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

*(but still independent variables) were considered, with a constant percent () plus-minus cost:*

**same 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.