An Introduction to Quality
Assurance in Analytical
Science
Dr Irene Mueller-Harvey
Mr Richard Baker
Mr Brian Woodget
University of Reading
Part 5 - Expression of Results
Contents:
• Validation, traceability and measurement
uncertainty (slides 3,4)
• The ‘what’, ‘why’ and ‘how’ of measurement
uncertainty (slides 5-15)
• Reporting results (slide 16,17)
The presentation contains some animation which will be activated
automatically (no more than a 2 second delay), by mouse click or by use
of the ‘page down’ key on your keyboard.
The Famous Trio:
When expressing results of analytical measurements you
will need to bear in mind the 3 inter-linking parameters of:
Has the method
been validated
and it is fit for
purpose?
Will the results
be traceable
to an accepted
reference
standard?
VALIDATION
TRACEABILITY
MEASUREMENT
UNCERTAINTY
How sure will you
be of the accuracy
of the results
obtained?
About validation, traceability &
measurement uncertainty
As you have seen in Part 1 of this presentation, all
analytical results have an error associated with them.
Measurement uncertainty is an estimate of the potential
size of that error and is affected by both the time and
effort put into method validation and the traceability
of standard reference materials and substances
Note: refer to Part 2 of the presentation for a description
of method validation and to Part 3 for a description
of traceability
Measurement
Uncertainty (1)
Analysis of a sample of soil has
shown it to contain 30 + 5 mg/kg of lead
Mean result from
replicate analyses
Estimate of the
measurement
uncertainty
You need to consider from where the uncertainty is likely to arise
Note: accredited laboratories (ISO 17025) carrying out this analysis would
need to be aware of the levels of uncertainty but would not necessarily have to
present this data unless asked. So the result could well be presented as 30 mg/kg
Measurement
Uncertainty (2)
Sources of uncertainty arise from ALL aspects of the analysis these could include:
Volumetric
glassware
Calibration standards
sampling
Potential sources of error
sample
preparation
operator
skill
instruments
Measurement
Uncertainty (3)
Analytical
balance
To estimate the measure of overall uncertainty, errors
likely to occur in all aspects of the analysis need to be
taken into account in the form of individual standard
deviations (SD). Data may be obtained from:
• manufacturers of equipment and reagents (e.g. balances,
volumetric glassware, standard reagents etc)
• data from method validation
• estimates from the literature or from previous experience
An overall estimate of the uncertainty can then be calculated
by using accepted procedures.
Measurement
Uncertainty (3a)
The accuracy of an analytical
balance is fundamental to all of
the procedures carried out within
an analytical laboratory. The
balance should be capable of
weighing accurately to + 0.1 mg
and is the starting point for most
measurements (sample weight,
preparation of standards,
method validation etc.)
The balance must be calibrated periodically against weights traceable to the
UK standard held at the National Physical Laboratory (NPL), and checked
at least every day against a set of weights held in the laboratory,
specifically for this purpose. All calibration data must be stored.
Measurement
uncertainty (4)
The uncertainty estimation process can be illustrated
diagrammatically:
SPECIFICATION - clear
statement of what is being
measured and the relationship
between it and parameters on
which it depends
IDENTIFY UNCERTAINTY
SOURCES - list sources for
each part of the process or
for each parameter
CONVERT TO STANDARD
DEVIATIONS - express error
QUANTIFY UNCERTAINTY
COMPONENTS - estimate the
component as a standard
deviation
size of each uncertainty component
CALCULATE THE
COMBINED UNCERTAINTY
RE-EVALUATE THE PROCESS
IF NECESSARY
Measurement
uncertainty (5)
Standard uncertainties
A measure of the SD of an uncertainty component [u(y)]
- may be calculated from:
• experimental data
• accuracy guaranteed by a piece of equipment
– e.g. balance accurate to + 0.1 mg @ 95% confidence
which may be converted to a SD
– pipette guaranteed to deliver 25 + 0.2 ml. Although no
confidence level has been stated, SD may again be
calculated.
Measurement
uncertainty (6)
Combined uncertainties
Dependent upon the type of analysis carried out, the
standard uncertainties may be combined to produce
a combined uncertainty [uc(y)]
One of three equations may be used, the choice being
dependent upon the complexity of the analysis and the
relationship between the components parts
A model equation must be devised which describes in simple
algebraic terms the whole analysis process
Measurement
uncertainty (7)
The rules for estimating combined uncertainties depend
upon the model algebraic equation devised to illustrate
the analysis process. You only need consider two at the
present time:
Rule 1 - for models involving only a sum or difference of quantities eg.
