NABL 174
NABL
NATIONAL ACCREDITATION BOARD FOR TESTING AND CALIBRATION LABORATORIES
SAMPLE CALCULATIONS for
UNCERTAINTY OF MEASUREMENT IN ELECTRICAL TESTING
ISSUE NO : 02 ISSUE DATE: 04.10.2004
AMENDMENT NO : 01 AMENDMENT DATE: 05.07.2005
ACKNOWLEDGEMENT NABL acknowledges the keen interest taken by Dr. M. Ramamoorty, Director, Electrical Research and Development Association (ERDA), Vadodara in guiding and advising the Committee in preparing this document as Chairman of NABL Technical Committee – Electrical Testing. NABL also acknowledges the contributions made by the members of the Technical Committee – Electrical Testing in sparing their valuable time for their contribution and expertise in preparing this document. NABL would also like to thank the Experts of Central Power Research Institute (CPRI), Bangalore; Electrical Research and Development Association (ERDA), Vadodara and Institute for Design of Electrical Measuring Instruments (IDEMI), Mumbai in giving their valuable inputs in various sections of this document. Issue 2 is being brought out to harmonise all examples. All examples shown are at confidence level of approximately 95% and for normal distribution, the coverage factor, k=2.
Dr. Sulbha M. Gupta Director, NABL & Adviser Deptt. of Science and Technology
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: i
AMENDMENT SHEET Sl
1
Page No. At all
Clause No. -
Date of Amendment made Amendment ISO/IEC 17025: 1999 & 05.07.05
Reasons Implementation
refer-
ISO/IEC 17025 replaced of ISO/IEC
ences
by ISO/IEC 17025: 2005 17025: 2005
Signature QM Sd/-
Signature Director Sd/-
2
3
4
5
6
7
8
9
10
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Last Amend No: 01 Amend Date: 05.07.2005
Page No: ii
CONTENTS
Sl
Page
Title Acknowledgement
i
Amendment Sheet
ii
Contents
iii
1.
Introduction
1
2.
Scope of Document
3
3.
References
4
4.
Uncertainty Calculation for Voltage
5
5.
Uncertainty Calculation for Current
9
6.
Uncertainty Calculation for Power Loss in Energy Meters
13
7.
Uncertainty Calculation for Tripping Characteristic In MCB
17
8.
Uncertainty Calculation for Transformer
23
9.
Uncertainty Calculation for Power Measurements in 3 Phase
29
Inductor Motor 10.
Technical Committee Members – Electrical Testing
35
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: iii
1.
INTRODUCTION In the broad field of Electrical Engineering, various equipment and systems are used to cater to the application for Electrical power generation, transmission, distribution, control, instrumentation, Communication and domestic application. Each one of the products/ equipment requires a wide variety of tests and hence a need of specialized testing facility. The field of Electrical Testing covers tests of an essentially electrical nature performed on instruments, equipment, appliances, components and materials. The Specific Criteria for Electrical Testing Laboratories (NABL 104) has been brought out which deals with the technical issues and serve the purpose of giving all the necessary action and guidelines for the preparation of application for NABL Accreditation by the laboratories and conducting assessment by the Technical Assessors. As per the requirements of clause 5.4.6 of ISO/ IEC 17025: 2005, the testing laboratories are required to estimate the Uncertainty of Measurement. When estimating the Uncertainty of Measurement, all uncertainty components which are of importance in the given situation shall be taken into account, which shall include but not be limiting to: a
reference standards and reference materials with reported uncertainty in the calibration certificate(s)
b
method employed
c
equipment used with reported uncertainty in the calibration certificate(s)
d
environmental conditions
e
properties and condition of the item being tested
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 01 Amend Date: 05.07.2005
Page No: 1/ 36
The testing laboratories shall identify all the components of uncertainty and make a reasonable estimation for all test parameters, and shall ensure that the form of reporting of the result does not give a wrong impression of the uncertainty. The degree of rigor needed in an estimation of Uncertainty of Measurement depends on the requirements of test method, requirements of client and the existence of narrow limits on which decisions on conformance to a specification are based. All laboratories will calculate the uncertainty of measurement at 95% confidence level.
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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2.
SCOPE OF DOCUMENT This document is supplementary to “Specific Criteria for Electrical Testing Laboratories� (NABL 104). As per the requirements of clause 5.4.6 of ISO/ IEC 17025: 2005, the testing laboratories are required to estimate the Uncertainty of Measurement. This document guides the laboratory to estimate the Uncertainty of Measurement for Electrical Testing. A few examples of Uncertainty of Measurement of in the field of Electrical Testing have been illustrated in this document.
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 01 Amend Date: 05.07.2005
Page No: 3/ 36
3.
REFERENCES ISO/ IEC 17025: 2005
1.
General Requirements for the Competence of Testing and Calibration Laboratories
2.
ISO: 10012: 1992
Quality
Assurance
Requirements
for
Measuring
Equipment 3.
NABL 104
Specific Criteria for Electrical Testing Laboratories
4.
NABL 141
Guidelines
for
Estimation
and
Expression
of
Uncertainty in Measurement 5.
