Secondary variables

Secondary variables may be defined which support a more detailed evaluation of the primary endpoints or alternatively such endpoints may relate to secondary objectives. These variables may not be critical to a claim but may help in understanding the nature of the way the treatment works. In addition, data on secondary endpoints may help to embellish a marketing position for the new treatment. 

If the primary endpoint gives a negative result then the secondary endpoints cannot generally recover a claim. If, however, the primary endpoint has given a positive result, then additional claims can be based on the secondary endpoints provided these have been structured correctly within the confirmatory strategy. In Chapter 10 we will discuss hierarchical testing as a basis for such a strategy. 

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The principal secondary variable that influences yields of gaseous products from petroleum feedstocks of various types is the aromatic content of the feedstock. For example, a feedstock of a given H/C (C/H) ratio that contains a large proportion of aromatic species is more likely to produce a larger proportion of Hquid products and elemental carbon than a feedstock that is predominantly paraffinic (5). 

On-line analysis is often more expensive and difficult to set up initially but can be more accurate and rehable if performed properly. On-line analyzers can also be used to provide real-time control of a process through a secondary variable such as severity or conversion, as opposed to controlling a primary variable, such as temperature (36,52). 

For steam turbines the cost should be correlated vs. horsepower w ith steam inlet and outlet pressure as secondary variables. 

Unfortunately, neither the computer nor the potentiometric recorder measures the primary variable, volume of mobile phase, but does measure the secondary variable, time. This places stringent demands on the LC pump as the necessary accurate and proportional relationship between time and volume flow depends on a constant flow rate. Thus, peak area measurements should never be made unless a good quality pump is used to control the mobile phase flow rate. Furthermore, the pump must be a constant flow pump and not a constant pressure pump. 

EPM has been developed to simulate as a function of time all the phases, species, and the detailed )tinetic mechanism of the previous section. The structure of EPM consists of material balances, the particle number concentration balance, an energy balance, and the calculation of important secondary variables. 

Once the primary variables were obtained, numerous secondary variables were also calculated such as overall conversion, monomer A and B conversions, polymer composition from the moles of A and B in the copolymer, and number average molecular weight. The latter was obtained by dividing the mass of monomers A and B in the polymer by the moles of polymer. 

Figure 11.1c shows a series cascade system. There are now two controllers, The secondary controller Bi adjusts M to control the secondary variable X. The setpoint signal Jfto the Bi controller comes from the primary controller, i.e., the output of the primary controller Bi is the setpoint for the controller. The Bi controller setpoint is Jfy -... 

If objective variables are considered by the investigator when making a global assessment, then those objective variables should be considered as additional primary, or at least important secondary, variables. ... 

If regulatory control is used, the cure cycles should be developed as efficiently and effectively as possible. The cost of cure cycle development is open-ended because there is no limit on the number of possible variations to cure cycles. There is no guarantee either that the results will be transferable to other processing equipment or materials because the relationship between primary and secondary variables is unpredictable in such complex, path-dependent processes. 

An alternate to statistical methods is the analytical study of the material behaviors and mechanisms that link the primary variables to the secondary variables that are more easily controlled. This is often called processing science. 

Regardless of the quality of the model, process cycles designed with models have all of the same problems of process cycles designed by process science, DOE, or SPC. Preplanned regulation of secondary variables does not allow controlled adaptation to unanticipated disturbances in the cycle. 

The shortcoming of all methods for predetermining cure cycles that regulate secondary variables is that they deal only in expectations and probabilities. No matter how many eventualities are anticipated, there is always one more that is unexpected. Unexpected variations in material properties, process equipment malfunctions, and changes to geometries of tool and part all contribute to the uncertainty of the outcome. As a result, in-process, inferential control is needed for the process environment as well as the boundary conditions and material state. Inferential control is relatively new to the polymer processing industry, especially in complex processes where good models are not yet common. 