For y = a + b + c, the combined uncertainty is given by:
[uc(y)]2 = u(a)2 + u(b)2 + u(c)2
Rule 2 - for models involving only a product or a quotient eg:
For y = a.b.c or y = a/(b.c) , the combined uncertainty is given by:
[uc(y)/y]2 = [u(a)/a]2 + [u(b)/b]2 + [u(c)/c]2
Measurement
uncertainty (7a)
Example to illustrate a
calculation involving rule 1
Suppose that you have four
components (a, b, c, d) and you
need to know their combined
mass and the uncertainty
associated with this mass.
The following information is
available:
a = 27.81 g, u(a) = + 0.01 g;
b = 32.45 g, u(b) = + 0.02 g
c = 46.10 g, u(c) = + 0.08 g
d = 19.01 g, u(d) = + 0.02 g
Total mass (T) is given by:
T=a+b+c+d
= 27.81 + 32.45 + 46.10 + 19.01
= 125.37
[uc(T)]2 = u(a)2 + u(b)2 + u(c)2 + u(d)2
= 0.012 + 0.022 + 0.082 + 0.022
= 0.0073
uc(T) = + 0.085
Thus: T = 125.37 + 0.085
Measurement
uncertainty (7b)
Example to illustrate a
calculation involving rule 2
You have performed an acid/base
titration to measure the molarity (M)
of a solution of HCl, by titration with a
standard solution of KOH. The
following information is known or was
obtained during the titration
CKOH = 0.0990 M, [u(CKOH) = 0.00017]
VKOH = 25.54 ml, [u(VKOH) = 0.032]
VHCl = 25.00 ml, [u(VHCl) = 0.021]
The equation for the calculation
may be expressed as:
CHCl =
CKOH X VKOH
VHCl
= 0.1011
Each of the individual standard
uncertainties needs to be
expressed as an RSD so for:
CKOH = 0.00017/0.0990 = 0.00172
VKOH = 0.032/25.54 = 0.00125
VHCL = 0.021/25.00 = 0.00084
Thus:
uc(CHCl) =[(0.00172)2+ (0.00125)2
+ (0.00084)2]1/2 X 0.1011
uc(CHCl) = [0.0000051]1/2 X 0.1011
= 0.00226 X 0.1011
= 0.00023 M
CHCl = 0.1011 + 0.0002 M
Measurement
uncertainty (8)
Coverage factor
In order to give confidence to the value for the combined
uncertainty, the calculated value uc(y) is often multiplied
by a coverage factor (k). For a 95% level of confidence
the value of k is 2 [ See Student’s ‘t’ test table]
Note: a more complete description of the principles used for calculating
uncertainties may be found in:
“Quantifying Uncertainty in Analytical Measurements”, Eurochem, 1995.
“Quality in the Analytical Laboratory”, E. Prichard (Ed), Wiley, 1995,
Chapter 6.
Reporting results
The test report of an accredited laboratory must
conform to the requirements of the accreditation
body - usually the report must clearly identify-
-
the laboratory
the client
the samples
the date they were received
the method of analysis
the analyst
the date of the report
the unique Test Report no. on every page
The report format must ensure that there can be no confusion
over which results refer to which samples and it should give
any information about the condition of the samples that may
have affected the test results.
Amiable Laboratory
A UKAS accredited testing laboratory No. £$%&
TEST
REPORT
HEADER
For
Accredited
Tests
(example for
demonstration
only)
Benevolent Department
Well-intentioned Organisation
Tel: 01234 567890
Fax: 01234 567891
Test report number
T02 JAN 002
Test batch number
mc218
Date received
02/01/02
Client
XYZAB
Recipient's name
Date reported 09/01/02
£$%&
A Client
Analyst
C.
Batch description
208 Raw milks
Details of analyses
Fat, Protein, Lactose by Milk-o-scan (FAL method 7.3.1)
Method 7.3.1 is carried out in accordance with
BS EN ISO/IEC 17025 standard
Calibration data
Typical calibration range for milk samples:
Fat:
1.6 - 6.6 %
Protein: 2.6 - 4.0 %
Lactose: 3.8 - 5.0 %
Comments
8 missing samples 51,99,100,135,138,145,164,189
.
Signed
(authorised signatory)
Print name