users according to some assumed standard cost- and utility-functions.
Determine for each group of consumers and each group of instruments
an experimental design (number of points and location of them), calcula-
tion rules!4) and suggestions for decision for different outcomes of the
calculations. This has to be published not only for routine tests, but also
for delivery control tests of instruments. The basis for reaching this goal
will be futher theoretical research according the mentioned principles
and futher investigations of the practical population of errors of the
existing instruments.
In this paper the decision problem has been regarded as a game against
nature. The instrument tested has been assumed (for example in deter-
mination of the curve in figure 1) as a random sample out of the produ-
cers population of instruments. The theory of decision will be more
interesting, if it is assumed that the seller chooses the instrument
according to his thoughts about the buyer's abilities to test and way of
testing. This means that more pure game theory has to be applied and
the decision maker will choose an action strategy according to the rules
of, for example, a two-person-non-zero-sum-game.15)
References:
[1]. Berg, H.: On Quality Control in Survey Technique. (In Swedish). Svensk
Lantmáteritidskrift 1966: 1. P. 135—147.
[2]. Burkhardt, R.: Standard Tests for Photogrammetric Plotters. International
Society of Photogrammetry, II: 2. Frankfurt a. M. 1967.
[3]. Hald, A.: Statistical Theory with Engineering Applications. New York 1955.
(Especially Capter 14.)
14) Of course it may pay to computerize all the described calculations in the
decision procedure. In that way — for an input of cost functions and probability
distribution functions and decision criterion — the computer automatically will
give the optimum number of points and the critical value of the result. (For the
case of normal distributions and linear costs, the EVSI is tabulated in for example
[5]. These tables are very useful for practical decision problems.) The graphical
method of presentation in this paper is thought as pedagogic in order to communi-
cate the message of the paper to the reader.
15) It could be observed that the entire decision procedure above is seen only
in the buyers point of wiev. It is thus, for example, assumed that the deci-
sion procedure is stated in the buying contract. Otherwise there will exist risks
for expensive conflicts between the buyer and the seller, when the seller can not
accept that the decision is based on the calculated critical value.
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