Correlation of Error Sources

Correlations can exist between measurement process errors for a given variable or parameter.  In the case of a multivariate uncertainty analysis, cross-correlations can also exist between the measurement process errors for different variables or parameters.  If a correlation exists between process uncertainties, or between component uncertainties, it can affect the way in which they are combined.  This, in turn, will impact how the overall measurement uncertainty is computed. 

The Correlation Analysis Screen is a straightforward tool for correlating error sources for direct measurement, multivariate measurement and system model analyses.  Two error sources are dependent (i.e., correlated) if one exerts an influence over the other or if both are consistently influenced by a common agency.  For example, measurement errors are dependent if the measurements are made with the same measuring device and measuring parameter.

Error List

This section of the screen is used to select which pairs of error sources that you wish to correlate. To place an error source under Error 1 or 2, click an error source to be correlated, drag it (holding the left mouse button down) to the appropriate box and release the mouse button. 
 
Correlated Pairs

Once the correlation coefficient has been established, the correlated pairs and their associated correlation coefficient is listed in the Correlated Pairs list. This process is repeated for all other pairs of error sources that you wish to establish correlations for. 

Enter Correlation Data

Sample pairs are entered into the Correlation Data table.  In each pair, the errors of the variables are linked. The Correlation Coefficient is automatically computed and displayed after the data have been entered.  The Mean Value and Standard Uncertainty are also computed and displayed for each of the two error sources along with the number of data sample pairs entered (Sample Size).

If data are not available, you can enter a known or estimated value for the correlation coefficient in lieu of entering sample pairs. 

Compensating Biases

The Compensating Biases box is checked if the bias or error of one measured variable offsets the bias or error of another measured variable.  For instance, if the same measuring parameter is used to measure the inside diameter of a sleeve and the outside diameter of a shaft that fits into the sleeve, any error or bias in the two measurements will not affect the quality of fit. In other words, the measurement biases offset each other.