Measurement and metrics topics

 

Note

Personal Notes, not for distribution

  • Motivation: Show the problem that can be formulated as a Measurement Problem. E.g.
    • IOT, Supply Chain Visibility, Control Systems, Fraud Detection, …
  • Math helps us be precise about this: Measures
    • What is a Measurement
      • Look at a thing and say something about it
      • Compare a thing to a standard
      • Assign a value from a set to an object through a well defined procedure.
    • Measurements depend on the “set of values” (scale) that is used to do the assignment
      • Categorical Sets: Labeling // Descriptive statistics (counts, mode)
      • Ordered Sets: Ordering // Compare, Median, Percentiles, …
      • Interval: Measure Distances // Difference, Addition, Averages, Variances (not quite Stdev), Errors, …
      • Rational: They have a True Zero // ratios, stdev, derivatives, etc…
  • Engineering Models allow us to actually interface the world
    • A Measure is intended to assign a value to a property of interest of an object in the world
    • The assignment procedure is an “Observation”
      • Must be repeatable (when applied to the same object and context, it results on same measure)
      • It is performed at a given moment in time (which is usually part of the “context” of the observation)
      • It is usually done through an instrument that implements the measurement procedure
    • Observations can have errors that affect
      • Repeatability of results across multiple Observations (Precision)
      • How closely the resulting measure represents the “ideal” property of the object (Accuracy)
    • Errors:
      • Are due to (a) Instrument imperfections (b) Unavoidable variations of the context or the context or object
      • Can be systemic (bias) or random (noise)
  • Instrument Calibration
    • Against reference instruments
    • By repeated observations
    • By adjustment to theoretical behaviors and uncorrelated observations
  • Measures happen in time
    • Timestamped: When did it happen
    • Time Series Report
      • Measurement Frequency.
      • Accumulation Interval
      • Reporting Period
    • Bi-Timestamped: When did I know about it: Required for understanding/auditing “non-reversible” actions
  • Impact on Systems Engineering
    • Measure vs. Control
    • Big-System Instruments: IOT, Chemical Plants, National Weather System
    • Understand the Information Content of your system