Repeat determinations

An analytical procedure is often tested on materials of known composition. These materials may be pure substances, standard samples, or materials analyzed by some other more accurate method. Repeated determinations on a known material furnish data for both an estimate of the precision and a test for the presence of a constant error in the results. The standard deviation is found from Equation 12 (with the known composition replacing /x). A calculated value for t (Eq. 14) in excess of the appropriate value in Table 2.27 is interpreted as evidence of the presence of a constant error at the indicated level of significance. 

E) The number of repeat determinations performed on any one worked-up sample D. 

Particularly if the industry is government regulated (i.e., pharmaceuticals), but also if the supply contract with the customer stipulates numerical specification limits for a variety of quality indieators, the compliance question is legal in nature (rules are set for the method, the number of samples and repeat determinations) the analyst can then only improve precision by honing his/her skills,... 

Figure 1.8. Schematic frequency distributions for some independent (reaction input or control) resp. dependent (reaction output) variables to show how non-Gaussian distributions can obtain for a large population of reactions (i.e., all batches of one product in 5 years), while approximate normal distributions are found for repeat measurements on one single batch. For example, the gray areas correspond to the process parameters for a given run, while the histograms give the distribution of repeat determinations on one (several) sample(s) from this run. Because of the huge costs associated with individual production batches, the number of data points measured under closely controlled conditions, i.e., validation runs, is miniscule. Distributions must be estimated from historical data, which typically suffers from ever-changing parameter combinations, such as reagent batches, operators, impurity profiles, etc.

The quotient Q is fixed for a given situation. The problem could also be solved graphically by drawing a horizontal d.iy - Q m Figures 1.17 or 1.19 and taking the intercept as an estimate of n. The necessary number of repeat determinations n is depicted in Figure 1.26. 

The quintessential statistical operation in analytical chemistry consists in estimating, from a calibration curve, the concentration of an analyte in an unknown sample. If the regression parameters a and b, and the unknown s analytical response y are known, the most likely concentration is given by Eq. (2.19), y being the average of all repeat determinations on the unknown. 

Example 32 (see Section 2.2.1) assume that the measurement of a test article yields an absorbance of 0.445 what is the probable assay value Even for m = 10 repeat determinations, the true value of X(y ) is only loosely... 

Ok) function is sought by repeatedly determining the direction of steepest descent (maximum change in for any change in the coefficients a,), and taking a step to establish a new vertex. A numerical example is found in Table 1.26. An example of how the simplex method is used in optimization work is given in Ref. 143. 

It is interesting to see that the two curves for the photometer and the HPLC nearly coincide for the above assumptions, HPLC being a bit more expensive at the low end but much cheaper for the best attainable precisions. Note the structure that is evident especially in the photometer data This is primarily due to the number m of repeat determinations that are run on one sample... 

For each group of repeatedly determined signals mj > 2) the basic statistics are given. 

At each concentration xj the CV found for the group of mj repeat determinations is plotted and connected (dotted lines). 

At each concentration xj the relative confidence limits 100 t Sy/ymeanj found for the group of Mj repeat determinations is plotted and connected (dashed lines). Because file VALID2.dat contains only duplicate determinations at each concentration, n = 2 and / = 1, thus t(f, p = 0.05) = 12.7, the relative CL are mostly outside the 30% shown. By pooling the data for all 6 days it can be demonstrated that this laboratory has the method under control. 

Shades of Gray When repeat determinations are carried out on a sample and one or more of the individual results are outside the specs, the following criteria could apply ... 

The means resulting from several (k) repeat determinations on every of (j) samples and/or sample preparations must comply several such sample averages Xmean, would go into the over-all average Xmean,total-In the simplest case oi j = Ijk - 2 (duplicate determinations on each of two sample work-ups), both sample averages xji and Xj2 would have to comply. It could actually come to pass that repeat measurements, if foreseen in the SOP, would in this way not count as individual results this would cut the contribution of the measurement s SD towards the repeatability by v/2, x/3, etc. For true values /x that are less than 2-3 a from the limit, the OOS-risk would be reduced. 

Figure 4.34. The confidence limits of the mean of 2 to 10 repeat determinations are given for three forms of risk management. In panel A the difference between the true mean (103.8, circle ) and the limit L is such that for n = 4 the upper confidence limit (CLu, thick line) is exactly on the upper specification limit (105) the compound risk that at least one of the repeat measurements yi >105 rises from 23 n = 2) to 72% (n = 10). In panel B the mean is far enough from the SLj/ so that the CLu (circle) coincides with it over the whole range of n. In panel C the mean is chosen so that the risk of at least one repeat measurement being above the SLu is never higher than 0.05 (circle, corresponds to the dashed lines in panels A and B).

