Definition problem

There is a wide range of tools in the Six-Sigma toolbox, used during the define phase of a Six-Sigma project, which can be applied effectively for problem definition. Such tools 

Answering all of the questions (and more ) can be a daunting task, but it can be argued that all of them are directly relevant to the strategy that one should choose for chemo-metric modeling development, testing, and deployment. 

Most industrial control systems use the multiloop SISO diagonal control structure. It is the most simple and understandable structure. Operators and plant engineers can use it and modify it when necessary. It does not require an expert in apphed mathematics to design and maintain. In addition, the performance of these diagonal controller structures is usually quite adequate for process control apphcations. In fact there has been little quantitative, unbiased data showing that 

So the multiloop SISO diagonal controller remains an important structure. It is the base case against which the other structures should be compared. The procedure discussed in this chapter was developed to provide a workable, stable, simple SISO system with only a modest amount of engineering effort. The resulting diagonal controller can then serve as a realistic benchmark, against which the more complex multivariable controller structures can be compared. 

The limitations of the procedure should be pointed out. It does not apply to openloop unstable systems. It also does not work well when the time constants of the different transfer functions are quite different i.e., some parts of the process much faster than others. The fast and slow sections should be designed separately in this case. 

The procedure has been tested primarily on realistic distillation column models. This choice was deliberate because most industrial processes have similar gain, deadtime, and lag transfer functions. Undoubtedly some pathological transfer functions can be found that the procedure cannot handle. But we are interested in a practical engineering tool, not elegant, rigorous all-inclusive mathematical theorems. 

The procedure is called the LACEY procedure (not because it is full of holes, as claimed by some ) from its developers Luyben, Alatiqi, Chiang, Elaahi, and Yu. The steps are summarized below. Each step is discussed in more detail in later sections of this chapter. 

In the preceding discussion we considered equilibrium void stability however, actual processing conditions involve changing temperature and pressure with time. Whereas equilibrium calculations provide bounds on void growth, it is the time-dependent growth process that is most important from a product quality viewpoint. 

An excellent article, explaining the basics of Partial Least Squares (PLS), is given by Geladi and Kowalski (1986). 

As in PC A, the data matrix is represented by a score matrix. The idea of PLS is to develop a model that relates the scores of the X data to the scores of the Y data. The PLS model consists of outer relations (X and Y data individually) and an inner relation that links the X data to the Y data. 

The outer relationship for the input matrix or matrix with predictor variables is written as  

Similarly, the outer relationship for the output matrix or matrix with predicted variables can 

For the inner relationship, the idea is to describe Y as best as possible. Also, a good relationship between X and Y shonld be developed, therefore F shoiddbe minimized. 

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Another problem for fault trees is the uniqueness of the result. Eault trees produced by two different teams of analysts most often show a different stmcture. However, this problem is reduced as the detail in the problem definition increases. 

Disciplined Approach to Problem Definition Specific technical objectives Quality function deployment or similar process Acquisition of background, literature, etc Networked to many technology resources Scientific Method... 

Whenever an economic evaluation is undertaken, a corresponding problem definition should be provided as the basis on which the evaluation is made. This definition, sometimes called an economic scope, should clearly differentiate between specifications that have actually been selected and features that have been assumed for the evaluation. In a comparison of alternatives, all of the assumptions, data, and conditions must be consistent, reaUstic, and devoid of bias. 

Problem Definition InteUigent selection of a separator requires a careful and complete statement of the nature of the separation problem. Focusing narrowly on the specific problem, however, is not sufficient, especi ly if the separation is to be one of the steps in a new process. Instead, the problem must be defined as broadly as possible, beginning with the chemical reactor or other source of material to be separated and ending with the separated materials in their desired final form. In this way the influence of preceding and subsequent process steps on the separation step will be iUuminated. Sometimes, of course, the new separator is proposed to replace an existing unit the new separator must then fit into the current process and accept feed materials of more or less fixed characteristics. At other times the separator is only one item in a train of new equipment, all parts of which must work in harmony if the separator is to be effective. 

Assistance in problem definition and in developing a test program should be sought from persons experienced in the field. If your organization has a consultant in separations of this land, by all means m e use of the expertise available. If not, it may be wise to employ an outside consultant, whose special knowledge and guidance can save time, money, and headaches. It is important to do this early after the separation equipment has been installed, there is httle a consultant can do to remedy the sometimes disastrous effects of a poor selection. Often it is best to work with established equipment manufacturers throughout the selection process, unless the problem is unusually sensitive or confidential. Their experience with problems similar to yours may be most helpful and avoid many false starts. 

