Possible performance indices

The methods just presented can be used for any number of variables. However, optimizing all the possible variables of a plant in one massive optimization is a Herculean task. The usual approach is to reduce the number of variables to those that strongly affect the performance index. For instance, in the polystyrene example the cost of electricity is almost insignificant and can be ignored. However, the amount of water added to the reactor may be very important. An optimization is made for the major variables. Then the effects of the minor variables are considered either in groups or separately. 

If participants in an external quality assessment scheme simply receive the results and check the performance index or some other measure to see if it is satisfactory, a great deal of valuable information is lost. Data from these schemes offer an opportunity to study a laboratory s assay and to assist in the education of laboratory personnel. Simple graphical approaches can be used that do not require complicated calculations. If a laboratory has a computer, more elaborate calculations can be carried out. Basically, the participating laboratory has analysed a sample for a particular analyte and has then to compare the value found with the True value. Possible estimates of the True value include the overall mean for all participants, the method mean, the mean value obtained by designated reference laboratories, or a stated spiked value. Some schemes provide all these values, but the majority provide an overall mean, which will be used in the following discussion. The overall mean has limitations if the technique for elimination of outliers is unsatisfactory or if a particular method, which causes a marked bias at certain concentrations in the overall mean, is used by a significant number of laboratories. 

One possible compromise here would be to develop an index based on the performance of a neutral agent that only mechanically removes viruses from hands. In the past, nonmedicated soaps have often been used for this purpose. However, soaps on the market differ widely, especially in properties such as pH and detergent action. Tap water also differs at different geographical locations. Therefore, a simple, safe, and readily available solution such as standard hard water (e.g., with 200 ppm hardness) could be used to establish the reference point for this index. Product efficacy claims could then be allowed at a certain differential above the mechanical virus removal with hard water. Manufacturers could publish the performance index of their formulation on the label to aid in product selection. To prevent minor differences in indices being used as a sales feature, a simple product classitication scheme could be developed. 

Attempts have been made to combine the different parameters of a separation into a single criterion that describes the overall quality of a column or a separation. We would like to combine a measure of the narrowness of the buds, the analysis time, and the pressure needed to drive the separation. Since we want to maximize efficiency while minimizing analysis time and pressure, a possible measure would be the simple ratio of plate count to the product of analysis time and pressure. However, since we end up with two parameters that we want to minimize in the denominator and only one parameter that we want to maximize in the numerator, we end up with a measure that minimizes plate count To compensate for this, we n to raise the plate count in the numnator to the second power. This measure of overall column performance is the performance index, first developed for gas chromatography by Golay (18) ... 

One possible global performance index can be constructed by comparing the measuring system performance with the one corresponding to the same system but in which all variables are measured. When only a few variables are of interest, only these will be considered, being S the set of variables of Interest ... 

The SUNflower approach was first presented in 2002 (Koomstra et al., 2002), when the road safety efforts of the three safest countries worldwide were compared Sweden, the United Kingdom and the Netherlands. The main aim of this comparison was to acquire better insight into the policy development processes of these three countries. It was hoped that this comparison would identify the crucial points that had made it possible for these nations to improve their respective road safety records, and to learn how further improvements could be achieved. Later, this approach was expanded to include nine countries (Wegman et al., 2008). These efforts eventually resulted in a proposal to benchmark the safety performance of countries and jurisdictions (states within countries, provinces) using a composite road safety performance index (Wegman et al., 2008 Wegman and Oppe, 2010). 

The weak maximum principle can certainly be used to maximize the performance index of Eq. 13.33, for instance, for the independent deactivation problem given by Eqs. 13.40 through 13.45 with the addition of a heat balance at the pellet-bulk fluid interface for the pellet surface temperature 7 [( )s]. Nevertheless, the optimal inlet temperature will be a function of time. Thus, the inlet temperature is to be manipulated in a prescribed manner in time without any regard to what happens to the reactor. This open-loop control is rarely practiced in actual applications because of the uncertainties regarding the model, measurements, and disturbances. Rather, closed-loop control using feedback from the process is usually practiced. This fact should not discourage one from using the maximum principle for optimization, for it will at least indicate what the best possible performance is in a relative sense. At the same time it can yield in some simple cases a very powerful optimal policy such as the constant conversion policy, which can be implemented by a feedback control scheme. 

Working capital can range from about 10 percent to almost 100 percent of the invested capital, depending on the industry, and is an important fac tor in the profitability index of a business. For this reason, it is best to compare the performance of an individual company with that of others that are as similar as possible. 

A third parameter to consider is the column construction. Thus the sample applicator should provide optimal sample application to give the most performance possible out of the packed bed. Constructions should also allow simple, fast, and reproducible packing of the column. Because costs for repacking of columns are a substantial operating cost item in industrial chromatography, the selection of column construction from this point of view is also important. Some novel column constructions allow very simple procedures both for laboratory and for industrial scale (e.g., INdEX columns, see Section V). 

If the mixture to be separated contains fairly polar materials, the silica may need to be deactivated by a more polar solvent such as ethyl acetate, propanol or even methanol. As already discussed, polar solutes are avidly adsorbed by silica gel and thus the optimum concentration is likely to be low, e.g. l-4%v/v and consequently, a little difficult to control in a reproducible manner. Ethyl acetate is the most useful moderator as it is significantly less polar than propanol or methanol and thus, more controllable, but unfortunately adsorbs in the UV range and can only be used in the mobile phase at concentrations up to about 5%v/v. Above this concentration the mobile phase may be opaque to the detector and thus, the solutes will not be discernible against the background adsorption of the mobile phase. If a detector such as the refractive index detector is employed then there is no restriction on the concentration of the moderator. Propanol and methanol are transparent in the UV so their presence does not effect the performance of a UV detector. However, their polarity is much greater than that of ethyl acetate and thus, the adjustment of the optimum moderator concentration is more difficult and not easy to reproduce accurately. For more polar mixtures it is better to explore the possibility of a reverse phase (which will be discussed shortly) than attempt to utilize silica gel out of the range of solutes for which it is appropriate. 

The search for amounts to successive solution of three-point equations of the form (E - - r i2(j)w = F by the elimination method for every component of the vector w with the index account from a to a -b 1. One possible way of covering this is connected wdth the performance of the following algorithm ... 

The NSS concept corresponds to an operator attached to an arbitrary number of nested sums. In other words, a NSS represents a set of summation symbols where the number of them can be variable. In a general notation one can write a NSS as E (j=i,f,s,L) where the meaning of this convention corresponds to perform all the sums involved in the generation of all the possible values of the index vector j under the fulfillment of the set of logical expressions collected in the components of the vector L. The elements of the vector j have the following limits ... 

---