NABL 142
Policy
on
Calibration
and
Traceability
Measurements 6.
NABL 151
Application Form for Testing Laboratories
7.
NABL 160
Guide for Preparing a Quality Manual
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 01 Amend Date: 05.07.2005
Page No: 4/ 36
of
Sample 1
UNCERTAINTY CALCULATION
FOR
VOLTAGE
Product
:
MCB, 32 A, 240/ 415V, Single pole
Test
:
Short circuit test of MCB
Equipment used
:
Digitizer with Amplifier
Range used for calibration
:
62.5 –1000 Volt
Accuracy
:
0.16 % of Reading
Uncertainty of Digitizer with Amplifier from its calibration certificate
:
0.281 %
Resolution
:
0.0001 Volt
Reading No.
Voltage (Volts)
1 2 3 4 5
250.2 250.3 250.1 250.2 250.3
Type A Evaluation
Mean Rdg. (Volts)
=
250.22 Volts (R1+R2+R3+R4+R5)/ 5
Standard deviation
=
0.0836 Volts
Std. uncertainty Ur
=
0.0374 Volts Standard Deviation/ sqrt(5)
Degree of freedom
=
V1 = 5-1 = 4
Std. uncertainty (% Ur)
=
0.0149 %
Ur *100/ Mean Reading
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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Type B Evaluation
1. Uncertainty of Digitizer with Amplifier from its calibration certificate. The distribution is normal and the coverage factor for approximately 95% confidence level is 2 U1(%)
= A1/ 2
= 0.281/ 2
= 0.141 %
U1
= 0.141 * 250.22 * 0.01
= 0.352 Volts
Estimate
= 0.281* 250.22 * 0.01
= 0.703 Volts
Degree of freedom V2 = infinity
2. Accuracy of Digitizer with Amplifier from its calibration certificate A2
= 0.16 % of reading =
0.16 * 250.22 * 0.01 = 0.400 Volts = Estimate
For rectangular distribution, the standard uncertainty = U2 = A2/ sqrt(3) U2
= 0.231 Volts
% U2
= 0.0924 %
U2 * 100/ Mean Reading
Degree of freedom V3 = infinity
3. Uncertainty due to resolution of Team Pro software = U3 A3
= 0.0001/ 2
= 0.00005 Volts
= Estimate
For rectangular distribution, the standard uncertainty = U3 =A3/ sqrt(3) U3
=
0.000028 Volts
% U3
=
0.0000115 %
U3 * 100/ Mean Reading
Degree of freedom V4 = infinity
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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Combined standard uncertainty (Uc) Uc
= sqrt(Ur*Ur)+(U1*U1)+(U2*U2)+(U3*U3)
Uc
=
0.423 Volts
% Uc
=
0.169 %
Uc * 100/ Mean Reading
Effective degrees of freedom (Veff) = Veff
Veff
=
=
Veff
=
Veff
=
(Uc)4 -------------------------------------------------------------------(U1)4 (U2)4 (U3)4 (Ur)4 ------+ ------ + ------ + ------V2 V3 V4 V1 (0.169)4 -----------------------------------------------------------------------------------(0.0149)4 (0.141)4 (0.0924)4 (0.0000115)4 ------------ + ---------+ ------------- + ---------------4 ∞ ∞ ∞ (0.169)4 ------------------------(0.0149)4 ------------ + 0 4 ∞
Expanded Uncertainty at approximately 95% level of confidence, the coverage factor k=2, Thus U
= k*Uc
U
= 0.85 Volts
%U
= 0.34 %
= 2 * 0.423 Volts
U * 100/ Mean Reading
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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Uncertainty Budget Source of Uncertainty Xi
Estimates Limits xi %
Probability Distribution Type A or B Factor
Standard Uncertainty (Volts) Volts %
Sensitivity Coefficient Ci
Uncertainty Contribution Ui (y) Volts %
Degree of freedom Vi
U1
0.281
Normal type B – k=2
0.352
0.141
1.0
0.352
0.141
Infinity
U2
0.16
Rectangular Type B sqrt(3)
0.231
0.0924
1.0
0.231
0.0924
Infinity
U3
0.000019
Rectangular Type B sqrt(3)
0.000028
0.0000115 1.0
0.000028
0.0000115 Infinity
--
Normal Type A
0.0374
0.0149
0.0374
0.0149
4
0.423
0.169
0.423
0.169
Infinity
0.85
0.34
Infinity
Repeatability (Ur)
250.22
Uc Expanded Uncertainty (U)
k=2
1.0
Reporting of results: Voltage = 250.22 Âą 0.85 Volts
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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Sample 2
UNCERTAINTY CALCULATION
FOR
CURRENT
Product
:
MCCB, 800 A, 415V, Four pole
Test
:
Short circuit test of MCCB
Equipment used
:
1) Digitizer with Amplifier Range used for calibration
:
0.625 –10 Volts
Accuracy
:
0.19 % of Reading
Uncertainty of Digitizer with Amplifier from its : calibration certificate
0.281 %
Resolution
0.0001
:
2) Shunt Uncertainty of shunt (%) from its calibration certificate
Reading No.
