Alternative Problem Statements and Solutions

Fig. 2. (a) Conventional pattern recognition (b) alternative problem statement and solution format. 

This Section addresses cases with a continuous performance metric, y. We identify the corresponding problem statements and results, which are compared with conventional formulations and solutions. Then Taguchi loss functions are introduced as quality cost models that allow one to express a quality-related y on a continuous basis. Next we present the learning methodology used to solve the alternative problem statements and uncover a set of final solutions. The section ends with an application case study. 

To address the modified problem statements and uncover final solutions with the desired alternative formats, data-driven nonparametric learning methodologies, based on direct sampling approaches, were described. They require far fewer assumptions and a priori decisions on the part of the user than most conventional techniques. These practical frameworks for extracting knowledge from operating data present the final uncovered solutions to the decisionmaker in formats that are both easy to understand and implement. 

The last entry in Table 1.1 involves checking the candidate solution to determine that it is indeed optimal. In some problems you can check that the sufficient conditions for an optimum are satisfied. More often, an optimal solution may exist, yet you cannot demonstrate that the sufficient conditions are satisfied. All you can do is show by repetitive numerical calculations that the value of the objective function is superior to all known alternatives. A second consideration is the sensitivity of the optimum to changes in parameters in the problem statement. A sensitivity analysis for the objective function value is important and is illustrated as part of the next example. 

Propose solutions Proposes one or more solutions/ alternatives that indicate a deep comprehension of the problem and sensitive to all ethical, ecological, and cultural dimensions of the problem Proposes one or more solutions/ alternatives that indicate comprehension of the problem and sensitive to one of the following ethical, ecological, and cultural dimensions of the problem Proposes one solution/alter-native that is generic and not specific to the problem Proposed solution does not reflect the problem statement or the problem at hand... 

Solutions of the equation provide alternate plans wherein the annual soil loss from a specific field can be held within the limits that can be tolerated under the soil topographic conditions involved. In spite of the fact that nearly 15 X 10 has been spent on soil conservation in the U.S.A. since the mid-1930 s, soil erosion remains one of the biggest and most pervasive problems still facing the nation (Carter, 1977). The dust storms that occurred in early 1977 underline this statement. Nationally, erosion losses have been estimated at about 2.5 kg m" each year, but soil scientists believe that even deep soils cannot sustain a fraction of this loss within serious reductions in productivity. Discounting erosion losses, top soil possibly forms at the rate of about 0.35 kg m" y in humid regions. 

Step 4, plan and implement solution, is a statement of how the team intends to solve the problem. It is important that the team understand the limits of its authority, so that it will develop local solutions that are very focused on the root cause(s) identified in Step 3. They are not authorized to change the entire system. The team needs to analyze the problem and identify different alternatives to solving the problem. It is valuable for the team to assign the tasks of implementing the solution using the 4 Ws and 1 H who, when, where, what, and how. 

It would certainly be wrong to introduce critical evaluation of TA by the question of whether it makes sense. The sense and purpose are uncontested. However, the question of whether TA is always feasible in individual cases and whether it also leads to useful answers with dependable statement values is not inappropriate. TA does not make decisions, but finds potential problems, provides data for evaluation, and shows weak points and possible alternative solutions. This, of course, should be done with the maximum possible objectivity and with scientific neutrality, though this is easier said than done. 

Students also find it difficult to accept anything other than empirical facts as evidence for the existence of a problem which requires a solution. Second year students at the University of Western Australia were asked to critically analyse alternative sources of energy with a social justice lens in their preliminary analysis of the effect of wind turbines, it was clear that they were dismissive of subjective statements made by farming communities about the effect of the noise on their health. Downplaying the health costs of development is a common problem, particularly in the mining sector (e.g. Brueckner and Ross 2010) and students are asked, not just whether it is possible to be objective, value-free and scientific but to what extent self-interest drives these positivist attributes. They are introduced to different knowledge systems, and also asked to question notions of scientific expertise which often assume there to be one basic truth known by the experts. 

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