Robustness influencing variables

To determine Sb in marine sediments by ETAAS, a direct method was developed based on quantitating the analyte in the liquid phase of the slurries (prepared directly in autosampler cups). The variables influencing the extraction of Sb into the liquid phase and the experimental setup were set after a literature search and a subsequent multivariate optimisation procedure. After the optimisation, a study was carried out to assess robustness. Six variables were considered at three levels each (see Table 2.13). In addition, two noise factors were set after observing that two ions, which are currently present into marine sediments, might interfere in the quantitations. In order to evaluate robustness, a certified reference material was used throughout, BCR-CRM 277 Estuarine Sediment (guide value for Sb 3.5 0.4pgg ). Table 2.13 depicts the experimental setup. 

Figure 7 shows the influence of the coefficient of variation of the standard deviation of the influencing variables on the mean and standard deviation of the robustness index (the number of samples n remains constant). The graph indicates that both statistics increase significantly as soon as the coefficient of variation is higher than 0.2. The standard deviation increases more than the mean value. 

The range of p is — 1 to +1 the value is invariant to variable transformations that keep the sequence of the values that means that for instance a logarithmic transformation has no influence. Because the Spearman correlation is based on ranks, it is relatively robust against outliers. 

The group means and covariances can also be estimated robustly, for example, by the minimum covariance determinant (MCD) estimator (see Section 2.3.2). The resulting discriminant rule will be less influenced by outlying objects and thus be more robust (Croux and Dehon 2001 He and Fung 2000 Hubert and Van Driessen 2004). Note that Bayes discriminant analysis as described is not adequate if the data set has more variables than objects or if the variables are highly correlating, because we need to compute the inverse of the pooled covariance matrix in Equation 5.2. Subsequent sections will present methods that are able to deal with this situation. 

Without introduction of IAF into the Kraus plot, the coefficients of determination generated for the rubber nanocomposites are found to be significantly less than unity (around 0.608). In terms of statistics, it means that although the present function relating the independent variable to the dependent variable is robust, its accuracy of mapping is hindered possibly because of neglecting certain other parameters that influence the independent variable. 

For determining the robustness of a method a number of parameters, such as extraction time, mobile-phase pH, mobile-phase composition, injection volume, source of column lots and/or suppliers, temperature, detection wavelength, and the flow rate, are varied within a realistic range and tlie quantitative influence of the variables is determined. If the influence of a parameter is within a previously specified tolerance, this parameter is said to be witliin the robustness range of the method. These method parameters may be evaluated one factor at a time or simultaneously as part of a factorial experiment. 

The idea behind this methodology is to apply a technique of experimental design with the goal of finding levels of the controlled factors that make the process robust to the presence of noise factors, which are uncontrolled. The controlled factors are process variables that are adjusted during the normal operation of a process. The noise factors are present in combination with controlled factors and have a significant influence on the response or quality of the product. Noise factors are either impossible... 

The great majority of statistical procedures are based on the assumption of normality of variables, and it is well known that the central limit theorem protects against failures of normality of the univariate algorithms. Univariate normality does not guarantee multivariate normality, though the latter is increased if all the variables have normal distributions in any case, it avoids the deleterious consequences of skewness and outliers upon the robustness of many statistical procedures. Numerous transformations are also able to reduce skewness or the influence of outlying objects. 

Although the influence of relevant biotic and abiotic variables on the fate and effects of chemicals can, to a certain extent, be explored through controlled experiments and observations of natural systems, the combinations of factors that can be tested in practice are very limited. Mesocosm and field studies are often expensive to perform, can be difficult to replicate sufficiently, and are frequently complicated to interpret. Because they typically represent one unique scenario (species composition and density, temperature, light, nutrient level, and timing of pesticide application in relation to the environmental conditions), questions are often raised about the generality and robustness of the results. Likewise, unexpected or uncontrollable events may occur (e.g., it may have been an unusually rainy, sunny, hot, or cool season), the influence of which on the estimate of risk can be difficult to assess. 

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