Problem formulation level

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. 

Usually models are created for a certain purpose, and that purpose drives their structure, level of detail, level of complexity, etc. A model may be excellent, but it must not be used for inappropriate purposes. If the output of the model does not match the assessment endpoint and the questions raised in the problem formulation phase, then the model obviously is not suitable for the specihc case. 

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. 

Classical Two-Level Optimisation Problem Formulation for Binary Mixtures... 

Mujtaba (1989) considered the separation of a binary mixture (Benzene-Toluene) with off-cut recycle. The optimal operating policy, computation time, etc. were determined using the two level and the one level optimisation problem formulations and the results were compared. 

If the consequences of setting a standard will have important environmental, economic, or social consequences, we envisage an approach in which a social and economic analysis forms part of the overall decision in conjunction with the scientific analysis. The two activities come together in an MCDA that seeks to integrate all the factors that will deliver the required level of environmental protection at an acceptable economic and social cost. If that cost can be defined during problem formulation, this will greatly facilitate the process because it puts limits on what is, and is not, permissible. 

There are a number of general techniques suggested by the problem formulation. At the most detailed level of design, the design parameters need to be optimized in relation to performance criteria based on a nonlinear dynamic model. This points to a need for effective tools for dynamic optimization. At a more preliminary level in a hierarchy of techniques, it might be useful to evaluate steady-state performance or to carry out tests on achievable dynamic performance to eliminate infeasible options. Appropriate screening techniques are therefore needed. All these methods can use nominal models for initial analysis, but a full analysis should be based on design with uncertainty. 

The first phase of the framework is problem formulation. Problem formulation includes a preliminary characterization of exposure and effects, as well as examination of scientific data and data needs, policy and regulatory issues, and site-specific factors to define the feasibility, scope, and objectives for the ecological risk assessment. The level of detail and the information that will be needed to complete the assessment also are determined. This systematic planning phase is proposed because ecological risk assessments often address the... 

Using information obtained from the exposure analysis, the exposure profile quantifies the magnitude and spatial and temporal patterns of exposure for the scenarios developed during problem formulation and serves as input to risk characterization. The exposure profile is only effective when its results are compatible with the stressor-response profile. For example, appraisals of potential acute effects of chemical exposure may be averaged over short time periods to account for short-term pulsed stressor events. It is important that characterizations for chronic stressors account for both long-term low-level exposure and possible shorter term, higher level contact that may elicit similar adverse chronic effects. 

In addition to these extrapolations, an evaluation of indirect effects, other levels of organization, other temporal and spatial scales, and recovery potential may be necessary. Whether these analyses are required in a particular risk assessment will depend on the assessment endpoints identified during problem formulation. 

Modern science and engineering requires high levels of qualitative logic before the act of precise problem formulation can occur. Thus, much is known about a physicochemical problem beforehand, derived from experience or experiment (i.e., empiricism). Most often, a theory evolves only after detailed observation of an event. Thus, the first step in problem formulation is necessarily qualitative (fuzzy logic). This first step usually involves drawing a picture of the system to be studied. 

To address national development in the area of road safely, it is desirable to view road safely level in a global context. Road safely is a complex issue and there is a high number of factors and indicators involved in the accidents. This situation leads me to examine several theories and models in order to compare the achievements in road safety between diffeient countries and regions. The problem itself is underestimated in many countries, especially in developing countries where the issue is challenging. The progress in any country will be minimum unless the country has a good and standard measurement to rely on (e.g. RSDI), in comparisons and problem formulation. 

For sake of simplicity in the problem formulation and discussion of results, only the MOV of the AFWS is considered in order to formulate the APSA for this simple example of application. Table 1 shows data used for modelling the MOV basic event into the level 1 APSA, including description of parameters and corresponding constant value or probability distribution function (pdf). In the same way as in the standard PSA, all variables except motor-operated failure rate have been considered constant, i.e. mean values have been used. MOV failure rate has been modeled as a random variable assuming a Gamma probability distribution. 

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