Target quantity

ANOVA was developed by Fisher [1925,1935] as a statistical procedure that investigates influences (effects) of factors on a target quantity y according to a linear model which holds in the simplest case... 

Frequently the signal intensity of the analyte A is the target quantity, the influences on which are described by Eq. (3.16a). Handling all the influences (interferences and other factors) in the same way and holding xA at any constant value so that a0 = yAo + SAAxA, Eq. (3.16a) can be written... 

In analytical chemistry the target quantity y which has to be optimized is frequently the signal intensity, absolute or relative (signal-to-noise ratio), but occasionally other parameters like yields of extractions or chemical reactions, too. The classical way to optimize influences, e.g., in an optimization space as shown in Fig. 5.3a is to study the factors independently one after the other. In Fig. 5.3b,c it can be seen that an individual optimum will be found in this way. 

Knowledge of the maximal possible yield coefficients as target quantities on the one hand, and the reasons for discrepancies between these values and experimentally obtained values on the other, can help reduce the experimental expenditure needed for optimizing yield, and recommend worthwhile approaches and measures to test. 

This appendix presents a review of experimental work in the field of packed-bed combustion of biomass. It deals with the measurement methods used to analyse the thermochemical conversion of the biomass. This implies that thermochemical conversion studies of coal is outside the scope of this literature study. Wood stove research is not considered in this review either. Of special interest in this survey is the choice of sought physical quantities (target quantities) and measurands of interest in each study and how they are modelled and verified, and if uncertainty analysis is carried out. 

First, all physical parameters necessary to describe the problem are listed. This so-called relevance list of the problem consists of the quantity in question and of all the parameters that influence it. In each case, only one target quantity must be considered it is the only dependent variable. On the other hand, all the influencing parameters must be primarily independent of each other. 

We facilitate the procedure by systematically listing the target quantity and all the parameters influencing it ... 

The relevance list of this task consists of the target quantity (mixing power P) and the following parameters stirrer diameter d, density p, kinematic viscosity v of the liquid, and stirrer speed ... 

Mixing time 6 is the time necessary to completely homogenize an admixture with the liquid contents of the vessel. It can easily be determined visually by a decolorization reaction (neutralization, redox reaction in the presence of a color indicator). The relevance list of this task consists of the target quantity (mixing time 6) and of the same parameters as in the case of mixing power— on condition that (contrary to Example 3) both liquids have similar physical properties ... 

In all these tasks, the achievable (as narrow as possible) droplet size distribution represents the most important target quantity. It is often described merely by the mean droplet size, the so-called Sauter mean diameter J32 (Ref. 19), which is defined as the sum of all droplet volumes divided by their surfaces. Mechanisms of droplet formation are ... 

This equation (Ref. 21), is useless for scaling-up purposes because the (unknown) target quantity process number Oh. In the combination... 

The flne grinding of solids in mills of different shape and mode of operation is used to produce the finest particles with a narrow particle size distribution. Therefore—as in the previous example—the target quantity is the median value dso of the particle size distribution. 

Once preformulation screening has identified which excipients are able to stabilize the API, a series of prototype formulations can be developed, which will be more reflective of the targeted quantities of excipients and drugs present in the final... 

Example 2 The Determination of the Pi Set for the Stirrer Power in the Contact Between Gas and Liquid. We examine the power consumption of a turbine stirrer (so-called Rushton turbine see inset in Fig. 1) installed in a baffled vessel and supplied by gas from below (see Sketch 2). We facilitate the procedure by systematically listing the target quantity and all the parameters influencing it ... 

Quantities of the square core matrix may eventually appear in all of the dimensionless numbers as fillers, whereas each element of the residual matrix will appear in only one dimensionless number. For this reason the residual matrix should be loaded with essential variables like the target quantity and the most important physical properties and pro-cess-related parameters. 

With the basic dimensions of mass, length, and time denoted as [M], [L], and [T], respectively, the relevance list for the target quantity H [ML T ] (mechanical tensile strength of the tablet) included ... 

Multiple regression of the target quantity (H k) on a combined data set (including data for two materials, two presses, two speed levels for each press, and a... 

It was demonstrated that dimensional analysis of the tableting process can produce a scientifically reliable way of predicting tablet properties across the range of materials and with diverse compaction mechanisms. A theoretically sound scale-up method is thus readily available for tableting equipment of different capacity. The method can be readily expanded to include other materials and tablet presses and other target quantities, such as tablet stability (disintegration) and bioavailability (dissolution). 

Equation 23.6 gives the approximate relationship between the charging current and the peak faradaic current, ip (the target quantity), for a test compound of concentration C° (mM) assuming normal double-layer capacitances [1],... 

Target quantities power consumption P, axial screw force F, pumping pressure Ap, temperature of the extrudate expressed in temperature difference AT = T — To, and volumetric throughput Q... 

Target quantity maximum temperature inside the part due to exothermic reaction Tmax (ATmax = 7— To), pressure rise inside the die Ap, and pull force F,... 

The simplest method to produce droplets is to drip a liquid slowly out of a capillary under the influence of gravity. Due to the low shear rate, the viscosity of the liquid will, as a rule, have no influence. In this case the target quantity, particle diameter (here droplet diameter) dp, will depend only on the wetted capillary diameter d, the surface tension o and the weight gp of the dripping liquid ... 

Roasting is an endothermic process. The meat is ready when a certain temperature distribution (T) is reached within it. The target quantity is the time duration, 0, necessary to achieve this temperature field. 

The nature of the steps which have to be carried out now makes this dimensional matrix less than ideal because it is necessary to know that each of the individual elements of the residual matrix will appear in only one of the dimensionless numbers, while the elements of the core matrix may appear as fillers in the denominators of all of them. The residual matrix should therefore be loaded with essential variables such as the target quantity and the most important physical properties and process-related parameters. Variables with an, as yet, uncertain influence on the process must also be included in this group. If, later, these variables are found to be irrelevant, only the dimensionless number concerned will have to be deleted while leaving the others unaltered. 

This example, taken from [12], belongs to the field of heat transfer by convection. Here the heat transfer coefficient, h, represents the target quantity. This quantity can be determined only via the general heat transfer equation... 

Electrically heated wires and pipes with the diameter, d, are mounted horizontally and are cooled by an air stream. The relevance list reads target quantity heat transfer coefficient, h... 

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