operation meant achieving a high value for y. However, it became evident after the first set of experiments were made, that the percentage of the flow retreated (flow returned to treatment plant), which we denote by z, also had to be taken into account. Referring to Figures 1.1.1b and 1.1.2a, influent flow to the screens is denoted by Figure 1.1.2 Original version of the screening unit (a) detailed diagram and (b) simplified diagram.
1.1.4 A Summary of the Various Phases of the Investigation
Phase a
In this initial phase, an experiment was run in which the roles of three variables were studied: collar screen mesh size (fine, coarse), horizontal screen mesh size (fine, coarse), and flow rate (gpm). At this stage,
1 The experimenters were encouraged by the generally high values achieved for y.
2 Highest values for y were apparently achieved by using a horizontal screen with a coarse mesh and a collar screen with fine mesh.
3 Contrary to expectation, flow rate did not show up as an important variable affecting y.
4 Most important, the experiment was unexpectedly dominated by the values, which measure the flow retreated. These were uniformly very low, with about 0.01% of the flow being returned to the treatment plant and 99.9% leaving the screen for discharge into the river. Although it was desirable that the retreated flow be small, the values were embarrassingly low. As the experimenters remarked, “[T]he horizontal screen produced a solid concentratedry enough to shovel. This represented a waste of effort of concentrating because the concentrated solids were intended to flow from the units.”
Phase b
It was now clear (i) that
Unfortunately, after only two runs of this experiment, this particular phase had to be terminated because of the excessive tearing of the cloth screens. From the scanty results obtained it appeared, however, that with no horizontal screen high solid removal could be achieved with a higher portion of the flow retreated. It was therefore decided to repeat these runs with screens made of stainless steel instead of cloth.
Phase c
A third experiment, using stainless steel collar screens of two mesh sizes, similar to that attempted in phase b, was performed with the same collar screen mesh size, collar screen speed (rpm), and flow rate (gpm) used before.
In this phase, with a stainless steel collar screen, high removal rates y were possible for eight sets of conditions for the factors just mentioned. However, these high y values were obtained with retreated flow z at undesirably high values (before, they had been too low). The objective was to get reasonably small values for z, but not so small as to make shoveling necessary; values between 5% and 20% were desirable. It was believed that by varying flow rate and speed of rotation of the collar screen, this objective could be achieved without sacrificing solid removal.
Phase d
Again, using a stainless steel collar screen, another experiment, with two factors, namely collar screen speed (rpm) and flow rate (gpm),set at two levels each, was run. This time, high values of solid removal were maintained, but unfortunately, flow retreated values were even higher than before.
Phase e
It was now conjectured that intermittent back washing could overcome the difficulties. This procedure was now introduced with influent flow rate and collar screen mesh varied.
The results of this experiment lead to a removal efficiency of
For detailed analysis of this experiment, the reader should refer to Box et al. (1978, p. 354). Of course, these types of experiments and their analyses are discussed in this text (see Chapter 18).
1.2 A Survey
The purpose of a sample survey is to make inferences about certain characteristics of a population from which samples are drawn. The inferences to be made for a population usually entails the estimation of population parameters, such as the population total, the mean, or the population proportion of a certain characteristic of interest. In any sample survey, a clear statement of its objective is very important. Without a clear statement about the objectives, it is very easy to miss pertinent information while planning the survey that can cause difficulties at the end of the study.
In any sample survey, only relevant information should be collected. Sometimes trying to collect too much information may become very confusing and consequently hinder the determination of the final goal. Moreover, collecting information in sample surveys costs money, so that the interested party must determine which and how much information should be obtained. For example, it is important to describe how much precision in the final results is desired. Too little information may prevent obtaining good estimates with desired precision, while too much information may not be needed and may unnecessarily cost too much money. One way to avoid such problems is to select an appropriate method of sampling the population. In other words, the sample survey needs to be appropriately designed. A brief discussion of such designs is given in Chapter 2. For more details on these designs, the reader may refer to Cochran (1977), Sukhatme and Sukhatme (1970), or Scheaffer et al. (2006).
1.3 An Observational Study
An observational study is one that does not involve any experimental studies. Consequently, observational studies do not control any variables. For example, a realtor wishes to appraise a house value. All the data used for this purpose are observational data. Many psychiatric studies involve observational data.
