Description Usage Arguments Details Value Author(s) References See Also Examples

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 for Microsoft Excel user interface.

1 2 |

`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 will all share the same variable name. The default is to assume all standard uncertainties are assessed independently, resulting a value of shared.u.i that is identical to var.name. |

`cl` |
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. |

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.

A list containing the 9 components:

`y` |
Value of the measurement result obtained by evaluating the measurement function at the input variable values. |

`uc` |
The combined standard uncertainty of the measurement result, y. |

`nu.eff` |
The effective degrees of freedom associated with uc, computed using the Welch-Satterthwaite formula. |

`cl` |
The nominal confidence level used to obtain the coverage factor, k. |

`k` |
The coverage factor used to control the confidence level associated with the expanded uncertainty of the measurement result. |

`U` |
The expanded uncertainty of the measurement result, computed as U=k*uc. |

`contributions` |
Relative variance contributed to the standard uncertainty (uc) of the measurement result from each input variable. |

`sensitivities` |
Sensitivity coefficient associated with each input variable. |

`msgs` |
Error and warning messages that point out potential problems with the inputs to the |

Hung-kung Liu hung-kung.liu@nist.gov and Will Guthrie will.guthrie@nist.gov

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.

`GUM.validate`

a function to assess the statistical performance of GUM uncertainty intervals
for the application of interest in terms of average attained coverage probability.
`uncert`

for a family of functions focused on the study and comparison of different approaches
and numerical options in uncertainty analysis.

1 2 3 4 5 6 7 8 9 10 11 | ```
## 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"))
``` |

```
Attaching package: 'metRology'
The following objects are masked from 'package:base':
cbind, rbind
$y
[1] 2.53
$uc
[1] 0.04774149
$nu.eff
[1] 21.88965
$cl
[1] 0.95
$k
[1] 2.074479
$U
[1] 0.099
$contributions
x1 x2
[1,] 0.4777887 0.5222113
$sensitivities
x1 x2
[1,] 1.1 2.3
$msgs
[1] "No errors or warnings." "" ""
[4] "" "" ""
[7] "" "" ""
[10] "" "" ""
[13] "" "" ""
$y
[1] -0.7
$uc
[1] 0.3676955
$nu.eff
[1] 134
$cl
[1] 0.95
$k
[1] 1.977826
$U
[1] 0.73
$contributions
s1 s2
[1,] 0.5 0.5
$sensitivities
s1 s2
[1,] 1 -1
$msgs
[1] "No errors or warnings." "" ""
[4] "" "" ""
[7] "" "" ""
[10] "" "" ""
[13] "" "" ""
$y
[1] -0.7
$uc
[1] 0.3676955
$nu.eff
[1] 134
$cl
[1] 0.95
$k
[1] 1.977826
$U
[1] 0.73
$contributions
s1 s2
[1,] 0.5 0.5
$sensitivities
s1 s2
[1,] 1 -1
$msgs
[1] "No errors or warnings." "" ""
[4] "" "" ""
[7] "" "" ""
[10] "" "" ""
[13] "" "" ""
```

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