:
1.156
Current (kAmp.)
1 2 3 4 5
50.26 50.23 50.28 50.24 50.23
Type A Evaluation
Mean Rdg. (kAmp.)
= 50.248 (kAmp.)
Standard deviation
= 0.0216 (kAmp.)
Std. uncertainty Ur
= 0.00969 (kAmp.)
Degree of freedom
= V1 = 5-1 = 4
Std. uncertainty (% Ur)
= 0.0193 %
(R1+R2+R3+R4+R5)/ 5
Standard Deviation/ sqrt(5)
Ur *100/ Mean Reading
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 9/ 36
Type B Evaluation
1. Uncertainty of Digitizer with Amplifier from its calibration certificate. The distribution is normal and the coverage factor at approximately 95% confidence level is 2 U1(%)
= A1/ 2 = 0.281/2 = 0.141 %
U1
= 0.141 * 50.248 * 0.01 = 0.0708 kAmp.
Estimate
= 0.281 * 50.248 * 0.01 = 0.1412 kAmp.
Degree of freedom V2
= infinity
2. Digitizer with Amplifier Accuracy from its calibration certificate (Accuracy) A2
= 0.19% of reading
= 0.19 * 50.248 * 0.01 = 0.09547 kAmp. = Estimate
For rectangular distribution, the standard uncertainty = U2 = A2/ sqrt(3) U2
= 0.0551 kAmp.
% U2
= 0.109 %
U2 * 100/ Mean Reading
Degree of freedom V3 = infinity 3. Uncertainty due to resolution of Team Pro software = U3 A3
= 0.0001/ 2 = 0.00005 kAmp.
= Estimate
For rectangular distribution, the standard uncertainty = U3 = A3/ sqrt(3) U3
=
0.000028 kAmp.
% U3
=
0.000057 %
U3 * 100/ Mean Reading
Degree of freedom V4 = infinity 4. Uncertainty of shunt from its calibration certificate. The distribution is normal and the coverage factor for approximately 95% confidence level is 2 U4 (%)
= A4/ 2
= 1.156/ 2
= 0.578 %
U4
= 0.578 * 50.248 * 0.01
= 0.290 kAmp.
Estimate
= 1.156 * 50.248 * 0.01
= 0.580 kAmp.
Degree of freedom V5 = infinity
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 10/ 36
Combined standard uncertainty (Uc) Uc
= sqrt(Ur*Ur)+(U1*U1)+(U2*U2)+(U3*U3) )+(U4*U4)
Uc
=
0.310 kAmp.
% Uc
=
0.617 %
Uc * 100/ Mean Reading
Effective degrees of freedom (Veff) = Veff
Veff
Veff
Veff
(Uc)4 = ---------------------------------------------------------------------------------------------(U1)4 (U2)4 (U3)4 (U4)4 (Ur)4 ------+ ------ + ------ + ------+ -----V2 V3 V4 V5 V1 (0.617)4 = -------------------------------------------------------------------------------------------(0.141)4 (0.109)4 (0.000057)4 (0.578)4 (0.0193)4 ----------- + ---------- + ---------- + --------------- + -----------4 ∞ ∞ ∞ ∞ (0.617)4 = -------------------------(0.0193)4 ----------- + 0 4 = 4178028
=
∞
Expanded Uncertainty for approximately 95 % level of confidence, the coverage factor k=2, Thus = 2 * 0.310 kAmp.
U
= k * Uc
U
= 0.620 kAmp.
%U
= 1.234 %
U * 100/ Mean Reading
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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Uncertainty Budget Source of Uncertainty Xi
Estimates Limits xi %
Probability Distributio n Type A or B Factor
Standard Uncertainty (Volts) kAmp. %
Sensitivity Coefficient Ci
Uncertainty Contribution Ui (y) kAmp. %
Degree of freedom Vi
U1
0.281
Normal Type B 2
0.0708
0.141
1.0
0.0708
0.141
Infinity
U2
0.190
Rectangular Type B sqrt(3)
0.0551
0.109
1.0
0.0551
0.109
Infinity
U3
0.00005
Rectangular Type B sqrt(3)
0.000028
0.000057
1.0
0.000028
0.000057
Infinity
U4
1.156
Normal Type B 2
0.2963
0.578
1.0
0.2963
0.578
Infinity
--
Normal Type A
0.00969
0.0193
1.0
0.00969
0.0193
4
0.310
0.617
0.310
0.617
Infinity
0.620
1.234
Infinity
Repeatability (Ur)
50.248
Uc Expanded Uncertainty (U)
k=2
Reporting of results: Current = 50.248 Âą 0.620 kAmp.
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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Sample 3
UNCERTAINTY CALCULATION FOR POWER LOSS IN ENERGY METERS Product
: Static energy meter
Test
: Power loss measurement in Energy Meters
Equipment used
: Digital wattmeter
Range
: 20 Watts
Accuracy
: 0.5 % of Reading
Uncertainty of watt meter from its calibration certificate
: 0.0953 %
Resolution
: 0.01 Watts
Reading No.
