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It is possible to make another serie in a different 
time in order to create a second datum with the 
same instrument but with another operator and 
different weather conditions. The influence of the 
operator and the environment is considered 
"accidental" in the comparison of the two series. 
Statistic theory is able to estimate instrumental 
standard deviation in operative conditions, using 
the addition of different series square errors. 
The series number is indicated by ji. 
The f value, number of the freedom grades of the 
operation, that is of the indipendent measures, can 
be obtained with the multiplication of the number of 
the indipendent measures of every stratum with the 
number of the strata: 
f = V-' n j 
The standard deviation s, referred to the measures 
made in the different series, is determined by the 
relation: 
s = 
This value is more or less different from de 
teorethical value a in order of the mesuraments 
number really made. The statistic methods make 
us determine an interval so that we can think that ct 
is contained with a certain probability. We can 
determine that standard deviation value that 
corresponds to the probability P=95% (as indicated 
in DIN 18723) simply multipling the value s with a 
coefficient x defined in function of f: 
Each procedure used in laboratory makes 
reference at this teoretical approach, with different 
forms according to the measurament kind: azimut, 
zenit, distances or difference of level. 
3 - Optimisation tests 
The aim of the optimisation tests is to verify how 
the standard instrumental deviation varies in 
function of the measures redundancy. When the 
redundancy varies, the coefficient x, which is to be 
considered a pejorative coefficient, also varies. It 
increases standard deviation according with the 
measures number, to consider the test 
significativity. Significativity increases with the 
number of indipendente measures. 
From one side one tends to make a high number of 
measures to give significance to the value (x 
below); on the other one tends to reduce the 
number of measures to reduce the time (and the 
cost) for any determination (high %)■ 
We decided to perform some tests to verify these 
values and we used WILD TC2000 teodolite. On 
the traditional survey scheme, we took many 
measures. On the 5 signals we made 3 series of 4 
strata. 
The 3 series have been carried out by 3 different 
able operators, in good weather conditions (fresh 
and with covered sky). 
In table 1 we indicated the number of series, the 
number of strata, the number of signals, the s 
value, the number of free grades f (the number of 
indipendent determinations), the x factor that 
correspond to 95% of probability, the value <j to be 
associated with the estimed population in the 
limited number of tests. 
It is easy to note that if we increase the measures 
number we modify the value s (25% more), while 
the c value changes only for 10%. When the strata 
number increases we have different types of errors 
that increase the dispersion of the tested values. 
The evaluations of the zenital angles, tested 
together with the azimut ones and described in 
table 2, are instead different. 
Minimum c isn’t obtained during the test with the 
biggest number of freedom; that is synonym of 
some outliers into measured values. 
Notwithstanding this, standard deviation isn’t 
substantially modified with the lower measure 
number. 
We considered an average value of about 14 
minutes per every serie corresponding to a 
complete reposition of the instrument, to a change 
of operator and, if possible, to a work day. Every 
stratum corresponds to 4 minutes. Every display 
operation (not the old teodolites) needs about 1 
minute; every point needs 2 minutes for the two 
testings. 
Regarding these data we can estimate the 
measure time for the six examples above: 2h 56’, 
2h 33', 1h 58', 1h 30', 1h 33' and 1h 2'. The relation 
between time and operations is very difference 
with the conditions choosed. The laboratory follows 
now the fourth procedure of table 1 (that is 2 series 
of 3 strata with 5 signals) for about 1 h 30' work. 
4 - Conclusions 
It is possible to project a reduction of the number of 
measures to perform for every laboratory test on 
behalf of the results above mentioned. We think 
anyway it is correct not to discend more than f =10. 
The real casuality of the population distribution 
remains a problem.This changes a lot the results. 
To avoid this problem the operators have to work 
very carefully and they have to be very precise. 
It’s possible to identify some outliers comparing 
meausures with high accuracy reference values. A 
real time check wuold be possible working into a 
references polygon, known with high accuracy. 
Each measure must be different from true value 
less then the instrument estimated (or nominal) 
standard deviation.