A slightly different scenario, but I recall a technician sorting 10% resistors, trying to find a handful that were exactly the correct value. He went through an entire bag and couldn't find any closer than 5%. So much for Gaussian distribution. Of course the reason was that all of the closer value resistors were already removed from the sample by the manufacturer to be sold as 5% resistors.
Great article Jon - it is important to understand uncertainty in measurements so that you can understand whether or not a reading is really within tolerance. Understanding the tolerance that is acceptable (range of acceptable readings due to measurement uncertainty not only of test equipment but also the device under test) are both important to understand. Repeatability and reproducibility are also factors. Gage R & R is an important tool in this area. Uncertainty is also another reason to make sure your measurement equipment is in calibration. Thanks for the link to the Evaluation of Measurement Data: Guide to the Expression of Uncertainty in Measurement - it is an excellent resource.
There are other real-world factors that this analysis ignores. One is calibration accuracy, another is calibration drift. A typical calibration cycle is annually. The day after an instrument is calibrated, the uncertainty can increase because of component aging, ambient temperature effects, etc. Reality always makes uncertainty increase, often well beyond the simplistic approach of resolution; it's close to the concept of entropy. Resolution puts a LOWER BOUND on uncertainty, but no upper one! That is the worst part of digital instrumentation, in that it misleads the user to trust the results far beyond what is merited.
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