1. How to Calculate MU? By Sanjay Tiwari Chief Chemist
Central Agmark Laboratory
Nagpur

2. Uncertainty
“A parameter associated with the result of a measurement, that characterizes the dispersion of values that could reasonably be attributed to the measurand.”
In general use the word uncertainty relates to the general concept of doubt. Knowledge of the uncertainty implies increased confidence in the validity of a measurement result.

3. Uncertainty components
In estimating the overall uncertainty, it may be necessary to take each source of uncertainty and treat it separately to obtain the contribution from the source.
Each of the separate contributions to uncertainty is referred to as an uncertainty component. When expressed as a standard deviation, an uncertainty component is known as standard uncertainty.

4. Error and uncertainty
It is important to distinguish between error and uncertainty. Error is defined as the difference between the result and the true value of the measurand.
As such, error is a single value. In principle, the value of a known error can be applied as a correction to the result.
Uncertainty on the other hand, is a quantification of the doubt about the measurement result.
In general the value of uncertainty can not be used to correct a measurement result.

5. Ways to estimate uncertainties
No matter what are the sources of uncertainties, there are two approaches of estimating them:
‘Type A’ and ‘Type B’ evaluations. In most measurement situations, uncertainty evaluations of both types are needed.

6. Ways to estimate uncertainties contd.
Type A evaluations - uncertainty estimation using statistics (usually from repeated readings)
Type B evaluations - uncertainty estimation from any other information. This could be information from past experience of the measurements, from calibration certificates, manufacturer’s specifications, from calculations, from published information, and from common sense.

7. 1. Method BIS 548- Part I 1961
EVALUATION AND EXCPRESSION OF UNCERTAINTY IN THE DETERMINATION OF ACID VALUE IN MUSTARD OIL
Weigh Sample
25 ml Alcohol
Add few drops of 1% Phenolphthalein indicator
Titrate with .1 NaoH Soln
Result

8. 2. Mathematical Model
Acid Value = 56.1xVx N W
Where V = Volume in ml of standard NaoH required for sample
N = Normality of standard NaoH Solution
W = Weight in grams of the oil for the test

9. 3. Identification of sources of uncertainty (fishbone diagram)
Weighing Balance
Calibration
certificate
Repeatability
Acid Value
Temp.
Purity Burette
Pipette
Standard Titration for
(Potassium Sodium Pthalate) Sample

10. 4. Information Available Uncertainty of Weighing Balance
Tolerance of Burette at 27 degree Celsius
Tolerance of pipette at 27 degree Celsius
Purity of Standard Potassium Sodium Pthalate .

11. 5. Set of values from previous analysis
Acid Value
Mass Of Sample
Titration Value
1.10
0.64
1.15
0.66
0.67
1.05
0.61
0.62
SUM
11.05
6.43
Mean
1.105
0.643
S.D.
Standard Uncertainty
0.006

12. Uncertainty associated with Weighing balance:
From Calibration Certificate of weighing balance no. Axis LCGC- AGN- 204, calibrated on by STQC, Mumbai.
Uncertainty =  gm
Std. uncertainty = /3
= 1.15 x10-4…………………………….. (i)
(ii) From Repeatability(n=10)
Standard Deviation =
Standard Uncertainty =
= 1.78x10-2 …………(ii)
Combined Uncertainty of balance for (i) and (ii)
­­(1.15x10-4)2 + (1.78x10-2)2
1.78 x 10-2

13. 7. Uncertainty associated with Titration of Sample:
(i) Burette (ii) Temperature (iii) Repeatability
(i) Burette: Cap 50 ml
Uncertainty =  0.002
Standard Uncertainty = 0.002/ ­­6
= 8.16 x 10-4 ………………..(1)
(ii) Temperature: Temp at the time of titration = 240C
here the equation of  x t x v is used
Where  is the sensitivity coefficient for expansion of water,
t is the difference in temp and
v is the mean volume for titration of sample.
 = 2.1 x 10-4 ml /0C
t = 30C (burette is calibrated at 270C whereas titration is done at
240C)
v = ml
Std Uncertainty = 2.1 x 10-4 x 3 x 1.105 3
= 4.02 x 10-4 ……………….(2)

14. (iii) Repeatability of titration
No of titrations (n=10)
Titration values = 1.1, 1.1, 1.1, 1.15, 1.15, 1.05, 1.10, 1.05, 1.10, 1.15
Mean = ml
Standard Deviation =
Standard Uncertainty =
= 1.17 x 10‑2…………….(3)
Combined uncertainty of (i), (ii) and (iii)
=(8.16 x 10-4)2 + (4.02 x 10-4) +(1.17 x 10‑2)
= 1.17 x 10-2

15. Uncertainty =  0.05% (Coverage factor K = 2, confidence level 95%)
8. Uncertainty associated with Standard Potassium Hydrogen Phthalate (KHP)
Purity of Potassium Hydrogen Phthalate
Standardization of Sodium Hydroxide solution
Must be dried at C for 2 hrs
Weigh KHP
Titration with NaoH
Purity = %
Uncertainty =  0.05% (Coverage factor K = 2, confidence level 95%)
Standard Uncertainty = /3
= 2.9 x 10-4

16. 11. Summary Table Sl. No. Uncertainty Source Mean Estimated Value
Standard Uncertainty Ux
Std Uncertainty/Mean
Ux/Mean 1
Sample Mass gm
1.78 x 10-2
1.77 x 10‑3 2
Titration Sample
1.105 ml
1.17 x 10-2
1.06 x 10-2 3
Purity of Potassium Hydrogen Pthalate
0.1 N
2.9 x 10-4
2.9 x 10-3

17. 12. Overall Combined Uncertainty
Uc/ = (1.77x10-3)2 + (1.06x10-2)2 + ( 2.9x10-3)2
Uc/ =  1.11x10-2
Uc = x 0.011
Uc = 
13. Expanded Uncertainty at coverage factor K = 2
=  x 2
=  0.014
14. Reporting of results
Acid Value = 0.64  0.014
Coverage factor (k) = 2 at 95% confidence level.