Stage 2 Problem formulation

The objective of the problem formulation stage is to formulate the inventive problem in the form appropriate for using TRIZ. Specifically, the results of the problem definition stage must be translated into the TRIZ language or formulated in TRIZ terms. 

There is a three-step process to follow for any given system under consideration  

The problem identification stage provides information about the input and output of the system, the function of the system, and the functions of its individual elements and subelements. 

The first step requires a careful analysis of these first two pieces of information (input and output) in order to determine the major basic features, that is, those features that are incorporated in the description of the input and output and into the description of the system functions. 

In the second step we need to identify a technical contradiction involving the basic features that have been distinguished. In our simple example, this is easy We have a technical contradiction between strength and weight.  

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In the previous stage, problem formulation, both the problem s basic features and the technical contradiction have been identified. Now, they will be used to find inventive patterns, which might help to eliminate the identified technical contradiction. 

In this paper we present a meaningful analysis of the operation of a batch polymerization reactor in its final stages (i.e. high conversion levels) where MWD broadening is relatively unimportant. The ultimate objective is to minimize the residual monomer concentration as fast as possible, using the time-optimal problem formulation. Isothermal as well as nonisothermal policies are derived based on a mathematical model that also takes depropagation into account. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and time is studied. 

The first stage of any experimental design is the problem formulation, a basic step in which the objectives and thus the response variable to be optimized should be defined. After that, it is essential to identify all the factors that might have an influence on the selected responses, and for each factor, variability levels that take into account eventual constraints. 

The visual observation of the dissolution of a dosage form can quickly provide an indication of problems with the formulation or the dissolution test conditions without the requirement for sample analysis. This is particularly useful in the early stages of formulation and method development, when a variety of formulations or a range of dissolution media may be under consideration. 

In this section we formulate a high-dimensional multi-stage problem with consecutive exothermic reactions that take place in three consecutive adiabatic CSTRs with no recycle. This is done for a variable base set of parameters i, o.->, fix, [Y, 7i, and 72 for the two reactions. The dynamic characteristics of this system are obtained by numerical simulation. 

Usually, a mathematical model simulates a process behavior, in what can be termed a forward problem. The inverse problem is, given the experimental measurements of behavior, what is the structure A difficult problem, but an important one for the sciences. The inverse problem may be partitioned into the following stages hypothesis formulation, i.e., model specification, definition of the experiments, identifiability, parameter estimation, experiment, and analysis and model checking. Typically, from measured data, nonparametric indices are evaluated in order to reveal the basic features and mechanisms of the underlying processes. Then, based on this information, several structures are assayed for candidate parametric models. Nevertheless, in this book we look only into various aspects of the forward problem given the structure and the parameter values, how does the system behave ... 

Problem formulation will logically continue into the specification stage. The specification makes operational the issues identified in the problem formulation whereas problem formulation sets out what needs to be done, the specification sets out how this is to be achieved. 

Developing the specification is a critical part of the standard-setting process. It follows logically from the problem formulation stage. The specification makes the following clear ... 

Information compiled in the first stage of problem formulation is used to help select ecologically based endpoints that are relevant to decisions made about protecting the environment. An endpoint is a characteristic of an ecological component (e.g., increased mortality in fish) that may be affected by exposure to a stressor (Suter, 1990a). Two types of endpoints are distinguished in this report. Assessment endpoints are explicit expressions of the actual environmental value that is to be protected. Measurement endpoints are measurable responses to a stressor that are related to the valued characteristics chosen as the assessment endpoints (Suter, 1990a). 

Data are evaluated by considering their relevance to the measurement and assessment endpoints selected during problem formulation. The analysis techniques that will be used also are considered data that minimize the need for extrapolation are desirable. Data quality (e.g., sufficiency of replications, adherence to good laboratory practices) is another important consideration. Finally, characteristics of the ecosystem potentially at risk will influence what data will be used. Ideally, the test system reflects the physical attributes of the ecosystem and will include the ecological components and life stages examined in the risk assessment. 

Because a number of conceptualizations of patient satisfaction can be used, the measurement of patient satisfaction must fit the context of the overall research process. A research process proposed by Churchill involves six stages 1) formulate the problem 2) determine the research design 3) design data collection method and forms 4) select a sample and collect the data 5) analyze and interpret the data and 6) prepare the research report. Each stage is linked, and decisions made at one stage will affect decisions made at other stages. 

Problem formulation. Within this process all available information about a contaminated site is collected including the nature of the contaminants and their sources, obvious effects and potential receptors as well as environmental recipients. Within this very first stage of the risk assessment procedure, an assessment endpoint has to be determined. Assessment endpoints are the expression of an environmental value (represented by an ecological entity) that is at risk, e.g. a distinct population that faces harm due to pollution. It has to be emphasised that toxicity-test endpoints or other measurement endpoints (in general, measured effects under test conditions) in most cases do not represent assessment endpoints (response of population or ecosystem in the field). Measurement endpoints should be representative for assessment endpoints or have a known relationship to the assessment endpoint allowing the extrapolation of data. 

The relationships given by Eq. (1-26) may be reduced to one equation in one unknown in a variety of ways, and a variety of forms of the flash function may be obtained. One form of the flash function is developed below and a different form is developed in Chap. 4 in the formulation of multiple-stage problems. Elimination of the yf, s from the last expression given by Eq. (1-26) by use of the first expression, followed by rearrangement, yields... 

Many separations which would be difficult to achieve by conventional distillation processes may be effected by a distillation process in which a solvent is introduced which reacts chemically with one or more of the components to be separated. Three methods are presented for solving problems of this type. In Sec. 8-1, the 0 method of convergence is applied to conventional and complex distillation columns. In Sec. 8-2, the 2N Newton-Raphson method is applied to absorbers and distillation columns in which one or more chemical reactions occur per stage. The first two methods are recommended for mixtures which do not deviate too widely from ideal solutions. For mixtures which form highly nonideal solutions and one or more chemical reactions occur per stage, a formulation of the Almost Band Algorithm such as the one presented in Sec. 8-3 is recommended. 

The obvious answer to heightened complexity and uncertainty lies in utilizing financial engineering techniques to manage asset portfolios. This chapter reviews the current state of the art from a practitioner s perspective. The prime focus is on mean-variance optimization techniques, which remain the principal application tool. The key message is that while the methods employed by today s specialists are not especially onerous mathematically or computationally, there are major issues in problem formulation and structure. It is in this arena that imagination and inventiveness take center stage. 

The second-stage problem depends on the data f((u) = q random vector f = f(probability distribution is assumed to be known. The above formulation originated in the works of Dantzig (1955) and Beale (1955). 

Therefore, the above two-stage problem can be formulated as one large linear program ... 

In the general case, the problem formulated in the previous sections has no analytical solution at each stage dierefore, numerical methods for solving are used, as a mle. In this chapter, for the first stages, the numerical integration of the equation of motion of the nanoparticle atoms in the relaxation process are used in accordance with Verlet scheme [26] ... 

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