Repeatability sampling

Increa.se the number of mea.surements included in the mea.sure-ment. set by using mea.surements from repeated. sampling. Including repeated measurements at the same operating conditions reduces the impact of the measurement error on the parameter estimates. The result is a tighter confidence interval on the estimates. 

Detection limits of 0.0001 to 0.01 mg/P in soil samples and 0.1 to 1.0 mg/ in water samples have been reported. Lappala (1984) reported the results of repeated sampling on successive days at a... 

C) The number of repeat samples pulled in one location/time coordinate... 

Repeated sampling procedure for each element (GFAAS)... 

Suppose N independently repeated samples xi, x2,..., xjv are obtained to measure the value of a quantity X, where x represents an estimate of its true value x. Usually the best estimate of x is provided by the mean or average of x, x(N). The reliability of the estimator x can be characterized by the mean square error, (e.g., [29, 30])... 

Figure 65-1 shows a schematic representation of the F-test for linearity. Note that there are some similarities to the Durbin-Watson test. The key difference between this test and the Durbin-Watson test is that in order to use the F-test as a test for (non) linearity, you must have measured many repeat samples at each value of the analyte. The variabilities of the readings for each sample are pooled, providing an estimate of the within-sample variance. This is indicated by the label Operative difference for denominator . By Analysis of Variance, we know that the total variation of residuals around the calibration line is the sum of the within-sample variance (52within) plus the variance of the means around the calibration line. Now, if the residuals are truly random, unbiased, and in particular the model is linear, then we know that the means for each sample will cluster... 

Repeat samples provide a less formal check than conventional QC samples. Within an analytical process, samples may be analysed singly, in duplicate, in triplicate, etc. Normally, the repeat sample is a conventional sample, repeated later in the batch of samples, or perhaps in a different batch. The variation between the two sets of results is studied to ensure that the variation is within the acceptable limits (see Chapter 4, Section 4.6.2). Higher than expected variation (for example, variation greater than the stated repeatability for the method) provides an indication that there is a possible fault in the analytical system. The analyst is normally aware when repeat samples are used. 

Blind samples are types of sample which are inserted into the analytical batch without the knowledge of the analyst - the analyst may be aware that blind samples are present but not know which they are. Blind samples may be sent by the customer as a check on the laboratory or by laboratory management as a check on a particular system. Results from blind samples are treated in the same way as repeat samples - the customer or laboratory manager examines the sets of results to determine whether the level of variation, between repeat measurements on the blind sample or between the observed results and an expected value, is acceptable, as described in Section 5.4.3. 

Table 9.11 shows the effect of this concentration on the responses of the other pesticides. In every instance the peak height was increased while the peak area remained constant. All of the columns used for this study were aged by repeated sample injections, but had not deteriorated to the point where they would normally be replaced. No values are included in Table 9.11 where the chromatographic system was not suitable for the pesticide concerned. 

Because of the preceding properties, our profile procedure appears to produce highly sensitive and specific common pattern representations from limited numbers of defining sequences compared with other current methods (Figs. 5 and 7). This was shown by the construction of such profiles from more than 50 completely unrelated functional families. In more than 90% of the families, the sensitivity and specificity are more than 98%. This is also supported by the repeated sampling study of the complex bacterial transcription initiation factors. Finally, these methods allow for the localized recognition of entire domains within multidomain structures, as seen in Fig. 6. 

It was noted that not only were certain blood values above or below the "normal" range for specific individuals but also that, regardless of the positions in the ranges, each individual exhibited a distinctive pattern. Abundant evidence was obtained from these two studies alone to suggest the importance of studying biochemical individuality and its relationship to susceptibility to a host of diseases. The distinctiveness of these studies lies in the fact that repeated samples from the same well individuals, collected under basal conditions, were analyzed for many different constituents. This procedure is not often followed. 

It is obvious that one should not expect to find in the literature extensive information regarding the composition of the brains, livers, or even muscles of healthy human individualsespecially so since repeated samples would have to be taken for analysis in order to determine conclusively the importance of inter-individual differences. The best that could be hoped for would be extensive "horizontal" studies relative to the composition of blood, secretions, etc., of individual human specimens and, perhaps, more comprehensive data including tissue composition with respect to animals. However, satisfactory studies of this sort have seldom, if ever, been made. More often than not, such horizontal studies as have been made have not been published in complete enough form to give the kind of information needed to answer the questions which we are considering. 

Various organic constituents of blood have been found in normal individuals in the ranges of concentration shown in Table 7.16,2432 There are many items in the list for which there is a 3- or 4-fold variation, and about a dozen for which the variation is of the order of 10-fold or more. These data strongly suggest that marked interindividual differences exist, but they do not offer proof except where repeated samples have been analyzed from the same individuals. 

In Table 10 is given a summary of the uric acid and amino acid values obtained from repeated samples from 9 individuals of both sexes, all collected in the same manner. 

In a study in which individual urinary components were determined and repeated samples from the same individuals analyzed, Dobriner and co-workers23 found that the androsterone excretion in twenty normal males 21 to 76 years of age varied from 0.2 to 7.0 mg. per day, a 35-fold range. Age was a factor in contributing to the wideness of this range, since older individuals tended to excrete less, but each individual s androsterone excretion was distinctive, and large differences which were truly inter-individual were observed. One man of 72 excreted, for example, more than twice as much as one who was 21 years old. This study will be referred to further in a later discussion (p. 101). 

There are numerous reports from other laboratories which are in line with these findings respecting individuality in urine composition, though seldom has attention been paid to repeated samples from the same individuals. 

Studies of this sort, involving analyzing repeated samples from the same "normal" individuals, have been relatively rare, and for this... 

Figure 3.2 Correct and incorrect increment delimitation in process sampling. Generic illustration (e.g. of a conveyor belt). The three examples to the left are all delineated correctly with parallel sampling implement boundaries, while the remaining three cannot deliver a correct (nonbiased) transverse cut of the l-D stream. Repeated sampling results in unbalanced transverse proportions of the flux of matter, the effect of which is IDE and IME.

Section 5.3 described a number of alternative design and implementation strategies for near-infrared analyzers, suitable for operation in a process analytical environment. However, none of these analyzers can operate without a robust, maintainable and repeatable sampling interface with the process sample under consideration. In addition to this question of the optical interface to the sample, there is a whole wider area of concern, which is how far the particular sample interface is representative of the sample in the process as a whole. This complex issue is not addressed here, and is dealt with separately in Chapter 3. 

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