Linearity testing example

Table 5.1 summarises the characteristics of a method that require validation together with the method features contributing to these characteristics and some example test procedures. It can be seen that there is a certain amount of overlap in the contributions and their test procedures for the various characteristics. For instance, a linearity test can give information on both the accuracy and the sensitivity of a method. The ruggedness test is normally included as part of a precision study, however it can also contribute to other performance characteristics such as sensitivity and method limitations. Despite this it fits best as part of a precision study where it can be used to effectively and efficiently link repeatability to reproducibility tests. 

The test sample to use in qualification should be a small molecule that is soluble in water, has a strong UV chromophore, and possesses a charge at the intended separation pH value. A nonvolatile compound is also desirable, especially when used for assessing peak area reproducibility during the detector linearity test. Some examples of test samples that can be used are benzoic acid, 4-hydroxyphenylacetic acid, 4-hydroxybenzoic acid, and 4-hydroxyacetophenone. 

Formulae (6.3.19) and (6.3.20) can be used provided that the relation between the number of indentations with defects and the load applied is fairly linear. For example, when testing glass (Fig. 6.3.6), 1.15 N < Pt... 

Linearly increasing stress test Examples of Stress Corrosion Cracking see Models... 

There are countless examples in the literature of oedometer test graphs from whieh pre-consolidation or yield pressures have been determined that are completely absent when the data are re-plotted on linear scales. Examples are given in Figures 4 and 5. Figure 4 shows an example from a residual soil found in the southern part of the USA, known as Piedmont soil. Values of pre-eonsolidation pressure and over-consolidation ratios (OCRs) determined from the log plot are shown in the figure. The data have been re-plotted using a linear seale for pressure these linear plots show no evidenee of yield or pre-eonsolidation pressures. 

In oscillatory testing, great care has to be taken to ensure that the experiment takes place in the linear region where G and G" are independent of the maximum amplitude or stress of the oscillation. A number of examples of non-linear testing are shown in figures 35 - 40 where we see that the most sensitive parameters to breakdown is usually G, since it eventually falls faster, whereas when G" does change it can increase before decreasing. 

Normalised fiber mechanical properties are expressed in terms of unit linear density. For example, in describing the action of a load on a fiber in a tensile test, units of N/tex or gram force per denier (gpd) are generally used. If this is done, the term tenacity should be used in place of stress. The tme units of stress are force per unit cross-sectional area, and the term stress should be reserved for those instances where the proper units are used. 

Global Test The measurements do not close the constraints of the process. In the linear, material balance constraint example used above,... 

The value of the eorrelation eoeffieient using the least squares teehnique and the use of goodness-of-fit tests (in the non-linear domain) together probably provide the means to determine whieh distribution is the most appropriate (Keeeeioglu, 1991). However, a more intuitive assessment about the nature of the data must also be made when seleeting the eorreet type of distribution, for example when there is likely to be a zero threshold. 

This equation is the basis of linear viscoelasticity and simply indicates that, in a tensile test for example, for a fixed value of elapsed time, the stress will be directly proportional to the strain. The different types of response described are shown schematically in Fig. 2.1. 

There is another class of problems, known as noudeterministic polynomial time or class NP - problems, which may not iicco.ssarily be solvable in polynomial time, but the actual solutions to which may be tested for correctness in polynomial time. The problem of finding a size-iV preimage for a linear CA, for example, is a class NP problem. While it is obvious that P C NP, whether P yf NP remains an open question. 

This lack of sharpness of the 1-way F-test on REV s is sometimes seen when there is information spanned by some eigenvectors that is at or below the level of the noise spanned by those eigenvectors. Our data sets are a good example of such data. Here we have a 4 component system that contains some nonlinearities. This means that, to span the information in our data, we should expect to need at least 4 eigenvectors — one for each of the components, plus at least one additional eigenvector to span the additional variance in the data caused by the non-linearity. But the F-test on the reduced eigenvalues only... 

Even plastics with fairly linear stress-strain curves to failure, for example short-fiber reinforced TSs (RPs), usually display moduli of rupture values that are higher than the tensile strength obtained in uniaxial tests wood behaves much the same. Qualitatively, this can be explained from statistically considering flaws and fractures and the fracture energy available in flexural samples under a constant rate of deflection as compared to tensile samples under the same load conditions. These differences become less as the... 

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