5. Determine the Optimum Number of Observations 
The cost of sampling is shown in figure 3. It is calculated as the cost 
of putting the grid into the instrument, plus cost of measuring?) different 
number of points (regarding loss of income due to lost production), plus 
the cost of computation of s. Due to type of adjustment calculation there 
may be certain discrete steps, but the cost points are assumed to be on a 
straight line. 
The Expected Value of Sample Information, EVSI, is also shown in 
figure 3. Before we go through the calculation of the EVSI, we will 
take a quick look at the Expected Value of Perfect Information. That is 
what we would gain if we knew the population — or for each point on 
the loss function, the loss times the probability for that loss. That is the 
conditional value of perfect information, figure 2, weighted with the the 
probabilities according to figure 1. 
Now our sample does not give us perfect information, but it reduces 
the probability for a wrong decision by reducing the amount of variance 
from the prior to the posterior distribution of the probabilities for different 
varainces of our population. 
The Expected Value of Sample Information is calculated as the Ex- 
pected Value of Perfect Information, but using the expected reduction 
of probability instead of the original probability for a certain variance. 
Examples of the computation of EVSI are shown in the figures 4, 5 
and 6. They are all valid only for the single case of 15 degrees of free- 
dom (i. e. 21 measurements). 
Figures 4 shows the expected posterior distribution of the probability 
for different variances!?), where the distribution is shown around the 
mean we will get. This mean is unknown. In figure 5 we have the single 
case when the mean is 4.5 pm. The dashed lines in figure 5 show the 
9) The determination of the number of repeated settings on each point does not 
affect the cost function too much. Thus it might practically be done by — for an 
assumed value of o, e. g 5.0 ym — calculating the standard deviation of the mean 
of that number of settings that gives a sufficiently small contribution from the 
precision to the accuracy figure of 5.0 ;m. This latter figure consists of course of 
both the precision and the accuracy, see [4], page 10 f. 
10) Although the computations of course are made for distributions of variances 
of our error population, it has been choosen to show the square root of the variances 
in the figures. In this way we always get the standard error on the horisontal axis. 
The choice is made only because it is thought that the readers might be more 
familiar with the concept of standard error than that of variance. 
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