Tolerable error, ranges

The limit of tolerable error is generally smallest in a minor component assay. It will have been determined that a particular minor component must be at or below a threshold concentration for the product to be usable. Therefore, the decision to accept or reject an entire production batch may depend on the analytical result. Typical batches may contain the contaminant at a concentration very similar to the specification limit. In a minor component assay, the major component may be overloaded and out of the proper range of detection of the assay. Even so, the minor component may be at such low levels that assay noise interferes. 

For assays of stable materials with wide ranges of tolerable error, sample handling is of little concern. For assays of labile materials, especially assays for purity or for minor components, controlled sample handling procedures need to be established. There are three potential ways in which a sample may become contaminated, namely by the sampling tools, sample containers, and degradation on storage. 

Suppose over a number of results the mean error is not zero. In SPC the mean error as a percentage of the tolerance half-range (which is T when the tolerance is T) is known as the index of accuracy, or capability index for setting ... 

In the comparison phase, apart from the experimental peptide masses and the proteinase used to digest the proteins, some optional attributes may be specified to reflect experimental conditions and to reduce the search space. These optional attributes may include information coming from the sample such as species of origin, M, or pi of the whole protein with the accepted error range, possible chemical or artefactual modifications like carboxymethylation of cysteines or oxidation of methionines. Other parameters to be specified include the mass tolerance or the minimum number of matching peptides required for a protein to be suggested as a possible match. Providing a maximum of information available about the sample helps to decrease the number of candidate proteins, to reduce the probability of false positive matches, and thus to increase the confidence of the identification. However, one must be careful not to miss the correct protein either. 

In practice, Eq. (9.88) may be treated only over a finite range of the radial variable r e [0,rmax] fmax < oo) provided that r ax is a sufficiently large number that causes Pk rmax) 0 and Qk fmax) 0. With these constraints a tolerable error will be introduced due to the exponentially decaying behavior of the two radial functions. The potential functions Yku, r) require more attention, since a finite r ax leads to the modified upper boundary condition... 

Table 1 is condensed from Handbook 44. It Hsts the number of divisions allowed for each class, eg, a Class III scale must have between 100 and 1,200 divisions. Also, for each class it Hsts the acceptance tolerances appHcable to test load ranges expressed in divisions (d) for example, for test loads from 0 to 5,000 d, a Class II scale has an acceptance tolerance of 0.5 d. The least ambiguous way to specify the accuracy for an industrial or retail scale is to specify an accuracy class and the number of divisions, eg. Class III, 5,000 divisions. It must be noted that this is not the same as 1 part in 5,000, which is another method commonly used to specify accuracy eg, a Class III 5,000 d scale is allowed a tolerance which varies from 0.5 d at zero to 2.5 d at 5,000 divisions. CaHbration curves are typically plotted as in Figure 12, which shows a typical 5,000-division Class III scale. The error tunnel (stepped lines, top and bottom) is defined by the acceptance tolerances Hsted in Table 1. The three caHbration curves belong to the same scale tested at three different temperatures. Performance must remain within the error tunnel under the combined effect of nonlinearity, hysteresis, and temperature effect on span. Other specifications, including those for temperature effect on zero, nonrepeatabiHty, shift error, and creep may be found in Handbook 44 (5). The acceptance tolerances in Table 1 apply to new or reconditioned equipment tested within 30 days of being put into service. After that, maintenance tolerances apply they ate twice the values Hsted in Table 1.

The generality of a simple power series ansatz and an open-ended formulation of the dispersion formulas facilitate an alternative approach to the calculation of dispersion curves for hyperpolarizabilities complementary to the point-wise calculation of the frequency-dependent property. In particular, if dispersion curves are needed over a wide range of frequencies and for several optical proccesses, the calculation of the dispersion coefficients can provide a cost-efficient alternative to repeated calculations for different optical proccesses and different frequencies. The open-ended formulation allows to investigate the convergence of the dispersion expansion and to reduce the truncation error to what is considered tolerable. 

The sampling variance of the material determined at a certain mass and the number of repetitive analyses can be used for the calculation of a sampling constant, K, a homogeneity factor, Hg or a statistical tolerance interval (m A) which will cover at least a 95 % probability at a probability level of r - a = 0.95 to obtain the expected result in the certified range (Pauwels et al. 1994). The value of A is computed as A = k 2R-s, a multiple of Rj, where is the standard deviation of the homogeneity determination,. The value of fe 2 depends on the number of measurements, n, the proportion, P, of the total population to be covered (95 %) and the probability level i - a (0.95). These factors for two-sided tolerance limits for normal distribution fe 2 can be found in various statistical textbooks (Owen 1962). The overall standard deviation S = (s/s/n) as determined from a series of replicate samples of approximately equal masses is composed of the analytical error, R , and an error due to sample inhomogeneity, Rj. As the variances are additive, one can write (Equation 4.2) ... 

Accuracy (systematic error or bias) expresses the closeness of the measured value to the true or actual value. Accuracy is usually expressed as the percentage recovery of added analyte. Acceptable average analyte recovery for determinative procedures is 80-110% for a tolerance of > 100 p-g kg and 60-110% is acceptable for a tolerance of < 100 p-g kg Correction factors are not allowed. Methods utilizing internal standards may have lower analyte absolute recovery values. Internal standard suitability needs to be verified by showing that the extraction efficiencies and response factors of the internal standard are similar to those of the analyte over the entire concentration range. The analyst should be aware that in residue analysis the recovery of the fortified marker residue from the control matrix might not be similar to the recovery from an incurred marker residue. 

Output Errors. Output errors are analogous to input errors they can lead to biased parameter values or erroneous conclusions on the ability of the model to represent the natural system. As noted earlier, whenever a measurement is made, the possibility of an error is introduced. For example, published U.S.G.S. stream-flow data often used in hydrologic models can be 5 to 15% or more in error this, in effect, provides a tolerance range within which simulated values can be judged to be representative of the observed data. It can also provide a guide for terminating calibration efforts. 

However, the amount of error in the data is not generally the limiting factor in data interpretation. Rather, the locations at which the data are taken most severely hinder progress toward a mechanistic model. Reference to Fig. 1 indicates that the decision between the dual- and single-site models would be quite difficult, even with very little error of measurement, if data are taken only in the 2- to 10-atm range. However, quite substantial error can be tolerated if the data lie above 15 atm total pressure (assuming data can be taken here). Techniques are presented that will seek out such critical experiments to be run (Section VII). 

The concentration of the FLUKA albumin, as determined in weighted samples of the product using the calibration line constructed with the NIST albumin, fluctuated around the weighted amount in the range of experimental error of the determination considered as the 95% tolerance limit. The data were evaluated using EXCEL 97. 

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