Analyzing uncertainty and errors
This presentation is the property of its rightful owner.
Sponsored Links
1 / 37

Analyzing Uncertainty and Errors PowerPoint PPT Presentation


  • 62 Views
  • Uploaded on
  • Presentation posted in: General

Analyzing Uncertainty and Errors. ISAT 253 Spring 2005. Objectives. Understand the concept of uncertainty Define measurement uncertainties and errors For a set of measurements, learn to calculate specific Sensitivities Accuracies Precisions. Objectives. Define measurement errors

Download Presentation

Analyzing Uncertainty and Errors

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Analyzing uncertainty and errors

Analyzing Uncertainty and Errors

ISAT 253

Spring 2005


Objectives

Objectives

  • Understand the concept of uncertainty

  • Define measurement uncertainties and errors

  • For a set of measurements, learn to calculate specific

    • Sensitivities

    • Accuracies

    • Precisions

Dr. Ken Lewis


Objectives1

Objectives

  • Define measurement errors

  • Differentiate between systematic and random errors

Dr. Ken Lewis


Key concepts

Precision

Accuracy

Precision error

Bias error

Sensitivity

Calibration

Calibration standards

Measurement standards

Key Concepts

Dr. Ken Lewis


Recall

Recall

  • Resolution

    • The smallest increment of a unit of measure that an instrument can detect or measure.

  • Accuracy

    • How close the measurement is to the “true value”

  • Precision

    • The consistent repeatability of a measurement.

Dr. Ken Lewis


Recall types of error

Recall -- Types of Error

  • Bias error ( average of the measurements – true)

    • Non random

    • Systematic

    • Destroys accuracy

  • Precision error (measurement readings – average)

    • Random

    • Hard to control without changing the measurement system

Dr. Ken Lewis


Error summary

Error summary

Precision Error

Random Error

Bias Error

Systematic Error

Accuracy

True

Value

Average

Measure

Dr. Ken Lewis


Which type of error is it

Which type of error is it?

  • A carpenter bought a piece of lumber at Lowe’s and measured it in the store as 8’-2”. At home, when she measured it again to cut it, she measured it as 8’-1” using the same tape measure.

  • We measure the pH of a solution of 0.1 mol acetic acid and 0.2 mol ammonium acetate as 4.8 at 25°C, but standards show it should be 4.78.

  • A statistical process control (SPC) gauge is 6 microns high every time it is used.

Dr. Ken Lewis


Quantifying uncertainty

Quantifying uncertainty

  • Ten measurements were made on a battery

  • The true voltage is known to be 6.11 volts.

  • The average of the measurements is

    • 6.03 volts

Find

The resolution error

The systematic error or accuracy

The precision

Dr. Ken Lewis


Quantifying uncertainty1

Quantifying uncertainty

The resolution uncertainty or resolution error.

±0.01 V

Dr. Ken Lewis


Quantifying uncertainty2

Quantifying uncertainty

The systematic error or accuracy

Accuracy = average value - true value

Accuracy = 6.03 V - 6.11 V = -0.08 V

-0.08 V

Dr. Ken Lewis


Quantifying uncertainty3

Quantifying uncertainty

The precision

Precision = Maximum deviation from the average

Precision = ±|5.96 V - 6.03 V| = ±0.07 V

±0.07 V

Dr. Ken Lewis


Quantifying uncertainty4

Quantifying uncertainty

  • Caution

    • Be sure that the precision statement isn’t based on one bad measurement

Dr. Ken Lewis


Reporting uncertainties

Reporting Uncertainties

  • Uncertainties can be reported as:

    • a number in the measurement units

    • a percentage of the instrument’s full scale

    • a percentage of the measurement itself

  • Resolution error can be reported as:

    • ± 1 of the least significant digit

    • ± ½ of the least significant digit

Dr. Ken Lewis


Numerical example

Numerical Example

  • Consider our battery/voltmeter problem:

    • Average measured value = 6.03 V

    • Assume meter range = 0-10 V

  • Precision can be reported in three ways:

    • Measurement units: 6.03 V ± 0.07 V

    • Percent of full scale: 6.03 V ± 0.7% FS

    • Percent of the measure: 6.03 V ± 1%

Dr. Ken Lewis


Range

Range

  • A measuring system is designed to operate over a finite range

    • 0 – 500°C

    • 20 – 200 psig

    • 0 – 300 lbs

  • The range given describes the limits of proper response

  • What happens outside the range is no gauranteed.

Dr. Ken Lewis


Analyzing uncertainty and errors

Span

  • The span is the difference between the high and low of the range

Dr. Ken Lewis


Accuracy example 5 full scale

Accuracy – example ±5% full scale

  • Problem: below the full scale reading the error will be greater than ±5%.

