Single measurement testing, pros and cons

There is a school of thought that believes making a single measurement of some parameter is a proper test procedure. For reasons of speed and the large number of measurements to be made on an item, so the reasoning goes, one cannot afford to make multiple measurements, calculate the average and the variation of the readings. What are the consequences of this approach? Can one test a unit to its specifications using this approach? What are the trade-offs inherent in single measurement testing? What happens if an erratic unit is tested? An alternative testing method involves taking a few repeat values, averaging them and estimating their repeatability. The same set of questions apply. The pros and cons of these two approaches will be discussed. Practical real world examples will be presented