IEEE Instrumentation & Measurement - September 2023 - 9

issue, which may have a relevant impact on company costs.
If we denote with CT
(T) the total costs directly or indirectly
related to the measurement and monitoring operations during
a metrological confirmation interval of duration T, it
follows that:
C () = MET ()+ ()+ ()PR
T T C TC TC T
CR
and CPR
(2)
where CMET refers to the costs related to calibration and/or
verification operations, while CCR
are the CR and PR
costs, respectively. Even though no univocal expressions for
such costs exist, all terms of (2) are roughly proportional to the
amount of measuring equipment that a company has to manage,
they are hardly scalable and, of course, they also depend
on T, although with an opposite trend. Indeed, the metrologyrelated
costs CT
MET () monotonically grows if T decreases,
not only because frequent calibrations and verifications require
the service of a (usually external) accredited laboratory
and/or internal labor costs, but also, and above all, because
calibration and verification reduce instrument availability,
thus slowing down productivity or, in the worst cases, even
causing the interruption of the monitored industrial process.
On the other hand, relaxing T excessively may unexpectedly
and unpredictably boost the CR- and PR-related costs, with
severe consequences for companies, especially when legal
metrology requirements are involved. Based on the remarks
above, the optimal calibration interval could be found by
minimizing function (2). However, quantifying such costs in
practice is very hard, as they depend on several context- and
company-related factors, which are rather specific and hardly
generalizable.
The ISO Standard 10012:2003 does not provide any clear
criterion on how to establish the duration of metrological
confirmation intervals. This problem is instead partially addressed
in the ILAC-G24:2007/OIML D10:2007 Guidelines
[15]. In particular, two sets of guidelines are mentioned in
[15], i.e, those to choose the initial calibration intervals and the
methods to review such intervals over time. The initial calibration
intervals must be chosen on the basis of:
◗ Instrument manufacturer's recommendations;
◗ Expected extent and severity of use;
◗ Environmental quantities of influence;
◗ Target measurement uncertainty;
◗ MPE limits (e.g., established by legal metrology
authorities);
◗ Adjustment of (or change in) the individual instrument;
◗ Influence of the measurand (e.g., high temperature effect
on thermocouples);
◗ Existing data records about instrument metrological
behavior.
The decision about the initial calibration interval should
be made by expert personnel for each instrument or group of
instruments, possibly taking into account the information (if
available) from other calibration laboratories.
The interval duration review should instead be based on
one of the following policies:
September 2023
◗ Calendar-time automatic adjustments ( " staircase " methods):
These techniques compute the calibration intervals based
on the results of the last few calibrations. If an instrument
is found to be metrologically compliant to the intended
purpose within a given threshold (e.g., 80% of the MPE)
one or more times, the following calibration interval is
extended; otherwise, its length is reduced. This approach
is rather simple to implement, but not so simple to
manage in practice, since it requires that each instrument
is handled individually, which might be complicated in
organizations where many instruments are employed.
Some further details on one of such staircase methods are
reported in the Simple Response Method (SRM) section
below.
◗ Calendar-time control charts: Such control charts rely on the
same approach commonly adopted for statistical quality
control, but they are applied to instrument calibration/
verification. In this case, significant calibration points for
each instrument are chosen and the results are plotted
against time to estimate the dispersion of results and/or
to detect possible drift phenomena. From data analysis,
the calibration intervals can be computed with various
optimization techniques (e.g., to minimize the risk of
exceeding given upper or lower specification limits or
to minimize the sum of Type I and Type II errors probabilities
[9]). Unfortunately, control charts can be hardly
applied in the case of bulky equipment or frequently
used instruments, as they would be too impractical or too
expensive.
◗ " In-use time " policies: Such policies are just variations of
the previous ones in which the intervals between calibrations
is determined considering the hours of actual
use instead of the calendar time. Such solutions are more
effective whenever the measuring equipment is used
in harsh environmental conditions that may contribute
to the degradation of its metrological performance.
Examples of measurement devices that are calibrated
with this policy are the thermocouples used at extreme
temperatures or instruments that may be subject to
mechanical wear with use. The main benefit of " in-use
time " policies is that the number of calibrations (and
the related costs) depend directly on the actual time an
instrument is used.
◗ In-service checking or black-box testing: Such techniques
are also variations of the " staircase " methods and of the
control charts. In this case however, only some critical
metrological parameters of an instruments " are checked
frequently (once per day or even more often) by a portable
calibration gear, or preferably, by a " black box " made
up specifically to check the selected parameters " [15]. If
the instrument fails the verification based on black-box
testing, then it must be fully calibrated. The main benefit
of this class of methods is that they tend to maximize
instrument availability for the user. Their main drawback
is instead that some pending metrological problems (e.g.,
affecting some parameters that are not monitored by the
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