CORRELATION EFFECT ON EFFECTIVE DEGREES OF FREEDOM
Abstract
The mathematical model of the measurement in the “Guide to the Expression of Uncertainty in Measurement” is <i>Y</i> = <i>f</i>(<i>X</i><sub>1</sub>, <i>X</i><sub>2</sub>,...,<i>X</i><sub>N</sub>), where <i>Y</i> is the meansurand and <i>X</i><sub>1</sub>, <i>X</i><sub>2</sub>,...,<i>X</i><sub>N</sub> are the influence quantities. The expanded uncertainty <i>U</i> is obtained by <i>U</i> = <i>k</i> <i>u</i><sub>c</sub>(<i>y</i>), where <i>u</i><sub>c</sub>(<i>y</i>) is the combined uncertainty and <i>k</i> is the coverage factor that depends on the effective degrees of freedom.<BR />The value of effective degrees of freedom is obtained from the Welch-Satterthwaite formula. It is assumed that there isn’t correlation between influence quantities. In this paper will be presented an example in which the use of this formula would be inadequate because there is a strong correlation between influence quantities. An alternative model of measurement was used to compare with the first model in the example case. Although the combined uncertainty of the two models is almost the same, there are differences between the expanded uncertainty, because there is a significant difference in the respective values of two effective degrees of freedom. This difference is caused by strong correlation between influence quantities.
Event details
- Event
- XVI IMEKO World Congress
- Place
- Vienna, AUSTRIA
- Time
- 25 September 2000 - 28 September 2000