Power loss (Watt)
1 2 3 4 5
0.67 0.68 0.68 0.68 0.68
Type A Evaluation Mean Rdg.(Watt)
= 0.678 Watt (R1+R2+R3+R4+R5)/ 5
Standard deviation
= 0.0044721 Watt
Std. uncertainty Ur
= 0.002 Watt Standard Deviation/ sqrt(5)
Degree of freedom
= V1 = 5-1 = 4
Std. uncertainty (% Ur)
= 0.295 %
Ur *100/ Mean Reading
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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Type B Evaluation 1. Uncertainty of watt meter from its calibration certificate. The distribution is normal and the coverage factor for approximately 95% confidence level is 2 U1(%)
= A1/ 2 =
0.0953/2
= 0.04765 %
U1
= 0.04765 * 0.678 * 0.01 = 0.323 * 10-3 W
Degree of freedom V2 = infinity
2. From watt meter specification (Accuracy) A2
= 0.5% of reading = 0.5 * 0.678/ 100 = 0.00339. Watt = Limit
For rectangular distribution, the standard uncertainty U2
= 0.00195 watt
% U2
= 0.2876 %
= U2 = A2/ sqrt(3)
U2 * 100/ Mean Reading
Degree of freedom V3 = infinity
3. Uncertainty due to resolution of watt meter = U3 A3
= 0.01/ 2 = 0.005 Watt. = Limit
For rectangular distribution, the standard uncertainty = U3 = A3/ sqrt(3) U3
= 0.002886 Watt
% U3
= 0.4257 %
U3 * 100/ Mean Reading
Degree of freedom V4 = infinity
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 14/ 36
Combined standard uncertainty (Uc) Uc
= sqrt(Ur*Ur)+(U1*U1)+(U2*U2)+(U3*U3) = 0.00402
% Uc
=
0.59 %
Effective degrees of freedom (Veff) = Veff
Veff
Veff
(Uc)4 = -------------------------------------------------------------------------(U1)4 (U2)4 (U3)4 (Ur)4 ------+ ------ + ------ + ------V2 V3 V4 V1 (0.59)4 = -------------------------------------------------------------------------(0.04765)4 (0.2876)4 (0.4257)4 (0.295)4 ----------- + ----------- + ---------+ ----------∞ ∞ ∞ 4 =
64
Expanded Uncertainty for approximately 95% level of confidence, the coverage factor k=2, Thus U
= k*Uc = 2* 0.00402 = 0.008 W
%U
= 1.18 %
U* 100/mean Reading
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 15/ 36
Uncertainty Budget Source of Uncertainty Xi
Estimates xi
Limits %
Probability Distribution Type A or B Factor Normal type B–2
Standard Uncertainty %
Sensitivity Coefficient Ci
Degree of freedom Vi
1.0
Uncertainty Contribution Ui(y) % 0.04765
0.04765
U1
0.0953
U2
0.5
Rectangular Type B sqrt(3)
0.2876
1.0
0.2876
Infinity
U3
0.7373
Rectangular Type B sqrt(3)
0.4257
1.0
0.4257
Infinity
Normal Type A
0.295
1.0
0.295
4
0.59
64
1.18
Infinity
Repeatability
0.678 W
Uc % Expanded Uncertainty
k=2
infinity
Reporting of results: Power loss = 0.678
Âą 0.008 Watt
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 16/ 36
Sample 4
UNCERTAINTY CALCULATION FOR TRIPPING CHARACTERISTIC IN MCB Product
: MCB, 4 A, WO 956, Sample 3
Test
: Tripping characteristic at 2.55 In as per
IS:8828-1996 Standard used
:
1) Digital time interval meter Range used
: 99.99 seconds
Accuracy
: 0.5 % of Reading
Uncertainty of time interval meter from its calibration certificate
: 0.015 %
Resolution
: 0.01
2) Current transformer (CT) Range used
: 20/ 5 A
Accuracy
: 0.2 % of Reading
Uncertainty of time interval meter from its calibration certificate
: 0.092 %
3) Digital AC Ammeter Range used
: 0-10 A
Accuracy
: 0.5 % of Reading
Uncertainty of time interval meter from its calibration certificate
: 0.0281 %
Resolution
: 0.01
Reading No.
