Uncertainty Analysis
To illustrate a simple but often ignored concept – what is the estimated total cost of the following?
Item | 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 | ![]() |
---|---|---|
.. | .. | .. |
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.

In accordance with the rules of quadrature, our uncertainty is:

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:





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.