Weighting by a Utility Function 
Of course we should not try to make the decision with the highest 
expected (monetary) value, but the one with the highest expected utility. 
The utility of money is mostly not linear with the amount of money 
(or deficit). The utility-function may, for example, look like figure 11. 
As this step may complicate the paper more than it helps the result, 
weights according to the utility function are not introduced in our 
example here. 
Sequential analysis and stratification 
So far there has been only two possible actions: accept or reject. In 
many cases it is very advantageous to divide the sample space into three 
regions: Acceptance, Rejection and Further Sampling, se figure 12. lt 
can be shown that for some general cases the sequential technique may 
have an expected average total sample size of only half the size we would 
get with the two-possible-action-technique. 
As we however have indirect measurements of our errors, these general 
advantages are not fully valid (except when we have an on-line computer 
— as the Analytical Plotter case). Further investigation on this topic has 
possibilities of leading to results of practical value. 
We should also remember the might-be posibility to divide the popu- 
lation space into different strata. To maximise the precision of estimation 
of the character of a population, we should construct strata so that their 
averages are as different as possible and their variances are as small as 
possible, and the sampling fraction in each stratum should be proportional 
to the square root of "the variance divided by the cost of an observation" 
in that stratum. 
Final remarks — further developement 
There are good grounds for doubting the practical significance of the 
whole business of writing down profit functions (or drawing curves) and 
finding points of zero partial derivates. Such devices are merely aids to 
thinking, as every real world problem is enormously complex. We think 
that the techniques suggested here will be of assistance in developing the 
field in which the mentioned working group "Standard tests" is working. 
One goal for such work could be the following. Group the instrument 
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