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  • ISO/IEC Guide 98-3:2008/Suppl 1:2008

ISO/IEC Guide 98-3:2008/Suppl 1:2008

Propagation of distributions using a Monte Carlo method

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This Supplement provides a general numerical approach, consistent with the broad principles of the GUM
[ISO/IEC Guide 98-3:2008, G.1.5], for carrying out the calculations required as part of an evaluation of
measurement uncertainty. The approach applies to arbitrary models having a single output quantity where the
input quantities are characterized by any specified PDFs [ISO/IEC Guide 98-3:2008, G.1.4, G.5.3].
As in the GUM, this Supplement is primarily concerned with the expression of uncertainty in the measurement
of a well-defined physical quantity—the measurand—that can be characterized by an essentially unique value
[ISO/IEC Guide 98-3:2008, 1.2].
This Supplement also provides guidance in situations where the conditions for the GUM uncertainty
framework [ISO/IEC Guide 98-3:2008, G.6.6] are not fulfilled, or it is unclear whether they are fulfilled. It can
be used when it is difficult to apply the GUM uncertainty framework, because of the complexity of the model,
for example. Guidance is given in a form suitable for computer implementation.
This Supplement can be used to provide (a representation of) the PDF for the output quantity from which
a) an estimate of the output quantity,
b) the standard uncertainty associated with this estimate, and
c) a coverage interval for that quantity, corresponding to a specified coverage probability, can be obtained.
Given (i) the model relating the input quantities and the output quantity and (ii) the PDFs characterizing the
input quantities, there is a unique PDF for the output quantity. Generally, the latter PDF cannot be determined
analytically. Therefore, the objective of the approach described here is to determine a), b), and c) above to a
prescribed numerical tolerance, without making unquantified approximations.
For a prescribed coverage probability, this Supplement can be used to provide any required coverage interval,
including the probabilistically symmetric coverage interval and the shortest coverage interval.
This Supplement applies to input quantities that are independent, where each such quantity is assigned an
appropriate PDF, or not independent, i.e. when some or all of these quantities are assigned a joint PDF.
Typical of the uncertainty evaluation problems to which this Supplement can be applied include those in which
– the contributory uncertainties are not of approximately the same magnitude [ISO/IEC Guide 98-3:2008,

Number of pages: 0

Published: 2008-11-20

International relationships:

ICS: 17.020 - Metrology and measurement in general

Item number: M225576