GUM: Propagation of Measurement Uncertainty for Typical Metrology Applications Using the Methods Outlined in the GUM

Description

A function for propagation of measurement uncertainty for typical metrology applications using the methods from the Joint Committee on Guides in Metrology (JCGM) Guide to the Expression of Uncertainty in Measurement (GUM). This approach approximates the uncertainty of a function of random variables that define a measurement result by computing the uncertainty of the first-order Taylor series for the measurement function. This function also serves as the primary computational tool underlying the GUM uncertainty templates found in the metRology.xls user interface.

Usage

GUM(var.name, x.i, u.i, nu.i, measurement.fnc, correlation = diag(length(var.name)),
shared.u.i = var.name, cl = 0.95, cov.factor = "Student's t", sig.digits.U = 2, ...)

Arguments

var.name

Character vector of input variable names.

x.i

Vector of input variable values.

u.i

Vector of standard uncertainties (i.e. standard errors) for each input variable value.

nu.i

Degrees of freedom associated with each standard uncertainty.

measurement.fnc

Character string specifying the functional relationship between input variables that defines the output measurement result.

correlation

Matrix giving the correlation between the different input variable values. Default is to assume no correlation between input variable values.

shared.u.i

Character vector giving the relative relationship between the standard uncertainties for each variable value. Groups of variables based on a common shared standard uncertainty share will all share the same variabl

Nominal confidence level to be used to compute the expanded uncertainty of the output measurement result. Default value is 0.95.

cov.factor

Type of coverage factor to be used. The default is to use the value from the Student's t distribution with confidence level specified above and nu.eff effective degrees of freedom.

sig.digits.U

Number of significant digits to be reported in the expanded uncertainty of the measurement result. The measurement result will be rounded to the same number of decimal places.

...

Arguments passed to other functions. Currently unimplemented.

Value

A list containing the 9 components:
yValue of the measurement result obtained by evaluating the measurement function at the input variable values.
ucThe combined standard uncertainty of the measurement result, y.
nu.effThe effective degrees of freedom associated with uc, computed using the Welch-Satterthwaite formula.
clThe nominal confidence level used to obtain the coverage factor, k.
kThe coverage factor used to control the confidence level associated with the expanded uncertainty of the measurement result.
UThe expanded uncertainty of the measurement result, computed as U=k*uc.
contributionsRelative variance contributed to the standard uncertainty (uc) of the measurement result from each input variable.
sensitivitiesSensitivity coefficient associated with each input variable.
msgsError and warning messages that point out potential problems with the inputs to the GUM function or with the interpretation of the function's output.

Details

Whenever possible, sensitivity coefficients are obtained analytically using the gradient attribute of the deriv function. In situations where some part of the measurement function is not found in derivative table, sensitivity coefficients are obtained by numeric partial differentiation using the grad function from the package numDeriv.

References

Joint Committee on Guides in Metrology (JCGM), Evaluation of Measurement Data Guide to the Expression of Uncertainty in Measurement, http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf, 2008.

Examples

Run this code

## a simple uncertainty analysis for the product of two quantities
GUM(c("x1","x2"),c(2.3,1.1),c(0.030,0.015),c(5,9999),"x1*x2")

## example of the difference in the measurements of two standards,
## each with a standard uncertainty
## based on a common value drawn from a control chart representative
## of the measurement process made 
## using a check standard that is comparable to the two individual standards
## under study
GUM(c("s1","s2"),c(45.3,46.0),c(0.26,0.26),c(134,134),"s1-s2",shared.u.i=c("s1","s1"))

## compare with results for equivalent, alternative specification of shared.u.i
GUM(c("s1","s2"),c(45.3,46.0),c(0.26,0.26),c(134,134),"s1-s2",shared.u.i=c("s2","s2"))

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