Tripping time seconds
1 2 3 4 5
18.01 18.26 18.76 18.68 18.16
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 17/ 36
Type A Evaluation Mean Rdg.(seconds)
= 18.374 seconds
Standard deviation
= 0.329 second
Std. uncertainty Ur
= 0.147 second
Degree of freedom
= V1 = 5-1 = 4
Std. uncertainty (% Ur)
= 0.801 %
(R1+R2+R3+R4+R5)/ 5
Standard Deviation/ sqrt(5)
Ur *100/ Mean Reading
Type B Evaluation 1. Uncertainty of time interval meter from its calibration certificate. The distribution is normal and the coverage factor for approximately 95% confidence level is 2 A1
= 0.015 %
U1(%)
= A1/ 2= 0.015/ 2
U1
= 0.0075 * 18.374 * 0.01
= 0.0075 % = 0.0014 second
Degree of freedom V2 = infinity
2. From time interval Meter specification (Accuracy) A2
= 0.5% of reading =
0.5 * 18.3740 * 0.01 =
0.092 seconds
For rectangular distribution, the standard uncertainty = U2 = A2/ sqrt(3) U2
= 0.0531 second
% U2
= 0.289 %
U2 * 100/ Mean Reading
Degree of freedom V3 = infinity
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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3. Uncertainty due to resolution of Meter = U3 A3
= 0.01/ 2 = 0.005 seconds
For rectangular distribution, the standard uncertainty = U3 = A3/ sqrt(3) U3
= 0.0029 seconds
% U3
= 0.016 %
U3 * 100/ Mean Reading
Degree of freedom V4 = infinity
4. Uncertainty of CT from its calibration certificate. The distribution is normal and the coverage factor for approximately 95% confidence level is 1.96 = 0.092 %
A4 U4 (%)
= A4/ 2= 0.092/ 2 = 0.046 %
Degree of freedom V5 = infinity
5. From CT specification (Accuracy) A5
= 0.2% of reading
For rectangular distribution, the standard uncertainty = U5 = A5/ sqrt(3) % U5
= 0.115 %
Degree of freedom V6 = infinity
6. Uncertainty of Ammeter from its calibration certificate. The distribution is normal and the coverage factor for approximately 95% confidence level is 1.96 A6
= 0.0281 %
U6(%)
= A6/ 2
= 0.0281/ 2
= 0.141 %
Degree of freedom V7 = infinity
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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7. From Ammeter specification (Accuracy) A7
= 0.5% of reading
For rectangular distribution, the standard uncertainty = U2 = A2/ sqrt(3) % U7
= 0.289 %
Degree of freedom V8 = infinity
8. Uncertainty due to resolution of Meter = U8 A8
= 0.01/ 2 =
0.005
For rectangular distribution, the standard uncertainty = U8 = A8/ sqrt(3) % U8= 0.005/ sqrt(3)= 0.016 % Degree of freedom V9 = infinity
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 20/ 36
Combined standard uncertainty = Uc Uc
= sqrt(Ur*Ur)+(U1*U1)+(U2*U2)+(U3*U3)+(U4*U4)+(U5*U5)+(U6*U6)+(U7*U7)+(U8*U8)
% Uc =
0.900 %
Uc * 100/ Mean Reading
Effective degrees of freedom (Veff) = (Uc)4 Veff
= -----------------------------------------------------------------------------------------------(Ur)4
(U1)4 (U2)4 (U3)4 (U4)4 (U5)4 (U6)4 (U7)4 (U8)4 ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------- + -----V1 V2 V3 V4 V5 V6 V7 V8 V9 (0.900)4 = ---------------------------------------------------------------------------------------------------------------------(0.801)4 (0.0075)4 (0.289)4 (0.016)4 (0.046)4 (0.115)4 (0.0141)4 (0.289)4 (0.016)4 -------- + ----------- + ---------- + --------- + --------- + ---------- + ---------- + --------- + --------4 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ (0.900)4 = ----------------------(0.801)4 ------------ + 0 4
= 6.375
Expanded Uncertainty for 95% level of confidence, the coverage factor k=2.45, Thus U = k*Uc = 2.45*0.900 %U
= 2.205 %
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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Uncertainty Budget Source of Uncertainty Xi
Estimates xi.
Limits %
Probability Distribution Type A or B Factor
Standard Uncertainty
Sensit. Coefficient
%
Ci
Uncertainty Contribution Ui(y)
Degree of freedom Vi
%
U1
0.015
Normal type B–2
0.0075
1.0
0.0075
infinity
U2
0.5
Rectangular Type B sqrt(3)
0.289
1.0
0.289
Infinity
U3
0.005
Rectangular Type B sqrt(3)
0.016
1.0
0.016
Infinity
U4
0.092
Normal type B–2
0.046
1.0
0.0046
infinity
U5
0.2
Rectangular Type B sqrt(3)
0.115
1.0
0.0115
Infinity
U6
0.0281
Normal type B–2
0.0141
1.0
0.0141
infinity
U7
0.5
Rectangular Type B sqrt(3)
0.289
1.0
0.289
Infinity
U8
0.5
Rectangular Type B sqrt(3)
0.016
1.0
0.016
Infinity
Normal Type A
0.801
1.0
0.801
4
0.900
6.375
2.205
Infinity
Repeatability
18.374
Uc (seconds) Expanded Uncertainty
k = 2.45
Reporting of results: Tripping time = 18.374 seconds ± 2.205 % = 18.374 ± 0.405 seconds
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 22/ 36
Sample 5
UNCERTAINTY CALCULATION
FOR
TRANSFORMER
Product
: Distribution transformer
Test
: Separate Source Voltage Withstand Test
(Power Frequency Voltage Withstand Test) Standards used
:
1) Capacitive voltage Divider and peak voltmeter Range used for testing
: 0-50 kV
Accuracy
: 0.03 % of FSD
Uncertainty of Capacitive voltage Divider and peak voltmeter from its calibration certificate
: 0.0443 %
Resolution
: 0.2 kV
2) Digital Stop watch Range used for testing
: 0-99.99 sec.
