sea water is required. Generally a 0.5 liter water sample is collected at sea and poisoned with HgCU to halt all biological activity. The water is returned to the laboratory and acidified, and the CO2 is extracted and purified. An aliquot of the CO2 is analyzed to determine and the remainder is converted to carbide and counted by AMS. Counting error for the AMS technique can be <2 ppt, however, replicate analysis shows the total sample error to be approximately 4.5 ppt. 

When an analyst performs a single analysis on a sample, the difference between the experimentally determined value and the expected value is influenced by three sources of error random error, systematic errors inherent to the method, and systematic errors unique to the analyst. If enough replicate analyses are performed, a distribution of results can be plotted (Figure 14.16a). The width of this distribution is described by the standard deviation and can be used to determine the effect of random error on the analysis. The position of the distribution relative to the sample s true value, p, is determined both by systematic errors inherent to the method and those systematic errors unique to the analyst. For a single analyst there is no way to separate the total systematic error into its component parts. 

Modern transducers and microprocessors have been used successfully to automate particulate sampling trains in order to eliminate the operating curves and manual adjustments (7). The automated samplers adjust continuously to maintain isokinetic conditions. In addition, the microprocessor continuously calculates and displays both instantaneous sampling conditions and the total sample volume collected at any given moment. The use of the automated system with the microprocessor, therefore, eliminates both operator and calculation errors. 

The errors arising in sampling, particularly in the case of heterogeneous solids, may be the most important source of uncertainty in the subsequent analysis of the material. If we represent the standard deviation of the sampling operation (the sampling error) by ss and the standard deviation of the analytical procedures (the analytical error) by sA, then the overall standard deviation sT (the total error) is given by... 

Example 1. If the sampling error is +3 per cent and the analytical error is 1 per cent, from equation (1) we can see that the total error sT is given by... 

If, in the above example, the analytical error was 0.2 per cent then the total error sT would be equal to 3.006 per cent. Hence the contribution of the analytical error to the total error is virtually insignificant. Youden7 has stated that once the analytical uncertainty is reduced to one-third of the sampling uncertainty, further reduction of the former is not necessary. It is most important to realise that if the sampling error is large, then a rapid analytical method with relatively low precision may suffice. 

For local exploration, samples with relative higher PGE contents, about 5% of the total, are selected for the duplicate determination to monitor sub-sampling error. 

The nugget effect causes sub-sampling errors in PGE determinations. Previously, large sub-samples (30 g) of all samples were analyzed to decrease sub-sampling errors. This is not cost-effective. Our new approach is firstly, a 10 g sub-sample is used for the routine analysis of all samples secondly, samples with anomalous values are selected for duplicate or triplicate determinations, and the average value of these determinations is considered trustworthy. The selection of these samples is mainly based on the Pt/Pd ratio, statistics of RD% of coded duplicate analyses and total batch data distributions. 

For the sake of completeness, of conrse analytical resnlts also inclnde the total analytical error (TAE) in addition to all sampling errors. The snm of these two categories is termed the global estimation error (GEE), which thus includes all possible errors which could ever be of interest in PAT ... 

The purpose of the statistical analysis is to estimate the bias and the precision (measured by the CVp of the total precision error of a subject method) and resolve the latter error into components CVg due to the sampling method (less pump error), due to the analytical method (including error in the desorption efficiency factor), and CVp (an assumed level of pump error). Appendix II gives the definitions and computational formulae for the statistical analysis. 

If the concentration at the face of the sampler fluctuates there is the possibility that the concentration inside the sampler air gap will not reflect the actual ambient concentration. The sampler would then not provide a true integrated response to the exposure concentrations. The response time of passive samplers is typically 1-10 seconds and provided that the total sampling time is large relative to the response time, errors will be small (Brown, 1993). 

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