Robustness Coefficient

A robust coefficient of variation can be calculated by using, VjqR or, vMad instead of, v, and the median instead of the mean. 

The three robustness criteria that are explained here (Weighted-Jones (WJ), Projected-Variance (PV) and Robustness-Coefficient (RC)) describe all three the robustness of a certain mixture composition in direct relation to the response to be optimised. All three express the concept of robustness into a numerical value that can be calculated for each mixture setting (composition) of interest. So each of the criteria can be calculated as a function of the mixture composition and belongs directly to a certain response of interest. In this way a robustness criterion can be dealt with in a normal way in a mixture optimisation strategy. 

The Robustness Coefficient (RC) has been developed especially to handle the kind of robustness problem as described in part 4.3.2 of this Chapter. The RC is extensively described in reference [20], the behaviour of the RC... 

For the sake of illustration the constant relative standard deviation (cvj for the three variable components was set to 5%. The demands concerning the calculation of the robustness coefficient were to have a deviation in the crushing strength (6> ) of ION at most with a reliability (m ) of 0.95. 

The demands concerning the decision making method were a maximal value for the crushing strength and a maximal value for the robustness coefficient. 

Combining the behaviour of both criteria, maximisation of the crushing strength and the maximisation of the robustness coefficient, results in a PO-plot, as shown in Figure 4.21. 

Every point in figure 4.21 corresponds directly to a predicted value of the crushing strength and the calculated value of the robustness coefficient, at one mixture composition. These points are called Pareto Optimal (PO) points, which are listed in Table 4.5. The PO points can also be placed in the corresponding mixture triangle, which is presented in Figure 4.22. 

The PO points are not directly comparable to each other. Moving from point 1 to 2 in the PO plot results in a higher crushing strength but a lower robustness coefficient. Between points 7 and 6 the reverse is valid, moving... 

Considering the set PO points presented in Table 4.5, the following statement can be made there exists no mixture composition with a higher robustness coefficient and, simultaneously, a higher crushing strength than a PO mixture composition. 

J.H. de Boer, A.K. Smilde and D.A. Doombos, Introduction of a robustness coefficient in optimization Procedures Implementation in mixture design problems. Part I Theory, Chemometrics and Intelligent Laboratory Systems, 7 (1990) 223-236. 

Data can be obtained from tests in uniaxial tension, uniaxial compression, equibiaxial tension, pure shear and simple shear. Relevant test methods are described in subsequent sections. In principle, the coefficients for a model can be obtained from a single test, for example uniaxial tension. However, the coefficients are not fully independent and more than one set of values can be found to describe the tension stress strain curve. A difficulty will arise if these coefficients are applied to another mode of deformation, for example shear or compression, because the different sets of values may not be equivalent in these cases. To obtain more robust coefficients it is necessary to carry out tests using more than one geometry and to combine the data to optimize the coefficients. 

Oils showing a median of the bitter and/or pungent attribute of more than 5.0 should be addressed to blending. The calculation of the robust coefficient of variation provides a measure of the reliability of panel tasters according to data reported in Table 2.6. 

Table 2.6 Median values of defects and fruity aroma, and their corresponding robust coefficients of variation, in relation to virgin olive oil categories...

Median of defects Robust coefficient of variation % Median of fruity aroma Robust coefficient of variation % Olive oil category... 

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