Multivariate Parameter Worksheet Features

The Multivariate Parameter Worksheet provides a powerful and versatile tool for conducting a measurement uncertainty analysis for a parameter or quantity that is indirectly determined from other measured variables or quantities.  The Parameter Value Equation can contain up to 25 root variables or quantities and an unlimited number of nested variables.  All equations are entered in the extremely versatile and non-proprietary VB Script format, which allows for the development of complex equations, the inclusion of nested functions, and other programmable controls.  Despite this powerful capability, entering parameter value equations can be as simple as entering equations into any spreadsheet application. 

Parameter Value Equation

The mathematical equation that describes the value of interest is entered in the Parameter Value Equation field.  The parameter value equation can contain numbers, constants, root variables, nested variables, functions, and mathematical operators.  Nested variables are defined by separate equations and are entered after the parameter value equation.  All equations are entered in the extremely versatile and non-proprietary VB Script format.

Sensitivity Coefficients

The sensitivity coefficient of a given root variable is the partial derivative of the parameter value equation with respect to the root variable.  Uncertainty Sidekick Pro automatically computes the partial derivatives. 

Root Variables Data Table

After the user defined error equation and any associated nested variables equations have been entered into the Parameter Value Equation field, uncertainties in the root variable errors must be estimated.  This can be done by entering the requisite data for each root variable directly into the Root Variables Data table or by using the Error Source Worksheet, which is activated by clicking the gray button to the left of the variable name.  Up to 25 individual error sources can be listed in the Root Variables table. 

Computed Parameter Value

The bottom portion of the Worksheet displays the Computed Parameter Value, which Uncertainty Sidekick Pro calculates from user specified adjusted mean values for the root variables.  The adjusted mean values are incorporated into the user defined error equation and any associated nested variable equations to obtain the mean value for the user defined error.  

Combined Uncertainty and Degrees of Freedom

The bottom portion of the Worksheet also displays the total uncertainty due to the user defined error.  The uncertainties resulting from the root variables are combined in a root-sum-square (RSS) manner if none of the errors are correlated.  However, in some instances, root variable errors may be correlated.  If so, the value of the Combined Uncertainty will reflect any correlations between root variable errors specified in the Correlation Coefficients Worksheet.  The associated Degrees of Freedom for the Combined Uncertainty is computed using the Welch-Satterthwaite formula.

Relevant information can be entered into the Root Variables Data table.  Alternatively, drill-down Error Source Worksheets can be used to develop Type A, Type B and Type A,B uncertainty estimates for each root variable.  Sensitivity coefficients are automatically computed for root variables or sensitivity coefficient equations can be entered for these variables. The sensitivity coefficient is a weighting factor multiplier for the standard uncertainty of the root variable error.  The product of the sensitivity coefficient and the standard uncertainty of a root variable error is the component uncertainty that reflects the contribution of the uncertainty in the root variable error to the overall uncertainty in the multivariate parameter value.