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Xvii imeko world congress
Monte Carlo Simulation for Evaluation of Measurement Uncertainty of
pharmaceutical certified reference materials
Werickson Fortunato de Carvalho Rocha
1, Raquel Nogueira2
Duque de Caxias, Brazil, email@example.com
2 INMETRO, Duque de Caxias , Brazil, firstname.lastname@example.org
The Supplemental Guide to the Expression of
To avoid these limitations, the working group 1 of
Uncertainty Measurement (2004), which deals with the
the Joint Committee for Guides in Metrology (JCGM-WG1)
propagation of distributions, emphasizes the use of the
„„Expression of Uncertainty in Measurements‟‟ promotes
Monte Carlo simulation (MCS) for estimating the
the use of the GUM and prepares supplemental guides. The
uncertainty of measurands. This paper describes the
first supplemental guide „„The propagation of distributions‟‟
(2004) considers the propagation of distributions for general
recommended by the ISO GUM supplement, to evaluate the
probabilistic basis for uncertainty evaluation from the direct
measurement uncertainty of the active pharmaceutical
use of the probability density function (PDF) of the input
ingredient (API) content for two certified reference
quantities rather than just their means and standard
materials (CRMs): metronidazole and captopril. The Monte
uncertainties. It also recognizes the Monte Carlo method as
Carlo results complied with the GUM results for a critical
the most efficient numerical implementation for the
value δ of 0.005 for metronidazole and δ 0.05 for captopril.
Therefore, the GUM methodology was validated by the
2. Instrumentation, measurement procedures
Monte Carlo method with expression of the API content
with at least two decimal digit numbers.
The instrumental and experimental procedures used
for the certification of metronidazole and captopril reference
Monte Carlo Simulation; Evaluation of
materials were previously described [1,2] and were based on
Measurement Uncertainty; Certified Reference Materials;
the ISO Guides 34:2009 and 35:2006. They consisted
basically on material characterization (determination of
chromatography according to eq. 4-5, determination of
inorganic impurities by residue on ignition test, and determination of volatiles by loss on drying test), between-
Metrological activities are fundamental to ensure
bottle homogeneity testing, short- and long-term stability
the quality of scientific and industrial activities.
studies, calculation of the API content using the mass
Measurement results must be valid, comparable, and
balance approach, and uncertainty estimation of the property
reproducible, and their uncertainties are the quantitative
expression of their quality. In accordance to the ISO/IEC
17025:2005 standard, all calibration or testing laboratories must have and apply procedures to evaluate uncertainty in
measurements as a guarantee of their technical competence.
In order to establish an international consensus for
] is content of each organic impurity
International Standardization Organization (ISO) has
developed and published the Guide to the Expression of
is the analyte peak area
(diluted solution); DF
is the dilution factor from the
Uncertainty in Measurement (GUM) , which has been
concentrated to the diluted solution, and ΣA
widely accepted and followed . The GUM is based on sound
theoretical principles and supports a fully consistent and transferable estimation of measurement uncertainty and
traceability to the International System of Units (SI). However, this approach exhibits some important limitations
mainly derived from the use of the law of propagation of uncertainty and from the application of the central limit
] is the total organic impurities content.
2. Results and discussion
2.1 Application of the GUM Method
Initially the combined standard uncertainties of the
contents of organic impurities (uorg
), inorganic impurities (uinorg
) and volatiles (uvol
) were determined by the traditional method.
) and long-term stability (ults
) studies were estimated according to the ISO Guide 35:2006 . The combined standard uncertainty of each CRM (uCRM
) was calculated according to the law of propagation of uncertainties, which consists of “the square root of the total variance obtained by combining all the uncertainty components”. Finally the expanded uncertainty of the certified property value (UCRM
) was obtained by multiplying uCRM
by the coverage factor (k
2.2 Application of the Monte Carlo method
For the Monte Carlo simulation, the variables of eq.
5 (mass balance) and the results of the homogeneity and stability studies were taken into account. First it was necessary to define the types of the probability density functions (PDF) of each of these input parameters.
The compatibility of the results obtained by the
Monte Carlo method and the conventional method (GUM) has been demonstrated for two pharmaceutical CRMs. The Monte Carlo simulation is a practical tool for application of the principle of propagation of distributions and does not depend either on the assumptions or on the limitations related to the law of propagation of uncertainties (GUM uncertainty framework). Therefore, the risk of unreliable measurement uncertainties estimation, particularly in cases of complicated measurement models, can be reduced, and there is no need to evaluate partial derivatives.
The study showed that the agreement between the
Monte Carlo and GUM results are valid until a determined number of decimal digits and, in the case of the two studied CRMs, these numbers were compatible to the BIPM recommendations to express the certified property values and their measurement uncertainties.
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