Accuracy
: 0.02 % of RDG
Uncertainty of Digital Stop watch from its calibration certificate
: 0.0146 %
Resolution
: 0.0001
Reading No.
Voltage (kV)
1 2 3 4 5
28 28 28 28 28
Type A Evaluation Mean Reading (kV.)
=
28 kV
Standard deviation
=
0
Std. uncertainty Ur
=
0.0
Degree of freedom = V1
=
5–1=4
Std. uncertainty (% Ur)
=
0.0
(R1+R2+R3+R4+R5)/ 5
Standard Deviation/ sqrt(5)
Ur * 100/ Mean reading
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 23/ 36
Type B Evaluation A. Voltage Parameter
1. Uncertainty of Capacitive voltage Divider and peak voltmeter from its calibration certificate. A1
= 0.0443 %
The distribution is normal and the coverage factor for approximately 95% confidence level is 2 U1(%)
= A1/ 2 =
Estimate
= 0.0443 * 28 * 0.01
0.0443/ 2
= 0.02215 % = 0.0124 kV.
Degree of freedom V2 = infinity 2. Accuracy of Capacitive voltage Divider and peak voltmeter from its calibration certificate. = 0.03% of FSD A2 =
0.03 * 50 * 0.01
For rectangular distribution, the standard uncertainty U2
=
0.0086 kV
% U2
=
U2 * 100/ Mean Reading
=
0.0086 * 100/ 28
= 0.015 kV = U2
= A2/ sqrt(3)
= 0.031 %
Degree of freedom V3 = infinity
3. Uncertainty due to resolution of Capacitive voltage Divider and peak voltmeter = 0.2/ 2 = 0.1 kV = Estimate A3 A3(%)
= 0.1 * 100/ 28
= 0.357 %
For rectangular distribution, the standard uncertainty = U3 =A3/ sqrt(3) U3
= 0.0577 kV
% U3
= U3 * 100/ Mean Reading = 0.0577 * 100/ 28
= 0.206 %
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 24/ 36
Combined standard uncertainty (Uc) Uc
= sqrt(Ur2+U12+U22+U32)
% Uc =
0.21 %.
Effective degrees of freedom (Veff) = Veff
Veff
(Uc)4 = ------------------------------------------------------------------------(U2)4 (U3)4 (Ur)4 (U1)4 ------+ ------ + ------ + ------V2 V3 V4 V1 =
infinity
Expanded Uncertainty for approximately 95% level of confidence, the coverage factor k=2, Thus U = k*Uc = 2 * 0.21 % Total expanded uncertainty for voltage parameter % U = 0.42 %
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 25/ 36
Type B Evaluation B. Time Parameter
1. Uncertainty of Digital Stop watch from its calibration certificate. = 0.0146 % A1 The distribution is normal and the coverage factor for approximately 95% confidence level is 2 U1(%)
= 0.0146/ 2 = 0.0073 %
Estimate = 0.0146 * 60 * 0.01 = 0.00876 sec = infinity
Degree of freedom V2
2. Accuracy of Digital Stop watch from its calibration certificate A2
=
0.02 % of reading
For rectangular distribution, the standard uncertainty = U2 = A2/ sqrt(3) % U2
=
Estimate
= 0.02 * 60 * 0.01 = 0.012 sec
0.0115 %
Degree of freedom V3 = infinity
3. Uncertainty due to resolution of Digital Stop watch A3
= 0.0001/ 2
A3
= 0.00005 * 100/ 60 = 0.000083 %
= 0.00005 sec.
For rectangular distribution, the standard uncertainty = U3 U3
= 0.0000288 sec.
% U3
= U3 *100/ Mean Reading
= Estimate
=A3/ sqrt(3)
= 0.000048 %
Degree of freedom V4 = infinity
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 26/ 36
Combined standard uncertainty (Uc)
Uc
= sqrt(Ur2+U12+U22+U32)
% Uc
= 0.0137 %.
Effective degrees of freedom (Veff) =
Veff
Veff
(Uc)4 = ------------------------------------------------------------------------(U1)4 (U2)4 (U3)4 (Ur)4 ------+ ------ + ------ + ------V2 V3 V4 V1 =
infinity
Expanded Uncertainty for approximately 95% level of confidence, the coverage factor k=2, Thus U
= k * Uc
= 2 * 0.0137 %
Total expanded uncertainty for time parameter % U = 0.0275 %
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 27/ 36
Uncertainty Budget
A. VOLTAGE PARAMETER Estimate
Limits %
Probability distribution
Divisor
std. uncert.
Sensitivity Coefficient
U1 ('Uncertainty of CVD & PVM)
0.04430
Normal
2
0.02215
1
0.02215
Infinity
U2 ('Accuracy of CVD & PVM)
0.03% of FSD
Rectangular
1.73205
0.031
1
0.031
Infinity
Source of uncertainty
Uncertainty Degree of Contribution % freedom
U3 (Resolution of CVD & PVM)
0.2 kV
0.357
Rectangular
1.73205
0.206
1
0.206
Infinity
Ur (Type-ARepeatability)
28 kV
0.00000
Normal
1
0.0000
1
0.0000
4
0.21
Infinity
0.42
Infinity
Combined std. Uncertainty (%) Expanded uncertainty (%)
k =
2
Reporting of results: Applied Voltage = 28 kV Âą 0.42 %.
