Basic Concepts of Measurement Methods

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Basic Concepts of Measurement Methods
Feb.1, 2007
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Report on Exp. 1 Tensile Testing

• Long-form, group report
• Each group member should contribute
• Ask individuals to evaluate the performance
  of his/her group members
• Follow the format precisely
• Be sure to address the problems
• Spelling/grammar check
• If not readable, send back and cut 20 for
  re-grading
• Late policy

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General Measurement System
Signal modification subsystem
Measurand
Sensing element
Indicator or recorder
Controller

• Sensor-transducer stage
• Signal-conditioning stage
• Output stage
• Feed-back control stage

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General Measurement System

• Sensor
• Sense the variables being measured
• Transducer
• Convert the sensed information into detectable
  signal form electrical, mechanical, optical,
  etc.
• Signal-conditioning
• Modify the transduced signal to a desired
  magnitude
• Amplification
• Filtering remove some portion of signal
• Recorder
• Provide an indicator of the measured value
• Might be just a simple readout display
• Some devices can record the signal
• Feedback controller
• Interpret the measured signal and control the
  process

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Mercury-in-glass System
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Validity of Measurements Error

• Error a measure of validity
• Error measured value true value
• Error is not a mistake, but mistake can cause
  error
• Error is generally not known as the true value is
  unknown
• Uncertainty an estimate of the limits of error
  with some level of confidence
• Error systematic error random error

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Systematic Error

• Fixed/bias error consistent, repeatable
• Systematic error average of reading true
  value
• Sources
• Calibration error
• Loading error
• Spatial error
• Minimize systematic errors
• Careful calibration
• Analytical correlation

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Random Error

• Also known as precision error
• Random error reading average of reading
• Lack of repeatability, scattered
• Sources
• Measuring system
• Environment
• Minimize random error
• Eliminate uncontrolled variables by
  shielding/grounding
• Statistical analysis

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Systematic and Random Errors
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Systematic and Random Error

• The bulls eye is the true value
• Each throw represents a measured value
• Totally three throws

(1,2,3)
(1,2,3)
C
A
B
A systematic error ? 0 random error 0 B
Systematic error random error 0 C Systematic
error 0 random error ? 0
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Some Basic Definitions

• Range 0 to 10V, /-3V
• Span difference between upper and lower values
  of the range 10V, 6V
• Accuracy the closeness of agreement between a
  measured value and the true value, combines
  systematic and random errors
• Specified as a percentage of full-scale output
• Precision
• characterize random error
• Accuracy can not be better than precision
• Resolution resolution error, scale readability
• Zero error incorrect output at zero point
• Sensitivity ratio of the change in the magnitude
  of the output to the change of the input
• Drift the change in the output even though all
  the environmental factors remain contstant

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Statistical Analysis of Experimental Data
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General Definitions

• Population
• The entire collection of objects, measurements,
  etc.
• Sample
• A representative subset of a population
• Sample Space
• The set of possible outcomes of an experiment
  (discrete, continuous)
• Random Variable
• The variable being measured
• Probability
• The chance of the occurrence of an event in an
  experiment

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Measures of Central Tendency

• Mean (sample mean, population mean)
• Median
• Arrange in ascending or descending order
• Odd middle one
• Even avg. of the middle two
• Mode
• Highest frequency of occurrence

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Measures of Dispersion

• Dispersion
• Spread or variability of the data
• Deviation
• Mean deviation
• Standard deviation (Sample, Population)
• Variance

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HW1 6.1, 6.3, 6.6