Sampling point frequency considerations

In order to obtain some perspective of the task involved, BS 10175 2001 (p. 21) suggests a typical sampling grid density at 16-25/hectare for main investigations. Using the lower sampling frequency and the assumptions below, 

Number of sampling points per hectare = 16 Sampling depth=3 m Soil density=2.5 tonnes/m3 

Number of depths sampled per sampling point=5 (e.g. 0.15,0.5,1, 2and3m) The following can be derived  

Mass of soil assessed per hectare down to 3 m= 75 000 tonnes 

Mass of the site soil associated with each submitted sample=938 tonnes 

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Another problem with a discrete periodic representation is that it is very difficult to represent functions that are not equal at their end points. An abrupt discontinuity across the end points of a periodic representation causes considerable amplification of the high frequencies, which, in general, are very difficult to work with. Also, unless the sampling interval is taken very fine, this function cannot be adequately represented by the DFT. However, this problem can be dealt with by extending each end point in a smooth curve that joins smoothly with the next period so as to yield an overall periodic function that is reasonably smooth. This is a valid operation because it is only necessary that the function be adequately represented over the interval of interest. The advantage of a smooth curve is that the high frequencies are now much smaller, and the overall numerical problem much more tractable. 

An important consideration in all failure studies is the influence of material variability. Statistical distributions of failure incidence must be known and properly accounted for if reliability limits are to be set. Wiegand and co-workers (14, 113) have discussed propellant sample and batch variability, and its effect on failure behavior, in numerous reports. These studies point out the statistical nature of failure and the fact that knowledge of the distributions is required to set conservative design values for motor stress and strain capability. Statistical distributions permit the prediction of the probability of failure, but mission considerations dictate the allowable failure frequencies. 

In general, samples may be obtained from faucet outlets, at different points in pipe systems, from the surface of rivers and lake waters, and at different depths. The most important consideration is that the frequency and duration of sampling be sufficient to obtain a representative and reproducible sample. In some cases, composite samples may be used, in which individual samples taken at frequent intervals are combined. 

Both the frequency-domain and the time-domain techniques can be classified into camera, or direct imaging techniques, and scanning, or point-detector techniques. There are considerable differences between the ways the two detection principles interact with laser scanning. Figure 5.72 shows the excitation of a sample in the focus of a one-photon microscope (left) and a two-photon microscope (right). 

The sampling procedure used will obviously depend on the type of sample whether it is liquid or solid fresh, chilled or frozen and the type of container e.g. tinned, bottled). Other major problems are the frequency of sampling and the position on a production line from which a sample is taken. For example, when sampling from a food production line is carried out, an important consideration is whether or not the food has been subjected to sterilisation, or any form of pasteurisation after the point from which the sample was taken. This is considered further in the chapter on food microbiology under the concept of Hazard Analysis Critical Control Point (HACCP). Whatever the form of the sample, it should be collected in a sterile container using aseptic techniques, returned to the laboratory under conditions identical to those from which it was taken, and processed as rapidly as possible. 

The frequency of sampling and the number of test pieces (or repeat tests) per item sampled depend on circumstances, and obviously financial considerations play an important part. Certain long-winded (and expensive) tests call for one test piece only, although if multiple tests are done the method may be quite variable. The use of a single test piece is hardly satisfactory, but it may be that multiple tests in numbers sufficient to increase precision are totally uneconomic. This is the dilemma that quality control managers (and the writers of specifications) have to face. In a continuous quality control scheme it may be that the number of test pieces at each point is less important than the frequency of testing. 

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