B. TIME PARAMETER Estimate
Source of uncertainty
Limits
Probability distribution
Divisor
std. uncert.
Sensitivity Uncertainty Coefficient Contribution %
Degree of freedom
U1 ('Uncertainty of Stop watch)
0.01460
Normal
2
0.0073
1
0.0073
Infinity
U2 ('Accuracy of stop watch)
0.02000
Rectangular
1.73205
0.0115
1
0.0115
Infinity
U3 (Resolution of stop watch)
0.0001 sec 0.000083
Rectangular
1.73205
0.000048
1
0.000048
Infinity
Normal
1.00000
0.0000
1
0.0000
4
0.0137
Infinity
0.0275
Infinity
Ur (Type-ARepeatability)
60 sec
0.00000
Combined std. Uncertainty (%) Expanded uncertainty (%)
k =
2
Reporting of results: Time of Voltage Application = 60 seconds Âą 0.0275 %.
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 28/ 36
Sample 6
UNCERTAINTY CALCULATION FOR VOLTAGE FOR POWER MEASUREMENTS IN 3 PHASE INDUCTOR MOTOR
Product
:
3 phase Induction motor
Test
:
Full load test
Equipment used
:
Wattmeter-3phase 3 wire (2 wattmeter method)
Accuracy
:
Current Transformer Current Transformer Wattmeter 0.5
Uncertainty from calibration report
:
Wattmeter
0.0953 %
Resolution
:
Current transformer Current transformer Wattmeter
0.092 % 0.092 % 1W
CT Ratio
:
15/ 5 =
3
No. of Observation
:
5
Reading No.
1 2 3 4 5
Measured Power (Wattmeter rdg.) W 3260 3281 3260 3282 3284
Actual Power (=Wattmeter rdg * CT ratio) W 9780 9843 9780 9846 9852
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 29/ 36
Type A Evaluation
Mean Rdg. (Wattmeter rdg) =
3273.4 W
Mean Rdg. (Actual Power)
=
9820.2 W
Standard deviation
=
36.84 W
Standard Uncertainty Ur
=
16.475 W
Degree of freedom
=
V1 = 5-1 = 4
Std. uncertainty (% Ur)
=
0.168 %
(R1+R2+R3+R4+R5)/ 5
Standard Deviation/ sqrt(5)
Ur *100/ Mean Reading
Type B Evaluation
1. Uncertainty of Wattmeter from its calibration certificate. The distribution is normal and the coverage factor for approximately 95% confidence level is 2 A1
= 0.0953 %
U1(%)
= A1/ 2
U1
= 0.048 * 3273.4 * 0.01
= 1.571 W
Estimate
= 0.0953 * 3273.4 * 0.01
= 3.12 W
= 0.0953/ 2
= 0.048 %
Degree of freedom V2 = infinity
2. Accuracy of Wattmeter from its calibration certificate A2
= 0.5 %
For rectangular distribution, the standard uncertainty = U2 = A2/ sqrt(3) U2 (%)
= 0.289 %
U2
= 0.289 * 3273.4 * 0.01
= 9.46 W
Estimate
= 0.5 * 3273.4 * 0.01
= 16.367 W
Degree of freedom V3 = infinity
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 30/ 36
3. Uncertainty due to resolution of Wattmeter
= U3
A3
= 0.5 W
= 1/ 2
For rectangular distribution, the standard uncertainty = U3 = A3/ sqrt(3) U3
= 0.289 W
U3 (%)
= 0.008 %
Estimate
= 0.5 W
Degree of freedom V4 = infinity
4. Uncertainty of current transformer (755) from its calibration certificate. The distribution is normal and the coverage factor for approximately 95% confidence level is 2 A4
= 0.092 %
U4 (%)
= A4/ 2
= 0.092/ 2
= 0.046 %
Degree of freedom V5 = infinity
5. Ratio error for current transformer (755) from its calibration certificate A5
= 0.31 %
For rectangular distribution, the standard uncertainty = U5 = A5/ sqrt(3) U5 (%)
= 0.178 %
Degree of freedom V6 = infinity
6. Uncertainty of current transformer (757) from its calibration certificate. The distribution is normal and the coverage factor for approximately 95% confidence level is 2 A6
= 0.092 %
U6 (%)
= A6/ 2
= 0.092/ 2
= 0.046 %
Degree of freedom V7 = infinity
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 31/ 36
7. Ratio error for current transformer (757) from its calibration certificate. A7
= 0.426 %
For rectangular distribution, the standard uncertainty is = U7 (%)
U7 = A7/ sprt(3)
= 0.246
Degree of freedom V8 = infinity
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 32/ 36
Combined standard uncertainty (Uc) Uc
= sqrt(Ur*Ur + U1*U1 + U2*U2 + U3*U3 + U4*U4 + U5*U5 + U6*U6 + U7*U7)
% Uc
= 0.459 %
Effective degrees of freedom (Veff) = Veff
=
Veff
=
Veff
=
