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For design of wastewater treatment plants, a couple of chemical parameters of the collected wastewaters have to be analyzed following the above-mentioned procedures. For example, for designing the nitrification process, the wastewater content of ammonia is relevant. As concentrations of wastewater constituents are not constant, it is necessary to know how the relevant parameter varies with time (day-time, weekly time-course, seasonal deviations). Of course, also the volume flow of the wastewater is important, to calculate the mass flows of the relevant parameters. But which of the measured concentrations (or mass flows) should be taken into consideration? Is it good to select the highest value determined e.g. within a year? Or the mean? Using the maximum parameters determined will lead to "oversize" wastewater treatment processes which will cause high investment as well as high operational costs. A reasonable amount of the operational costs are caused by energy consumption. Thus, oversized treatment processes are not ecologically beneficial.

On the other hand, one of the most serious deficiencies results when the design of a treatment plant is based on average flow rates and average concentration of design-relevant wastewater constituents, with little or no recognition of peak conditions (Tchobanoglous and Burton 1991). Therefore, in Germany commonly that concentration of a parameter is used for design that is not exceeded by 85 % of all values determined within a campaign of measurements (85 percentile). However, this requires sufficient data being analyzed to yield a statistical safety of 95 % (Bever et al. 1993). Statistical analysis of flow data is given by Tchobanoglous and Burton (1991).

A method that can be used for deriving design parameters from a large amount of determined concentrations of one parameter is the method of Groche (1977).

Figure 13: An example for recording wastewater parameters xi (BOD5) analysed in a wastewater stream during a certain period) in a table in ascending order and deriving the part of all values that are equal to or less than the indicated value xi following the method described by Groche (1977)

In this method, a table is created containing all analysed data of a design parameter xi (BOD5 in the depicted example) in ascending order (see figure 13, 3rd column). In the first column of the table in figure 13 the rank serial number i is written starting with number 1. From the rank serial number i, a term (3×i - 1) is calculated and written into the 2nd column. This term divided by a term (3×n + 1) with n being the number of all analytical data obtained within the campaign gives the part of all values, that are equal to or less than the indicated value xi:

These values S% are noted in the 4th column. Finally, the data S% can be drawn as a function of xi using log-probability paper (see figure 14). The dashed lines drawn in figure 14 give a statistical certainty of 95 % and are dependent on the total number of analyses performed (n). For an infinite number of analyses, this is given for the 85 percentile value (corresponding to an xi of 17.7 mg BOD5/l in the given example). However, as only 34 data were available in this particular example, a statistical certainty of 95 % is not obtained with the 85 percentile. The helping line for this statistical certainty is intersected by the drawn line at an xi of 21.5 mg BOD5/l giving the tolerance limit for the determined 85 percentile BOD5 in this example. The helping lines are drawn using the right-hand ordinate, the so-called probits. The probits are depending on the number n of all analytical data of the parameter of concern measured in the campaign. Table 7 gives the probits as a function of the number of all data (n).

Table 7: Probits corresponding to the number of n of all available data of one parameter taken into consideration for design of treatmant processes; Bever et al. (1993)

Another aspect of statistics in chemical analyses is the complex of accuracy, reproducibilty, and detection limits of analytical procedures. Scattering of results of multiple analyses performed with one sample reflects sources of errors caused by the experimentator's actions (taking aliquot volumes from samples e.g. by pipetting, dosing reagents, contaminations of technical devices and reagents needed for the analyses etc.) as well as by inconstancies of technical devices used during the analytical procedure (e.g. instabilities of lamps - especially when aged - or photomultipliers in photometers). These errors are of increased relevance the smaller the concentration of analytes is. For analytical experts, Funk et al. (1995) is recommended as further reading material.

Figure 14: Example for applying the method described by Groche (1977) for deriving the 85 percentile of 34 BOD5 analyses of a wastewater (see figure 13)

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