Accuracy/unaccuracy/measurement uncertainty

Accuracy:

• Accuracy is a measure of how close the measured value is to the true value
• Accuracy is a qualitative concept

Measurement uncertainty:

• Uncertainty: parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand. The parameter may be, for example, a standard deviation (or a given multiple of it), or the half-width of an interval having a stated level of confidence.
• Standard uncertainty: uncertainty of the result of a measurement expressed as a standard deviation
• Expanded uncertainty: quantity defining an interval about the result of a measurement that may be expected to encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand.

Precision/repeatability/reproducibility

Precision:

• The closeness of agreement between independent test results obtained under stipulated conditions
• Qualitative concept
• Precision should not be confused with accuracy

Repeatability:

• Closeness of the agreement between the results of successive measurements of the same measurand carried out under the same conditions of measurement

• Same (repeatability) conditions include:

  • the same measurement procedure
  • the same observer
  • the same measuring instrument, used under the same conditions
  • the same location
  • repeition over a short period of time

• Precision under repeatability conditions

• Also a qualitative concept

Reproducibility:

• Closeness of agreement between the results of measurements of the same measurand carried out under changed conditions of measurement

• The changed conditions may include:

  • principle of measurement
  • method of measurement
  • observer
  • measuring instrument
  • reference standard
  • location
  • conditions of use
  • time

• Precision under reproducibility conditions

• Reproducibility is also a qualitative concept

Linearity

• A measure of how close is the output of an instrument to a straight line
• Use least-square method to do line-fitting ofthe output, the non-linearity is then defined as the maximum deviation of any of the output from the fitted straight line
• A quantitative number

Sensitivity of measurement

• A measure of the change in instrument output that occurs when the measurand changes by a given amount

• It can be caluclated as the slow of (or a portion of) the fitted straight line:

  Sensitivity = (Scale deflection) / (value of measurand producing the deflection)

• Note that the sensitivity might vary at different portion of measurement (e.g. sensitivity is zero at the top of a sinusoidal output)

Resolution

Classic definition based on analog output instruments:

• The smallest change of the magnitude of the measurand that produces a minimum observable output of the instrument
• Can be expressed either as an absolute value or a percentage of the full scale deflection

What if the instrument's output is digital?

• More and more modern instruments have digital outputs because of the wide usage of computer
• The "resolution" of the digital output can be a very small number, but this is not the resolution of the instrument (e.g. what is the "resolution" of a 32-bit IEEE floating point number?)
• The resolution of an digital output instrument should be limited by the front end rather than the digital computation

Threshold

• The minimum level of input that produces a large enough detectable output reading deflected from the initial states of the instrument, very often, the initial states of the instrument are at zero
• It can be expressed as either an absolute value or a percentage

Dead space

• Dead zone
• The range of input values over which there is no change in output values
• Example: rectifier circuits using diodes

Bias

• A constant value that the instrument adds to its output even at zero input

Hysteresis

• the non-coincidence between the loading (increasing) and the unloading (decreasing) measurement curves
• maximum input hysteresis, and maximum output hysteresis
• often seen in mechanical transducers or sensors with electrical windings formed around an iron core (transformers)

Environmental effects

Survivability in harsh environment - Storage conditions: instrument is not required to operate - Operational but not to the full specifications

Sensitivity to disturbance

• Temperature
• Humidity
• Ambient pressure (elevation, depth under water, etc.)
• Electromagnetic interference
• Radiation
• Acceleration
• Shock
• Vibration
• Duration exposed to harsh environment

Mathematical model

Transfer function of the instrument

• Mathematic description of the entire measurement system (as for any other systems)
• Break the entire measurement system into small sybsystems (blocks) along the signal path through the system
• There will be nonlinear blocks, and approximations have to be made to linearize them so that transfer functions can be obtained
• Once the transfer function of the system is established, the static (or steady state) response of the system can be derived
• The dynamic characteristics can also be obtained based on the transfer function of the instrument

Dynamic characteristics

• Frequency response/Bandwidth
• Warm up time
• Delay
• Stability/undershoot
• Jitter