(Uc)4 ---------------------------------------------------------------------------------------(U1)4 (U2)4 (U3)4 (U4)4 (U5)4 (U6)4 (U7)4 (Ur)4 ------- + ------ + ------ + ------ + ------ + ------- + ------ + ------V2 V3 V4 V5 V6 V7 V8 V1 (0.459)4 ---------------------------------------------------------------------------------------------------------(0.048)4 (0.289)4 (0.008)4 (0.046)4 (0.178)4 (0.046)4 (0.246)4 (0.168)4 ----------- + ---------- + ---------- + ---------- + --------- + ---------- + ---------- + --------∞ ∞ ∞ ∞ ∞ ∞ ∞ 4
222.9
Expanded Uncertainty for approximately 95% level of confidence, the coverage factor k = 2, Thus U
= k*Uc
%U
= 0.918 %
= 2 * 0.459
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 33/ 36
Uncertainty Budget Source of Uncertainty Xi
Limits %
Probability Distribution Type A or B Factor
U1
0.0953
Normal Type B–2
0.048
1.0
0.048
Infinity
U2
0.5
Rectangular Type B sqrt(3)
0.289
1.0
0.289
Infinity
0.015
Rectangular Type B sqrt(3)
U4
0.092
Normal Type B 2
0.046
1.0
0.046
Infinity
U5
0.31
Rectangular Type B sqrt(3)
0.178
1.0
0.178
Infinity
U6
0.092
Normal Type B 2
0.046
1.0
0.046
Infinity
U7
0.426
Rectangular Type B sqrt(3)
0.246
1.0
0.246
Infinity
--
Normal Type A
0.168
1.0
0.168
4
0.459
222.9
0.915
Infinity
U3
Repeatability (Ur)
Estimates xi
0.03
9820.2
Standard Uncertainty U (xi) %
0.008
Sensitivity Coefficient Ci
1.0
Uc Expanded Uncertainty (U)
Uncertainty Contribution Ui (y) Volts %
k=2
0.008
Degree of freedom Vi
Infinity
Reporting of results: Measured Power
= 9820.2 W ± 0.918% 9820.2
± 90.1W
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
Page No: 34/ 36
TECHNICAL COMMITTEE MEMBERS - ELECTRICAL Sl
Name & Organisation
Capacity
1
Dr. M. Ramamoorty Director Electrical Research & Dev. Association (ERDA), Opp. Makarpura Village; P.O. Makarpura Indusrial Area, Vadodara-390010
Chairman
2
Dr. A.K. Chakrabarty Adviser DST and Director NABL B-4/ B-6 Qutab Hotel Apartments New Mehrauli Road New Delhi – 110 016
Co-Chairman
3
Dr. Sachichidanand Director General Central Power Research Institute (CPRI) Prof. Sir C.V. Raman Road, Sadashivanagar Sub P.O P.B. No. 8066, Bangalore – 560 080
Special Invitee
4
Dr. K. Ramani Formerly Principal Director IDEMI & Presently Regional Co-ordinator NABL 557, Kher Section Ambernath (E) Thane Dist. Maharashtra - 421 501
Member
5
Sh. P.K. Mukherjee Director Bureau of Indian Standards (BIS), Manak Bhavan; 9, Bhadurshah Zafar Marg New Delhi – 110 002
Member
6
Sh. G.R. Patel
Member
Assistant Vice- President Asea Brown Boveri Limited (ABB), Maneja Village, Vadodara - 390 004
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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Sl
Name & Organisation
Capacity
7
Sh. R.K. Tiwari Senior Dy. General Manager (TTG) UHV Laboratory Bharat Heavy Electrical Ltd. (BHEL), Piplani Bhopal – 462 022
Member
8
Sh. M. N. Radhakrishna,
Member
Formerly Director, BIS Balaji Consultancy Services 20/ 1, 4th Main Road, 8th Cross, Malleswaram, Bangalore - 560 003 9
Sh. S.N. Moorching Formerly Jt. Director CPRI “Gurukrupa” 989; 25th Main, Srinagar Extn. Bangalore – 560094
Member
10
Sh. U.C. Trivedi Sr. Manager-Energy System Electrical Research & Dev. Association (ERDA), Opp. Makarpura Village; P.O. Makarpura Indusrial Area, Vadodara-390010
Member
11
Sh. A. Sudhindra Joint Director, QA Deptt. Central Power Research Institute (CPRI) Prof. Sir C.V. Raman Road, Sadashivanagar Sub P.O P.B. No. 8066, Bangalore – 560 080
Member
12
Sh. Anil Relia Director DST and Quality Manager NABL B-4/ B-6 Qutab Hotel Apartments New Mehrauli Road New Delhi – 110 016
Member Secretary
National Accreditation Board for Testing and Calibration Laboratories Doc. No: NABL 174 Issue No: 02
Sample Calculations for Uncertainty of Measurement in Electrical Testing Issue Date: 04.10.2004 Amend No: 00 Amend Date: -
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