Overall desirability

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... 

Figure 5. Multiresponse sensitivity analysis of the overall desirability value showing the optimum and the compositional region complying with all response limits.

When structured soy protein fiber was added to fermented salami at 15 or 30% levels, trained sensory panels found the flavor to be undesirable, whereas a 116-member untrained panel found the product containing 30% soy flour to be undesirable in flavor, tenderness and overall desirability (26). The flavor of beef patties containing 20% soy protein flour or concentrate was rated about equal to all beef patties by a 52-member panel, whereas patties containing 30% were scored lower by the panel (6). Berry et al. (7) found the characteristic "soy-like" flavor to be more... 

If the overall desired pH is between 4 and 9, it may be necessary to include a buffer. Thus, if an electrode reaction involves the creation or annihilation of H+ or OH", the pH in the viscosity of the electrode will tend to differ from that of the bulk. 

Many desirable meat flavor volatiles are synthesized by heating water-soluble precursors such as amino acids and carbohydrates. These latter constituents interact to form intermediates which are converted to meat flavor compounds by oxidation, decarboxylation, condensation and cyclization. 0-, N-, and S-heterocyclics including furans, furanones, pyrazines, thiophenes, thiazoles, thiazolines and cyclic polysulfides contribute significantly to the overall desirable aroma impression of meat. The Maillard reaction, including formation of Strecker aldehydes, hydrogen sulfide and ammonia, is important in the mechanism of formation of these compounds. 

The core issue for the seamless performance of the whole workflow is the early identification of the most time-consuming steps associated to the full high-throughput experimentation cycle to be able to adjust those bottlenecks to meet the requirements with regard to the overall desired screening speed. Below, we overview the topics addressed in this introduction and discuss the different features together with selected case studies. 

The most frequently used general response is Harington s [1, 4] overall desirability function. The basis of this construction of a general response is transformation of partial responses into a non-dimensional desirability scale. To construct a desirability scale we use the prepared, elaborated table of standard estimates, Table 2.6. 

Table 2.7 Partial responses, partial desirability and overall desirability...

Overall desirability is an abstract definition and therefore some of its properties have to be analyzed, such as lack of fit and statistical effectiveness. It has been asserted that the effectiveness and sensitivity of partial and overall desirability are not lower than the same properties of any technological response. Overall desirability is quantitative, singular, statistically effective, adequate, etc. It has found a large application in the research of polymeric materials, rubber products, etc. 

The qualitative demands made on the end product can be established by a study of consumer requirements. In an ideal situation the degree of importance would have to be established quantitatively, for instance as the d-function (desirability). By means of such a d-function the importance of the various properties can be measured and, consequently, also the influence of a change in one of the properties on the overall desirability. For practical reasons (practicability, time) the requirements to be satisfied by the end product in various applications usually are not indicated as d-functions, but are simple rated as unimportant, important and very important. This procedure is based on the results of consumer studies and gives the desirability profile for the application. Also the article properties obtained by suitable processing form a profile, viz. the product profile. 

The most commonly adopted approach is to rank compounds according to the total number of alerts. If molecules are to be prioritized with respect to properties such as permeability, solubility, and so forth, the goal is to find the best compromise between these continuous parameters. For this purpose, each property is scored by assigning a dimensionless scale di between zero ( criterion not met ) and one ( target achieved ), with intermediate values being obtained by interpolation between the minimum and maximum for each property. The score profile for each compound is summarized into an overall desirability D by calculating the geometric mean of the individual dt values [67, 68] ... 

It is seen, that a high value of D is obtained only if all individual desirabilities d are high. If one d is poor, this is enough to give an overall poor desirability. If all d are equal, then D = d. The geometric mean is therefore seen to meet the requirements of an overall desirability function. The problem is then to define the individual desirabih ties. 

There is, however, one application when the overall desirability D can be rather safely used, namely as a tool in conjunction with response surface modelling. In this context, it can be used to explore the joint modelling of several responses so that a near-optimum region can be located by simulations against the response surface models. The search for conditions which incrase D can be effected either by simplex techniques or by the method of steepest ascent. For the steepest ascent, a linear model for D is first determined from the experiments in the design used to establish the response surface models. The settings which increase D can be translated back into the individual responses by using the response surface models. Thus, it is possible to establish immediately whether the simulated reponse values correspond to suitable experimental conditions. Such results must, of course, be verified by experimental runs. 

In addition each criterion can be weighted in order to take into account criterion importance in the decision rule. In the case of weighted functions the overall desirability and utility of the i-th element are defined as follows ... 

Once D or U for each element has been calculated, all the elements are ranked according to their D (or U) value. The overall desirability is calculated combining all the desirabilities through a geometrical mean. It must be highlighted that the desirability product is very strict if any desirability dir is equal to 0 the overall desirability Dt will be zero, whereas the D, will be equal to one only if all the desirabilities have the maximum value of one. The overall utility is calculated less severely in fact the overall quality of an element can be high even if a single desirability/utility function is zero. 

A key finding from our interviews, that is confirmed across other expert accounts (reviewed by Ricci, 2006 McDowell and Eames, 2006) is that hydrogen futures are assessed in very different ways by different stakeholders, so that the overall desirability of hydrogen as an energy carrier becomes problematic. The same can be said about public attitudes towards moving to a hydrogen-based economy. 

The r individual desirability functions are then combined together, usually as the geometric mean, to obtain the overall desirability function (D) for the system whose maximum value can then be looked for within the domain. 

It is assumed that the experimenter, having carried out his experiments and analysed the results, will now have a satisfactory mathematical model for each response that is to enter into the global optimization. He can therefore calculate a partial desirability for each response in all parts of the domain, and obtain from these an overall desirability D. The problem becomes one of numerical optimization of the function D within the domain. 

The optimum is found to be insensitive to changes in around about -0.5, corresponding to a lubrification time of about 2.25 min. Taking this point as a "working" optimum, we calculate an overall desirability of 0.26. The calculated individual responses are ... 

The desirability function for the price is allowed to vary in a non-linear fashion from the maximum price (desirability = 0) to the minimum (desirability =1), with an exponent i = 5, so dp = [(675 - price)/535] The overall desirability is the geometric mean of the values of the 3 functions for each point of the design space. It is shown as a contour plot in figure 9.6. 

Overall, desirable characteristics of surfactants for soil remediation purposes include effectiveness, biodegradability, low toxicity, good solubility at groundwater temperature, low adsorption to soil, low surface tension, and a low CMC (West and Harwell, 1992 Mulligan, Yong, and Gibbs, 2001 Lee, 2004). 

Once the desirability functions have been specified for all the responses, we combine them into an overall desirability, normally calculated as the geometric average of the m individual desirabilities ... 

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