Uncertainties

1
Uncertainties

• Using Calculating Uncertainties for Electrical
  Measurement

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Expressing Uncertainty of Measurement

• All measurements, even the most accurate,
• have an unknown inaccuracy or doubt.
• The is known as the UNCERTAINTY
• As there is always an uncertainty with any
• measurement we need to estimate this
• amount. We also need to calculate our
• confidence in the estimate of uncertainty, which
  is
• how sure we are that the true value is within the
• uncertainty we have estimated.

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Expressing Uncertainty of Measurement

• As an example we may measure 1 Volt and
• be 95 confident that we are within 10uV

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Expressing Uncertainty of Measurement

• UNCERTAINTY vs. ACCURACY
• There is no connection between these terms.
• Uncertainty is purely the unknown in any
  measurement.
• Accuracy or Tolerance is the difference between
  the desired value and the actual measured value.

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Expressing Uncertainty of Measurement

• Example
• With a digital watch with 1 second resolution
• this resolution will limit the best uncertainty
• to which you can tell the time (ie. 1 second),
• however the watch itself may only be
• accurate to a few minutes.

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Expressing Uncertainty of Measurement

• There are many sources of uncertainty in any
• measurement which need to be combined
• using statistical techniques to give a total.
• Different types of uncertainty need to be
• treated differently to obtain an accurate
• estimation.

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Expressing Uncertainty of Measurement

• To calculate uncertainty you must first
• identify all the sources of error, estimate the
• size of the contribution from each source and
• also decide on the type of uncertainty for
• each source.
• There are two types of uncertainty
• Type A Based on using statistics
• e.g. repeated readings
• Type B Based on other factors
• e.g. manufacturers specifications

8
Sources of Uncertainty in Electrical Measurements.

• Imported Uncertainty
• Drift of reference instrument
• Temperature effects
• Lead and thermal errors (DC volts)
• Rounding errors due to resolution
• Repeatability
• Noise
• Self heating of high current shunts

9
Imported Uncertainty

• Imported uncertainty is taken directly from the
  certificate issued by the laboratory which
  calibrated the reference instrument. The
  probability distribution is NORMAL

10
Drift of reference instrument

• Drift of reference instrument can be either taken
  form historical data on the instrument or from
  the manufacture specification for stability. If
  the drift with time can be predicted it is
  possible to use a corrected figure for the actual
  value of the reference with a reduced figure for
  drift. However it is more normal to use an un
  corrected figure.
• The probability distribution is Rectangular.

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Temperature Effects

• The effect of temperature on many modern
  instruments is often very small, and in many
  cases the instruments specification covers a band
  of temperature without any further addition.
• Some reference standards for example resistors
  the Temperature coefficient may be quite
  important. The figure for TC can be taken from
  the manufactures spec or measured.
• The probability distribution is Rectangular.

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Lead and thermal errors (DC volts)

• Thermal emf can be difficult to evaluate. With a
  little care and correct leads it is normal for
  thermal EMF to be less than 1uV, or even 0.5uV
  which is a figure often used in calculations.
• The probability distribution is Rectangular.

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Resolution of Measurement

• It is firstly important to understand that there
  is a big difference between the resolution of a
  measuring instrument and that of a reference
  source.
• A source, such as a standard resistor may have
  no resolution at all, but can still be very
  accurate, while for a measuring instrument
  resolution is essential to achieve accuracy.
• It is only necessary to include measurement
  resolution in the uncertainty calculation. Note
  if a DMM is used to compare say two resistors
  then the resolution must be entered twice.
• The probability distribution is Rectangular

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Combining Uncertainties

• It is normal these days to use a spread sheet, in
  Excel, taking a template from M3003.
• Use column 1 for a description of source of
  uncertainty
• Use column 2 for the value of uncertainty usually
  in ppm
• Use column 3 for a description of type of
  Probability distribution
• Use column 4 for the divisor, 2 for a normal
  dist, 1.732 for rect
• Use column 5 for a coeficient used to convert say
  millvolts to microvolts
• Use column 6 column2(value) x column4(divisor)
  x column5(coeff)
• Use the sum of square to total column 6 to get
  the Combined Standard Uncertainty
• To obtain the Expanded uncertainty (K2, 95
  Confidance) multiply the result above by 2. Then
  round to 2 significant places.

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Expressing Uncertainty of Measurement

• Example

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Using ProCal to calculate Uncertainties

• ProCal use three key elements to dynamically
  calculate uncertainties as the test is run
• 1) A table with imported uncertainties and
  calibrator specifications
• 2) A laboratory procedure incorporating
  additional factors such as
• lead /connection errors etc.
• 3) The noise / flicker which can be input at the
  time of test

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Set Up Instrument Spec and Imported Uncertainties

• Use Proset, select instrument Traceability in the
  file menu.
• Select the Instrument required
• Select the uncertainties button to access the
  table
• Enter the data, note default table exists for
  2000 Series

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Set Up Procedure Template

• Use ProSet, select laboratory procedures in the
  file menu.
• Select the Instrument required
• Select the procedure spreadsheet template say for
  DC voltage
• Enter the parameters to be calculated, note the
  imported and reference specification will always
  be added automatically.
• Note the procedures for the main functions of the
  calibrator are
• Installed as default

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Set Up Calibration Procedure

• Use ProEdit, edit a procedure and go to the
  Instruments tab.
• Check the calibration instrument, lab. Procedure
  and uncertainty line.
• If a Transmille calibrator is in use these items
  will be set automatically, without having to be
  selected.

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Calibrating An Instrument

• Use ProCal, run a calibration
• Input the reading and select / enter the noise /
  flicker in the drop down box displayed.
• If required, click on the UNCERT button to view
  the uncertainty calculation.

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Where to Get More Information

• UKAS (www.UKAS.co.uk)
• National Physical Laboratory
• Transmille Ltd (www.transmille.com)