A sample of only 10 repeat determinations is statistically small, and far-reaching conclusions are hard to draw, particularly as far as the distribution of values is concerned. Claiming an extraordinarily high precision in the face of the alternative explanation—an average and very plausible precision—should raise eyebrows. 

Figure 4.39. Variability of back calculated concentrations Concbc- For each concentration range five calibration points were measured, over which a separate regression was run (not shown). Placebo tablets were spiked to the same concentrations and measured in triplicate (short horizontal lines gray trend lines in background). Ten repeat determinations of actual product (vertical bars = Mean + SD) were done. The bold lines pertain to compound A in all concentration ranges, the thin lines to compound B (middle concentration range only).

The HPLC method for which data are given had previously been shown to be linear over a wide range of concentrations what was of interest here was whether acceptable linearity and accuracy would be obtained over a relatively narrow concentration range around the nominal concentration in the product the specification limits were 90-110% of nominal. Three concentrations were chosen and three repeat determinations were carried out at each. Two different samples were prepared at each concentration, namely an aqueous calibration solution and a spiked placebo. All samples were worked up according to the method and appropriate aliquots were injected. The area counts are given in the second, respectively the fifth column of Table 4.42. 

Purpose Same as program LINREG it is assumed that repeat determinations were performed for most concentrations. (See VALlDl.dat.)... 

The relative standard deviation of ten repeated determinations of 500 ml distilled water containing 10 ng mercury (II) chloride was 17.4%. 

Whether or not the repeated determinations of column values are stable depends on the magnitudes of the increments h and k. In complex cases these may have to be found by trial. When kc = 0, however, it is known that the process is convergent when... 

Products were converted to the hydrochloride salt with IM HC1. The initial capacity determination on Ml (AgNO- titration) gave a value of 2.48 meq/g, calculated on free base. 00% conversion would give 3.88 meq/g. However, repeat determinations on the same sample gave values of 2.01 and 1.80 meq/g. Conversion of this sample to the hydrochloride with 0.1M HC1 resulted in a further drop to 1.66, and even eluting the nitrate form with 2M NaCl solution produced a further drop, to 1.57 meq/g. Evidently... 

A system similar to the one described above was used for determination of partition coefficients. A FIA system with segmented flow was devised so that the partitioning of a drug between aqueous buffer and chloroform could be measured. The aqueous and organic phases were separated using a phase separator. The system could be set up to measure the concentration of the drug in either the organic or the aqueous phase. Such a system enables rapid repeat determinations of partition coefficient at various pH values with minimal sample consumption." ... 

Once-daily dosing has potential practical advantages. For example, repeated determinations of serum concentrations are probably unnecessary unless aminoglycoside is given for more than 3 days. A drug administered once a day rather than three times a day saves time. And once-a-day dosing lends itself to outpatient therapy. 

If an estimate of the measurement uncertainty has been made and quoted for a single determination, it is possible to infer the measurement uncertainty for repeated determinations by going through the uncertainty budget and... 

Fig. 9. Time dependence of the relative viscosity of 1 g/dl of poly(isopropyl isocyanide in dichloroacetic acid at 30° C A original sample, B repeat determination after recycling the...

Experimental studies, particularly those involving the metabolism or mode of action of toxic compounds in animals (or, less often, plants), can be conducted either in vivo or in vitro. Because organisms or enzyme preparations are treated with known compounds, the question of random sampling techniques does not arise as it does with environmental samples. Enough replication is needed for statistical verification of significance, and it should always be borne in mind that repeated determinations carried out on aliquots of the same preparation do not represent replication of the experiment at best, they test the reproducibility of the analytical method. 

Many elements and compounds occur in a variety of matrices at concentrations that could not be detected by the analytical methods first developed in the nineteenth century. As analytical technology improved, and it became known that elements were present at these very low concentrations, the term trace was coined to describe them. Although modem analytical methods permit the accurate, repeatable determination of elements at such low levels, the generic terms trace and trace element are still in use. 

ISO uses two terms, trueness and precision , to describe the accuracy of a measured value. Trueness refers to the closeness of agreement between the average value of a large number of test results and the true or accepted reference value. Precision refers to the closeness of agreement of test results, or in other words the variability between repeated tests. The standard deviation of the measured value obtained by repeated determinations under the same conditions is used as a measure of the precision of the measurement procedure. The repeatability limit r (an intra-laboratory parameter) and the reproducibility limit R (an inter-laboratory parameter) are calculated as measures of precision. Again, precision and trueness together describe the accuracy of an analytical method. 

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