Desirability factor

If, in service, a material is required to have a certain strength in order to perform its function satisfactorily then a useful way to compare the structural efficiency of a range of materials is to calculate their strengdi desirability factor. 

Hence, if we adopt loading/weight as a desirability factor, Df, then this will be given by... 

Similar desirability factors may be derived for other geometries such as struts, columns etc. This concept is taken further later where material costs are taken into account and Tables 1.11 and 1.12 give desirability factors for a range of loading configurations and materials. 

If in the service of a component it is the deflection, or stiffness, which is the limiting factor rather than strength, then it is necessary to look for a different desirability factor in the candidate materials. Consider the beam sim-ation described above. This time, irrespective of the loading, the deflection, S,... 

Using equation (1.7) and an analysis similar to above it may be shown that on the basis of stiffness and cost, the desirability factor, D/, is given by... 

Desirability factors for some common loading configurations... 

The direct optimization of a single response formulation modelled by either a normal or pseudocomponent equation is accomplished by the incorporation of the component constraints in the Complex algorithm. Multiresponse optimization to achieve a "balanced" set of property values is possible by the combination of response desirability factors and the Complex algorithm. Examples from the literature are analyzed to demonstrate the utility of these techniques. 

A more subjective approach to the multiresponse optimization of conventional experimental designs was outlined by Derringer and Suich (22). This sequential generation technique weights the responses by means of desirability factors to reduce the multivariate problem to a univariate one which could then be solved by iterative optimization techniques. The use of desirability factors permits the formulator to input the range of property values considered acceptable for each response. The optimization procedure then attempts to determine an optimal point within the acceptable limits of all responses. 

Acceptable limits may differ considerably for the measured property values, however. For a majority of cases, responses can be classified as having either a maximum acceptable value, a minimum acceptable value, or a most desirable value within an acceptable range. For each response, these cases may be incorporated into a desirability factor having the range 0 < d < 1 with d 0 denoting an unacceptable response value and d 1 representing totally acceptable behavior. Intermediate values are determined by equations (22) based on the acceptable limits, the desired response value, and the type of response behavior desired by the formulator. 

The individual desirability factors are then combined into an overall desirability function by the geometric mean ... 

The consolidation of individual values into an overall value is possible by a number of other methods. The geometric mean calculation has a particularly distinguishing characteristic that if any individual desirability factor is zero, indicating that a response is outside of its acceptable limits, the overall desirability is zero. An optimization procedure to maximize the overall desirability function will therefore seek to remain within the acceptable ranges of all responses even though individual maximization, minimization, or an acceptable range of response values are required. By these criteria, the values maximizing the overall desirability function... 

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More recently an elegant solution to the problem of getting well defined multiplets in NMR spectra, under conditions of partial proton decoupling, has been devised. (161) This is known as J-scaling and leads to spectra in which all multiplet components have their normal intensities but all the splittings are reduced by any desired factor which is the same for each carbon. Typically a scaling factor of 30 is found convenient since then the residual one-bond H splittings... 

Dividing the right side by the left side yields the desired factor 8.314 J/mol K... 

Table 12.3 summarizes the typical products obtained in H2SO4 and HF processes. One key observation is that trimethylpentanes/dimethylhexanes (TMP/DMH) formation is far from thermodynamic equilibrium, a desirable factor given the octane spread - TMPs have RON numbers of 100 and higher, DMHs about 50-60. The various products formed are present for all feeds, catalysts and process conditions, only in different proportions. 

P9.32 The rate of tunnelling is proportional to the transmission probability, so a ratio of tunnelling rates is equal to the corresponding ratio of transmission probabilities (given in eqn 9.20a). The desired factor is T IT2, where the subscripts denote the tunnelling distances in nanometers ... 

Gammas. A beam of gammas going through a material of thickness t is attenuated by a factor exp(-/x,r), where ju. is the total linear attenuation coefficient of the gamma in that medium. The higher the value of ft is, the smaller the thickness t that reduces the intensity of the beam by a desired factor. In theory, the beam cannot be attenuated to zero level. In practice, the attenuation is considered complete if the radiation level equals the background. 

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