unreachable. Therefore we limit the definition of our population to: 
All errors of measurement (not due to the operator and not due to 
certain systematic parameters, which are based on the physical construc- 
tion of *he instrument) that would be made if the instrument has the 
physical status it has at the time of decision. 
Today the buyers and users of measurement instruments may trust too 
much in the manufacturers and accept instruments which could be in- 
ferior, see [1]. This phenomenon could be explained by lack of respect 
for the effects of bad instruments and lack of calibration and decision 
techniques. 
Prerequisites for the case study 
In order to make the theory more easily available, it will be applied to 
the test of a (fictitious) first order photogrammetric double-projector in- 
strument with mechanical projection. A privately owned map-making or- 
ganisation (with some profit-making goal) has bought the instrument 
from the producer. According to the buying contract the instrument 
should have a standard error of maximum 5.0 yum, (o9), when a preci- 
sion grid is measured in a certain way and six certain parameters are 
used in the specified adjustment computation according to the method 
of least squares. The problem is here limited to the following: When the 
six systematic parameters are corrected for — is then the basic accuracy 
of the instrument, o, to be regarded as sufficient or worse than the stand- 
ard error of 5.0 um? If it is thought on good grounds that it is worse, the 
instrument could be sent back to the factory and a better instrument 
demanded?). 
Simpel background of necessary classical statistics 
We think we have an instrument according to the specifications. Thus our 
statistical null hypothesis is Ho : 6 L 5.0 ym. We want to test this hypothesis. 
If our sample of errors gives us an standard error, s, we ask: what is the probability 
to get s out of a popolation with o £ 5.0 ym? If the probability is great we accept our 
  
  
3) Please note three things: First: Of course the sizes of the six systematic errors 
are of primary interest (except for the case of analytical photogrammetry). These 
sizes are however — for simplicity — not at all considered in this paper. Second: 
Of course the discussion about rejecting (the metric accuracy of) instruments is 
theoretical. The reader may convert the decision problem to whether to adjust an 
old instrument or not. Third: Of course metric accuracy is not at all the only im- 
portant thing that concerns decision about instrument conditions. 
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