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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

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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

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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

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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: -

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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 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: -

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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: -

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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: -

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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: -

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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: -

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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: -

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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: -

Page No: 35/ 36


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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National Accreditation Board for Testing and Calibration Laboratories 3rd Floor, NISCAIR 14, Satsang Vihar Marg New Mehrauli Road New Delhi – 110 067 Tel.: 91-11 26529718 – 20, 26526864 Fax: 91-11 26529716 Website: www.nabl-india.org


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