Estimates -- aka Adding in Quadrature
Uncertainty Analysis
To illustrate a simple but often ignored concept – what is the estimated total cost of the following?
Item | Cost | Cost |
---|---|---|
alpha | 100,000 | 5,000 |
beta | 75,000 | 7,500 |
gamma | 50,000 | 6,000 |
.. | .. | .. |
total | 225,000 | what is the total plus-minus range? |
I say the answer is:
Item | Cost | Cost |
---|---|---|
.. | .. | .. |
total cost | 225,000 | 11,000 (10,828) |
Notice that the plus-minus range for the total cost is less than the sum of the plus-minus ranges. This will always be true when adding in quadrature.
Uncertainty Analysis Reference
In accordance with the rules of quadrature, our uncertainty is:
Of course, no more than 2 significant digits are warranted here; therefore .
Caveat
The quantities alpha, beta, and gamma must have uncertainties which are uncorrelated and random.
Example Calculation
If say same-cost items were considered, with a constant percent plus-minus cost:
Therefore, if items of the same cost (but still independent variables) were considered, with a constant percent () plus-minus cost:
Here the plus-minus range for the total cost, percent, is much less than percent.
If items of a random cost (and still independent variables) were considered, with a constant percent () plus-minus cost, we might calculate percent instead of percent.