There are a number of tools available to the process engineer for designing a preset process cycle for regulating secondary variables such as temperature and pressure and for supervisory control of the process cycle based on inferred composite properties. Many of these have been tested in a variety of applications. None of these tools is capable of handling all of the tasks of a batch process controller but they can be combined, and the resulting systems have potential far beyond that of any one tool by itself. 

The secondary variables, such as shear rate, mean residence time, power consumption, throughput rate, etc., are expressed as a function of the primary variables. For example, the shear rate (or material displacement rate) in the screw channel is a function of the primary variables D, N, and H... 

Table 4 Geometric Scaling Ratios of Primary and Secondary Variables for Screw Extruder...

To summarize, while selection and scale-up of extruders is governed by extruder geometry, formulation, and process variables, secondary variables could be used to monitor the process on a continuous basis. Based on the reports thus far in the literature, the variables that seem to play a critical role in scale-up of extrusion are summarized in Table 7. 

Mathematical Models. Secondary variable interactions quantify the synergies which are common in food chemistry. These interactions cannot be computed from pooled primary variable/sequential design studies and interpolations from such pooled data would lack the information given by the secondary interaction terms. Prob > t is an estimate of the relative importance of each model term. Terms with the lowest Prob > t could well be the driving force of the reaction processes accounting for the quantity of the volatiles found. From Table IV, about 25% of the model terms present at >0.05 Prob > t are seen to be interaction terms. 

Cellular activities such as those of enzymes, DNA, RNA and other components are the primary variables which determine the performance of microbial or cellular cultures. The development of specific analytical tools for measurement of these activities in vivo is therefore of essential importance in order to achieve direct analytical access to these primary variables. The focus needs to be the minimization of relevant disturbances of cultures by measurements, i. e. rapid, non-invasive concepts should be promoted in bioprocess engineering science [110,402]. What we can measure routinely today are the operating and secondary variables such as the concentrations of metabolites which fully depend on primary and operating variables. 

Available measurements. For controlled variables that are not directly measurable, measurements have to be inferred by measurements of secondary variables and/or laboratory analysis of samples. Good inference relies on reliable models. In addition, the results of laboratory analysis, usually produced much less frequently than inferential estimates, have to be fused with the inferential estimates produced by secondary measurements. 

There are three primary and three secondary variables involved with the mode of action of dry heat. Temperature, water content, and time are the primary variables, and the secondary variables are open and closed systems, physical and chemical properties of... 

As discussed earlier, water has a direct influence on the resistance of microorganisms to dry-heat destruction. The destruction rate of spores is a function of the quantity of water in the cell at the time of heating. This water content is only constant under certain conditions and in most conditions, the moisture content of the cell can change so that the secondary variables cause confusion in analysis of results. The water vapor pressure in the atmosphere surrounding the cell determines the movement of water to or from microorganisms on surfaces. Research found that when the humidity in air passing over spores was increased from 0-0.2, the D value also increased by a factor of 100. Spores of intermediate moisture content with an RH between 0.1 and... 

In order to infer the composition from temperature an ANFIS net is used. Previously, a sensitivity study is performed in order to choose the correct set of temperatures to infer top and bottom compositions (figure 4). The sensitivity index proposed is defined as the partial derivative of each available primary variable (product composition) with respect to changes in each secondary variable (tray temperature). 

I Modest improvements in ADAS-cog, CIBIC. Inconsistent resnlts with secondary variables. 

Figure 3.6. The relationship between concentration (horizontal axis) and a secondary variable, e.g. absorbance, (vertical axis) can often be expressed as a straight line with a slope bi and an offset b0.

The primary variables are by definition those fluctuations which contribute directly to the dielectric fluctuation. The secondary variables are those variables that are dynamically coupled to the primary variables. 

The principal variables that must be controlled in crystallization are the solution supersaturation, the crystal surface area available for growth, and the nucleation rate. These are affected by multiple interacting secondary variables, which may be divided into two categories—equipment design variables and dynamic variables affecting the crystallization. It is the secondary dynamic variables, such as those listed in Table 9.1, to which automatic process control is applied in a typical crystallizer for these vari-... 

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