How to evaluate uncertainty

1. Devinder Dhingra
Principal Scientist
Indian Council of Agricultural Research
Uncertainty of
Measurement

2.  Measurement: process, determine the nature of
quantity.
 Value of quantity: varies for repeated
observations/ measurements.
 Reasons of variation:
Human/ operator
Instruments
Materials
Test method
Calibration
Environment
Reference
standards

3. Estimation of Uncertainty of Measurement
requirement under ISO17025: 2005
 Testing laboratory performing its own calibrations,
shall estimate the Uncertainty of Measurement for
all calibrations.
 Testing laboratories shall estimate Uncertainty of
Measurement.
 The Uncertainty of Measurement depends on:
Requirements of the test methods.
Requirements of the customer.
Existence of narrow limits on which decisions on
conformity to a specification are based.

4. Uncertainty in Measurement
 It defines a range that could be attributed to the
measurement result at a given level of confidence
e.g. 50.5±4.2 mg/ litre.
 Type A: Evaluated by statistical analysis of series of
observations.
 Type B: Evaluated from past experience of
measurements, calibration certificates,
manufacturers specifications.
 Type A & Type B: Uncertainties are based on
probability distribution.
 Type A is estimated on the basis of repeat
measurements (assumption, variation in the mean
follows normal or t-distribution.

5. Example: estimation of Type A
measurement of uncertainty
 Number of measurements (n) = 10
 Calculate mean (x ) = 79.4 mg/ kg
 Standard deviation or standard uncertainty (σ ) = 2.042
 Relative standard deviation (RSD) =
0.0257
Now, if measured value is 80 mg/ kg
Calculated uncertainty of measurement = −
1×80×RSD = 2.056
2×80×RSD = 2×80×0.0257 = 4.112 (95%)
3×80×RSD = 3×80×0.0257 = 6.168 (99%)
 Measured value is represented as
80±2.056 mg/kg (67 % level of confidence)
or 80±4.112 mg/kg (95% level of confidence)
or 80± 6.168 mg/kg (99 % level of confidence)

6. Type B Uncertainty
Data is given in terms of tolerance interval
 Pipette: 10cc ± 0.05 cc
 Standard uncertainty or standard deviation = 0.05/√3=
0.028 cc
Digital Instruments:
 Digital balance: Least count 1 mg ± 0.5 mg tolerance
 Eg. Measured result is 80.512 g
 Standard uncertainty = 0.5/√3 = 0.288 mg or 0.29 mg
 Result = 80.512 g ± 0.29 mg
 Least count = 0.1 mg (±0.05 mg)
 Standard uncertainty = 0.05/ √3 =0.029 mg
 Result = 80.5123 g ± 0.029 mg

7. Combining Uncertainties
i. Uncertainty of measurement = ±0.028 cc (U1)
ii. For class B pipette, when measurements are made
over a temperature range of 15 to 25◦C, the
Uncertainty of measurement = ±0.003 cc (U2)
iii. Uncertainty due to random factors = 0.01 cc (U3)
 Total uncertainty : √U1
2+ U2
2 + U3
2 = ±0.029 cc

8. Converting information from Calibration &
Specifications
 Uncertainty 129 µΩ at level of confidence of 99%
Standard uncertainty = 129 µΩ / 2.58
Mass of 10 kg body is 10.000650 kg and
Uncertainty is 300 mg at level of confidence 95.45 %
Standard uncertainty = 300/ 2 = 150 mg
Length of a standard slip gauge of nominal value 50 mm is
50.000002 nm
Uncertainty of this value is 72 nm at a confidence level of
Standard uncertainly = 72 nm / 3.0 = 24 nm

9. Cont.
100 ml class A volumetric flask is 100 ml± 0.08 ml
Standard uncertainty = 0.08/√3 = 0.046 ml
Purity of compound = 99.9 ± 0.1 %
Standard uncertainty = 0.1 / √3 = 0.057 %
Calibration weight is certified as 10.00000g ± 0.04 mg with a
with a level of confidence of at least 95 %.
Standard uncertainty = 0.04 / 1.96 = 0.02 mg.

10. Uncertainty of Measurement -Part
II
Microbiological tests prevent rigorous, metrologically and
statistically valid calculation of uncertainty.
Activities leading to uncertainty of measurement in
microbiological testing are:
 Size of the original sample from which sub-samples are
taken for testing.
 Sample and sub-sampling in selection of the required
quantity of matrix for testing.
 Time taken to homogenize the sample with diluents in a
blender/ stomacher.
 Volume of homogenate used for blending .

11.  The volume of diluents used in serial dilution of the
blended sample.
 The number of dilutions carried out before subjecting
the sample to tests.
 Variations in incubation temperature and time.
 Counting of the colonies.
 Techniques of preparation of microbiological media
and reagents
 The sterilization temperatures, the time and the total
duration of exposure of media to heat.
Cont.

12. The following factors are not used in estimation of
uncertainty in microbiological testing as there are no
means to address them.
 Non-homogenous distribution of analytes in food.
 Sample preparation and sample stability.
 Plate readings of less than 100 CFU/ ml.
 Qualitative results [presence/ absence].
 Methods needing additional step for confirmation.
 Methods based on counting positive tubes / cells (MPN,
micro-titer plates).
Cont.