  • 0 – 200°C ± 10°C

  • So at 30°C, the reading will be somewhere between 20°C and 40°C

Dr. Ken Lewis


Sensitivity

Sensitivity

  • The slope of the line relating input to output

Dr. Ken Lewis


Sensitivity thermocouples

Sensitivity – Thermocouples

Dr. Ken Lewis


Sensitivity thermocouples1

Sensitivity -- Thermocouples


Sensitivity calculation

Sensitivity Calculation

For example

For

Ideal

devices

Dr. Ken Lewis


Other measurement problems

Other Measurement Problems

Dr. Ken Lewis


Other measurement problems1

Other Measurement Problems

  • Hysteresis

    • Friction

    • Mechanical flexure of internal parts

    • Electrical capacitance

  • Will usually appear random

Dr. Ken Lewis


Example a tachometer

Example – A tachometer

  • Tachometer measures shaft rotation speeds in the range of 0 – 5000rpm

    • Accuracy: ±5% FS

    • Hysteresis: 30 rpm

    • Zero offset: 200 rpm

  • What is the maximum error you expect in a shaft speed reading of 3500 rpm?

Accuracy uncertainty

Hysteresis

±30 rpm

Zero offset 200 rpm

U = 250rpm + 30rpm + 200 rpm

U = 580rpm


Calibration

Calibration

  • A process wherein a set of measurements are made of measurand values that can determined independently

  • Readings are compared to the known ‘true’ values and errors determined

  • Implies that the measurements are referenced against a measurementstandard.

Dr. Ken Lewis


What is a meter measurement standards

What is a meter? Measurement Standards

  • 1793 Govt. of France decrees the unit of length to be 10-7 of the earth’s quadrant passing through Paris and called the meter.

  • 1889 Treaty of the Meter (Conférence Général des Poids et Mésures, CGPM) established a platinum-iridium bar.

Dr. Ken Lewis


What is a meter measurement standards1

What is a meter? Measurement Standards

  • 1960 definition based on the krypton86 radiation from an electrical discharge lamp.

  • 1983: The meter is the SI unit of length and is defined as the length of the path traveled by light in a vacuum during the time interval of 1/299,792,458 of a second.

Dr. Ken Lewis


What is a second measurement standards

What is a second?Measurement standards

  • The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

  • Other base units – great site

    • http://physics.nist.gov/cuu/Units/current.html

Dr. Ken Lewis


What is the point measurement standards

What is the POINT?Measurement Standards

  • There are many basic standards.

  • Before the French Revolution every different duchy had their own version of standards of weight, length, etc.

    • Need to standardize to allow transfers of knowledge

    • Need to have standards to allow calibration of instruments to make results reliable and interchangeable.

Dr. Ken Lewis


What s the point here 200 000 000 mars polar lander

What’s the Point? Here $200,000,000Mars Polar Lander

  • December 3, 1999

    • EDWARD EULER, Lockheed Martin: The mistake was that we had to give the Jet Propulsion Lab some data that is used to compute very, very small little thrust pulses onboard the spacecraft. And we did give them the data in the wrong units... and in English units, and it should have been in metric. And they used the data as if it were metric, and underestimated the magnitude of these small, little pulses that come out of the jets of the Orbiter by about a factor of five. And that in turn made it very difficult to get the proper navigation, or determine the position and velocity of the spacecraft, which eventually led to the failure.

Dr. Ken Lewis

http://www.pbs.org/newshour/bb/science/july-dec99/mars_lander_12-2.html


Measurement standards

Measurement Standards

  • Many standards;

    • 1 foot is 12 inches

    • 2.54 centimeters is exactly 1 inch

    • There are 28 grams in 1 ounce

    • A CD is 12 centimeters in diameter

    • All video players (VHS) can interpret correctly any VHS tape

    • The electric voltage and current in California is the same as it is in New Hampshire

Dr. Ken Lewis


Seven si base units

Seven SI Base Units

Dr. Ken Lewis


Standards

Standards

  • All primary standards except mass “can” be reproduced in a good well equipped laboratory.

  • The standard for mass ‘International Prototype Kilogram’ is a Pt—Ir cylinder kept in Paris France

  • Standards for all other physical variables are;

    • Derived from the base standards

    • Physical laws

Dr. Ken Lewis


Example force

Example -- Force

  • Recall Newton’s second law

    • Force = mass X acceleration

  • Acceleration = meter/second/second

    • =length/second2

Dr. Ken Lewis


Some si derived units

Some SI Derived Units

Dr. Ken Lewis


Some standard si prefixes

Some Standard SI Prefixes


  • Login