tiply the conditional profit by the probability of the state of nature, and
sum the products for each possible state) and take the act with the largest
expected value.
2. Decide possible outcomes and possible decisions
In this two-possible-action-case it is assumed to accept the instrument
if the resulting estimate of ¢ is on one side of a critical value. Otherwise
the instrument is rejected.
3. Decide type of probability distribution which applies to the process
This distribution is, in this example, assumed to be according to figure
1. The assumtion is based on publications”), prior experience and the
reputation of quality- and delivery-policy of the factory.
4. Determine the loss function
The right hand part of figure 2 gives the amount of Swedish kronor
we lose if we accept the instrument although it has a o given in the
figure. This function is calculated on estimates of the present value of
extra costs in practical work during the extimated economic lifetime of
the instrument (e. g. 10 years). Such extra costs are, for example, a)
longer relative and absolute orientation times, b) lower flying altitude
neccesary, c) more ground control neccesary to produce an acceptable
map. The cost function of figure 2 (which is made linear for
simplification) is the maximum of these extra costs and the cost of the
lost opportunity to buy a cheaper instrument.
The left hand part of figure 2 is similarly the opportunity loss if we
reject an exellent instrument. In the long run we would — according to
the figure — have gained much money) if we had accepted the instru-
ment.
7) For example the future manufacturers’ data according to resolution II: 6 from
Lisbon 1964: "Manufacturers of instruments and materials are requested to furnish
such information about the geometrical quality of their products that tolerances can
be established according to ordinary principles of theory of errors and statistics.
The confidence coefficient should be ordinarily set at 95 percent.”
8) Or we could have sold the exellent instrument to somebody else for the
amount shown in the figure.
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