PROBLEM DEFINITION. This is achieved through plant visits and discussions with risk analysts. In the usual application of THERP, the scenarios of interest are defined by the hardware orientated risk analyst, who would specify critical tasks (such as performing emergency actions) in scenarios such as major fires or gas releases. Thus, the analysis is usually driven by the needs of the hardware assessment to consider specific human errors in predefined, potentially high-risk scenarios. This is in contrast to the qualitative error prediction methodology described in Section 5.5, where all interactions by the operator with critical systems are considered from the point of view of their risk potential. 

PROBLEM DEFINITION, QUALITATIVE ERROR PREDICTION AND REPRESENTATION. The recommended problem definition and qualitative error prediction approach for use with SLIM has been described in Section 5.3.1 and 5.3.2. The fact that PIFs are explicitly assessed as part of this approach to qualitative error prediction means that a large proportion of the data requirements for SLIM are already available prior to quantification. SLIM usually quantifies tasks at whatever level calibration data are available, that is, it does not need to perform quantification by combining together task element probabilities from a data base. SLIM can therefore be used for the global quantification of tasks. Task elements quantified by SLIM may also be combined together using event trees similar to those used in THERP. 

Not all the problems that arise are clear-cut in fact, one problem may often mask another problem- or several minor problems may prove to be interdependent—providing a chain of cause and effect. As a result, different authorities may not always agree on the fundamental cause of a particular problem or even the precise chemistry involved. Terminology and problem definitions also may vary from country to country. 

Given the preceding problem definition, and after going through S, the final solution, X , chosen for implementation is (Fig. 7) ... 

Both situations with categorical and continuous, real-valued performance metrics will be considered and analyzed. Since Taguchi loss functions provide quality cost models that allow the different objectives to be expressed on a commensurate basis, for continuous performance variables only minor modifications in the problem definition of the approach presented in Section V are needed. On the other hand, if categorical variables are chosen to characterize the system s multiple performance metrics, important modifications and additional components have to be incorporated into the basic learning methodology described in Section IV. 

However, conflicts between the fulfillment of different objectives and aspiration levels may prevent any feasible zone of the decision space from leading to satisfactory joint performances. If the search procedure fails to uncover at least one feasible final solution, X, consistent with y, a number of options are available to the decisionmaker to try to overcome this impasse. Namely, the decisionmaker can revise the initial problem definition, by either... 

The problem definition itself does not pose any restrictions on the decisions described above. For all practical purposes all these choices are arbitrary. That, in fact, demonstrates the ill-posedness of the problem, which results in a variety of solutions depending on the partieular tool used and the specific choices that are forced. 

Typical examples such as the ones mentioned above, are used throughout this book and they cover most of the applications chemical engineers are faced with. In addition to the problem definition, the mathematical development and the numerical results, the implementation of each algorithm is presented in detail and computer listings of selected problems are given in the attached CD. 

Rosenblatt DH, Miller TA, Dacre JC, et al. 1975a. Problem definition studies on potential environmental pollutants. I. Toxicology and ecological hazards of 16 substances at the RMA. Technical Report 7508. U.S. Army Medical Bioengineering Research and Development Laboratory, Fort Detrick, Frederick, MD. 

Matson, F. R. (1981), Archaeological ceramics and the physical sciences Problem definition and results,. Field Archaeol. 8, 447-456. 

Berkowitz, J.B. Goyer, M.M. Harris, J.C. Lyman, W.J. Nelken, L.H. Rosenblatt, D.H. "Literature Review -Problem Definition Studies on Selected Chemicals. Vol. 

Dacre JC, Burrows WD, Wade CWR, et al. 1979. Problem definition studies on potential environmental pollutants v. physical, chemical toxicological, and biological properties of seven substances used in pyrotechnic compositions. U.S. Army Medical Research and Development Command Technical Report 7704. 

Kitchens JF, Harward WE, Lauter DM, et al. 1978. Preliminary problem definition study of 48 munitions-related chemicals. Vol. III. Pyrotechnic Related Chemicals. Alexandria, VA Atlantic Research Corporation. 

For convenience of presentation, model building can be divided into four phases (1) problem definition and formulation, (2) preliminary and detailed analysis, (3) evaluation, and (4) interpretation application. Keep in mind that model building is an iterative procedure. Figure 2.2 summarizes the activities to be carried out,... 

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