Let
us consider the problem involving measurements on one variable taken using two
instruments or methods: one is very precise but slow and expensive and another
is very quick, cheap but less precise. We are interested in estimating the value
of precise measure
X corresponding to the value of the imprecise measure
Y.
This is a typical univariate calibration problem. Usually, a calibration
experiment consists in running a series of experiments to obtain data on
Y
for fixed values of
X. In the absolute calibration we assume that the
measure
X is without error and the measure
Y is affected by the
experimental error. Generally, the practical “standard design” for the
calibration experiment involves the use of
n distinct values of
X
and the measure of the corresponding experimental values of
Y. We propose
to consider, in the first stage of calibration procedure, a “genuine replicate
design” to estimate the calibration curve. Specifically, let
x
be a vector of
n fixed known values of
X, enough representative of
the
X ’s range. For each
x
we run a completely randomized experiment to obtain measurements on
Y.
Moreover, we have to replicate
m times
this type of experiment,
with
Data
are taken in different and completely randomized experiments. Note that they are
not just repeated readings of Y but they are genuine replicates and they
provide an estimate of the pure error. In
this paper, we investigate the statistical properties of the point and interval
classical calibration estimator under a “genuine replicate design”. More
specifically, assuming a linear calibration model, we are interested to show,
using algebraic and geometric considerations, that the corresponding exact and
non symmetric confidence intervals obtained using this experimental design are,
under a general condition, shorter, i.e., more precise, than those obtained
under the “standard design”. 
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