7.
6QF-01
Salicon Nano Technology Pvt. Ltd.
Uncertainty Calculations
Date of Measurement: 28.08.2022
PARAMETER FOR UNCERTAINTY CALCULATION: DC Current(Source Mode)
Parameter 10 uA Uncertainty is 0.02888 uA
Uc in Percentage 0.2888 %
DETAILS OF UUC :
Instrument Under calibration(DUC) : Digital Multimeter
S No: VM-01 Least Count / Resolution: 0.0001 uA
Calibration value: 10 uA Range: 0 - 200 uA
Details of Standard Used Standard 1 Standard 2
Nomenclature : Multifuction Calibrator
Make/Model 9010
ID / S.No: 750181
Certificate No: AIPL/2021/0808
Calibration Valid Up to 18.11.2022
Meas Unc. of Master Equip: 0.00070 uA
Accuracy of Master Equip: 0.02500 uA
Temperature during calibration : 25±4 °C
Humidity during calibration: 30 to 75 % RH Cal Procedure No : SOP/ELC/---
MEASUREMENT DATA & TYPE A UNCERTAINTY EVALUATION.
Number of Readings taken(n) : 10
Observed Readings Average of Standard
Sr. No. (in uA) Readings Deviation
1 9.9946
2 9.9949
3 9.9948
4 9.9951
5 9.9956
6 9.9964
7 9.9958
8 9.9959
9 9.9963
10 9.9967
Total = 99.9561 9.9956 0.00073 Ua = 0.000231 uA
Mean value of the readings taken X1….X05=
Ua = s n-1
n
2
s n-1 = [ S ( Xi –`X) ]
n-1
2 2 2 2
= [ (X1 -`X) + (X2 -`X) + (X3 -`X) + … (Xn -`X) ]
n-1
Ua = (s n-1) / n = Type A Uncertainty 0.000231 uA
Degrees of freedom V1 = n-1 = 9
TYPE B UNCERTAINTY EVALUATION
Ub1: Source : Uncertainty of Std. used for calibration Ub1:
(Taken from the Calibration Certificate of the Std. used.)
Ub1= 0.00070 uA Diviser-k : 2
0.000350 uA
Degrees of freedom V1 =
Ub2 : Source : Uncertainty due to Accuracy of Master Equipment used for calibration Ub2:
(Taken from the Manual of the Std. used. or previous cal. certificate)
Ub2 = 0.02500 uA rectangular Diviser 1.732
0.014434 uA
Degrees of freedom V6 =
Ub3 : Source : Uncertainty due to Resolution error of the measuring Inst Ub3:
(Since the limits given are half the count, and assuming Rectangular Distribution)
Resolution Ub3 Multipier Ub3 Diviser Ub3
Sqrt(3)
0.0001 uA 0.5 0.00005 1.732 0.000
0.0000289 uA
Degrees of freedom V5 =
7.6QF-01
Ub4 : Source : Standard Uncertainty due to temp Cofficent. Ub4:
(Taken from the Manual of the Std. used.)
Ub4 = 0.000 uA rectangular Diviser 1.732
0.000 uA
Degrees of freedom V6 =
Ub5 : Source : Uncertainty due to Ub5:
Ub5 = 0.000 rectangular Diviser 1.732
0.000 0
Degrees of freedom V6 =
2 2 2 2............. 2
Combined Uncertainty Uc = [ (Ua) + ( U1) + (U2) + (U3) + (Un) ]
Ua Ub1 Ub2 Ub3 Ub4 Ub5 Ub6 Uc
0.000231 0.000350 0.014434 0.000029 0.014440
Combined Uncertainty Uc = 0.014440 uA
Expanded Uncertainty at 95 % confidence level :-
Combined Uncertainty Coverage Factor Expanded Uncertainty.
Uc Uc * k
Uc 0.014 k= 2 Ue = 0.029
Expanded Uncertainty U = k x Uc = 0.028880 uA
Effective degrees of freedom :-
4
Veff = Uc (y)
4
[ S{ Ui (y
/ Vi) } ]
Veff = 0.000000
0.00000000
Veff = 138182499.5
Final Result = 10.00 0.0289 uA
With Coverage Factor k =2 at 95% C.L.
UNCERTAINITY BUDGET -
Uncertainty
Source of Estimate of Prob. Standard Sensitivity
Divisor Contribution Degrees of freedom
Uncertainty Quantity Distribution Uncertainty Coefficient
ui(y)
Uncertainty of Std. used
0.00070 Normal 2 0.000350 1 0.000350
for calibration Ub1
Uncertainty due to
Accuracy of Master
0.02500 Rectangular 3 0.014434 1 0.014434
Equipment used for
calibration Ub2:
Uncertainty due to
Resolution error of the 0.0001 Rectangular 3 0.000029 1 0.000029
measuring Inst Ub3:
Standard Uncertainty due
0.000000 Rectangular 3 0.00000 1 0.000000
to temp Cofficent. Ub4:
Repeatablity Ua 0.000231 0.000231 -- 0.000231
Combine Uncertainty 0.014 0.014440
Expanded Uncertainty k= 2 0.0289
Final Result = 10.00 0.0289 uA
At 95% C.L with Coverage Factor k =2
