Variability consequences

Control loops can be either stable or unstable. Instability is caused by a combination of process time lags discussed earlier (i.e., capacitance, resistance, and transport time) and inherent time lags within a control system. This results in slow response to changes in the controlled variable. Consequently, the controlled variable will continuously cycle around the setpoint value. 

We shall now examine the consequences of Eqs. (18) and (21). For the case of two-phase vapor-liquid equilibria, there is only one degree of freedom and only one variable. Consequently, Eq. (18) leads to ... 

It is clear from this formula that the variance of the response is independent of x, the settings of the design variables. Consequently, there is no opportunity for achieving a more robust response in the presence of the environmental variation, z, by selecting particular settings for the design variables. 

It is generally assumed that under ordinary laboratory conditions the trans isomers of the azoxy compounds are formed. Although the cis isomers are generally much higher-melting and are much more insoluble than the corresponding trans isomers, their stabilities at room temperature appear to be highly variable. Consequently, only a few cis compounds have been isolated. 

The thermal stability of V-nitroso derivatives is highly variable consequently it is suggested that any effort to prepare such derivatives be carried out with extreme care. In particular, care must be exercised in avoiding contact of yV-nitroso compounds with strong alkaline media because the unstable diazoalkanes are generally prepared by this method (see Volume 1, Chapter 15). 

Equation 5.15 is now transformed to use / as the independent variable, with G as the dependent variable. Consequently... 

This is employed where a process is well-known and an adequate mathematical model is available. If there is an auxiliary process variable which correlates well with any changes occurring in process dynamics, then the best values of the controller parameters can be related ahead of time to the value of the auxiliary variable. Consequently, by measuring the value of the auxiliary variable, the adaptation of the controller parameters can be scheduled (or programmed). 

In a follow-up study, Calvert et al. (1996) examined the association between exposure to 2,3,7,8-TCDD and serum lipids. In the follow-up the authors chose not to adjust the 2,3,7,8-TCDD serum concentrations for total lipids to avoid the problems of interpretation that would arise when adjusting a covariate by the dependent variable. Consequently, the results obtained in this study cannot be compared directly with those from the Operation Ranch Hand study (see below). The median serum 2,3,7,8-TCDD concentration among the workers was 406.6 femtograms/g serum (fg/g) compared with 36.9 fg/g among the referents. 

A high correlation can be approximated by a straight regression line — sloped upward or downward — that is determined by the minimum sum of the squared distances of all the data points. One of the descriptors, g or gg, can be regarded as the dependent variable. Consequently, two regression lines with different slopes can exist. By defining... 

The control valve is a variable orifice device in which the size of the orifice is adjusted to control a process variable. Consequently, the manufacturer, type, or even the size of a control valve has no effect on the energy dissipated in the control of a selected stream once the process pressure, line size, and pumps have been selected. This energy-independence of the control valve assures that continuous throttling of the flow stream is required to control a process variable. In those cases where a valve is used for shut-off or override control (not a continuous throttling device), energy savings can be realized by selecting a valve with a minimum pressure loss in the full-open position. 

Even with the precautions noted above, response from vanadium was often quite variable. Consequently, the slope and intercept of response... 

Steady-state analysis implies that the combination of fluid kinetic energy per unit volume and dynamic pressure is not time dependent. The potential flow equation of motion suggests that this combination of fluid kinetic energy per unit volume and dynamic pressure is not a function of any independent spatial variable. Consequently,... 

The inclusion of irrelevant data is detrimental to the model because the mathematics attempt to account for variations observed in these irrelevant variables. Consequently the model is forced to model noise, resulting in a decrease in its predictive ability. Worse yet, the model could fit the data well and provide a seemingly useful prediction, until cross-validation shows otherwise. Finally, the inclusion of extraneous variables increases the demands on the computer system being employed, making model construction slower, or in some cases outright impossible. Thus, prior reduction of separations data to a manageable size is crucial. Figure 6 depicts situations where either too few or too many variables were used to model a system. 

Empirical evidence indicates that the majority of the respondents locate their service quality score at the right-hand side of the scale (Brown et al. 1993 Parasuraman et al. 1988 1991 Peterson and Wilson 1992). This distribution is referred to as negatively skewed. A skewed distribution contains several serious implications for statistical analysis. To begin with, the mean might not be a suitable measure of central tendency. In a negatively skewed distribution, the mean is typictilly to the left of the median and the mode and thus excludes considerable information about the variable under study (Peterson and Wilson 1992). Skewness also attenuates the correlation between variables. Consequently, the true relationship between variables in terms of a correlation coefficient may be understated (Peterson and Wilson 1992). Einally, parametric tests (e.g., t-test, F-test) assume that the population is normally or at least symmetrically distributed. 

Another advantage of using the concept of extent is that it permits a unique specification of the rate of a given reaction. This point is discussed in Section 3.0. The major drawbacks of the concept are that the extent is defined for a closed system and that it is an extensive variable. Consequently, the extent is proportional to the mass of the system being investigated. 

At one time, scientists selected variables for inclusion in a regression model based on some type of strong justification for including them. That justification would have been based on some a priori idea or hypothesis that the variables chosen were the critical factors in establishing the variability in the response variable. Although this approach may still be used by scientists, more often today researchers have no prior knowledge about the relative importance of the various independent variables. Consequently, many regression... 

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