1

Measurement Uncertainty

and Why It Is Important to

T&E

Air Force Test Center

Ben Castillo

412ENI/ENIO

661-277-6364

I n t e g r i t y - S e r v i c e - E x c e l l e n c e

Approved for public release; distribution is unlimited. 412TW-PA No.: 412 TW-PA-12733

War-Winning Capabilities … On Time, On Cost

Sept 2012

2

Overview

• Introduction

• Background

• Uncertainty Analysis

• Systematic Error

• Random Error

• Conclusion

3

Introduction

• A measurement result without a statement of

uncertainty lacks credibility

– A measurement is an approximation to the

true value

– Measurement uncertainty identifies variability

of the measurement

– Uncertainty is linked to the reliability of a

measurement

4

Background

• Fundamental instrumentation challenges

• Instrumentation intrusion effects

• Environmental effects

– Temperature

– Humidity

– Shock and vibration

– Electromagnetic interference

5

Uncertainty Analysis

0

200

400

600

800

1000

1200

0 0.005 0.01 0.015 0.02 0.025

sample 1

Plot of 14 measurements of the same parameter

over a .025 second interval

• A measurement is an approximation of the true value

• The true value is never known or knowable

6

Uncertainty Analysis

• Every measurement is accompanied by a

measurement error

• Types of errors

• Random

• Systematic

• Measurement uncertainty quantifies spread of

error distribution

• Total measurement uncertainty is the

combination of uncertainties due to

systematic and random errors

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Uncertainty Analysis

• Requirements for measurement uncertainty

analysis

– Objectives identified, test process defined

– Measurement system and process controlled

– Calibration corrections applied

– Data reduction process defined

– Data acquisition system characterized

8

Systematic Error

• Systematic error “… is the portion of the total

measurement error that remains constant in

repeated measurements of the true value.” (Reference ASME PTC19.1-1998)

• Total systematic error is the sum of the

elemental systematic errors

• Elemental systematic errors can be calibrated

out if known, ignored if negligible, or estimated

if unknown

9

Example Systematic Error

System Load Cell Strain Gauge

LoadCompression

Force Brake Torque

(Lbs) (lbs.) (mV)

run 1 0 248.1 0.764

run 2 0 248.9 0.782

run 3 0 249.8 0.782

• All data acquisition systems are prone to systematic

errors

• Zero load systematic errors detected during

calibration of a Data Acquisition System

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Example Systematic Error

• Systematic error due to affects of instrument

zero load offsets

• Approx 2.3K ft-lbs (5.5% FS)

• Plots of uncorrected data and data adjusted to

remove systematic error

-5000

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

-10.0000 0.0000 10.0000 20.0000 30.0000 40.0000

data including systematicerror

systematic error removed

11

Random Error

• “ Random error,…, is the portion of the total

measurement error that varies in repeated

measurements of the true value.” (ASME PTC19.1-1998)

• This type of error cannot be corrected

• Uncertainty due to random error is computed

from the standard deviation

Example Random Error

• Random error may be estimated by

inspection

0

200

400

600

800

1000

1200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Example Sources of Error

13

Input

Gs accel signal

conditioning

card

data

processing

• Block diagram data acquisition system (DAS)

• Accelerometer: excitation voltage, sensitivity,

amplitude response, nonlinearity, hysteresis, thermal

transient response, zero offset,…

• SCC: accuracy, quantization error, offset error,…

• Data processing: regression error

Volts Counts Gs

excitation

Example Sources of Error

14

• Data output in engineering units

• Sources of error must be considered

and added to the error budget

from the DAS

15

Conclusion

• Impact of combined systematic and random

errors can be significant

Random Error

2 std dev

Threshold

Pass Fail

16

Conclusion

• A test result that includes uncertainty

information holds more useful information

than one without

– Uncertainty identifies the spread of data

from the mean

– Identifies a confidence level

– Needed to pass/fail a specification or

performance limit

• Reduce the risk of making a mistake

• References: RCC Document 122-07, ASME

PTC 19.1, NIST TN1297 1994 Edition