Description Usage Arguments Details Value Author(s) References See Also Examples
Functions for estimating measurement uncertainty from standard uncertainties and either sensitivity coefficients or (for some methods) expressions or functions. Correlation is supported via either a correlation or covariance matrix.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  uncert(obj, ...)
## Default S3 method:
uncert(obj, c, method = c("GUM", "MC"), cor,
cov, distrib=NULL, distrib.pars=NULL, B=200, x=NULL, keep.x = TRUE,
u=obj, ...)
## S3 method for class 'expression'
uncert(obj, x, u, method=c("GUM", "NUM", "kragten", "k2", "MC"),
cor, cov, distrib=NULL, distrib.pars=NULL,
B=200, delta=0.01, keep.x = TRUE, ...)
## S3 method for class 'function'
uncert(obj, x, u, method=c("NUM", "kragten", "k2", "MC"),
cor, cov, distrib=NULL, distrib.pars=NULL,
B=200, delta=0.01, keep.x = TRUE, ...)
## S3 method for class 'formula'
uncert(obj, x, u, method=c("GUM", "NUM", "kragten", "k2", "MC"),
cor, cov, distrib=NULL, distrib.pars=NULL,
B=200, delta=0.01, keep.x = TRUE, ...)

obj 
An R object used for method dispatch; see below. Methods currently exist for numeric vector, expression, function, or formula 
u 
For the default method, a numeric vector of standard uncertainties. For
the formula or expression methods, a named list of standard uncertainties.Note that
for the default method, 
c 
A numeric vector of senstivity coefficients. 
x 
For the expression or formula methods, an R object which can be used
as an environment by 
method 
Method of uncertainty evaluation. The current list of methods is:

cor, cov 
A (square, symmetric) correlation or covariance matrix, respectively.
If neither is specified, 
distrib 
For 
distrib.pars 
For 
B 
Number of Monte Carlo replicates. 
delta 
Step size for numerical differentiation. 
keep.x 
For 
... 
Additional parameters to be passed to a function (for the function method) or used in an expression (for expression or formula method). 
The default “GUM” method applies firstorder error propagation principles to estimate
a combined standard uncertainty from a set of sensitivity coefficients and either a
set of standard uncertainties and a correlation matrix (which defaults to an identity matrix)
or a covariance matrix. Both options use the same calculation, which is simply
(t(c) %*% cov) %*% c
; standard uncertainties are first combined with
the correlation matrix provided to form the covariance matrix. Since the correlation
matrix defaults to the identity matrix, the default is combination without
correlation.
The default method takes obj
as a vector of uncertainty contributions unless u
is specified, in which case u
is used. It is not necessary to specify both.
The expression method requires obj
to be a differentiable R expression which can
be evaluated in the environment x
to provide a numeric value.
For the function method, obj
must be an R function which takes parameters from x and
returns a numeric value.
For the formula method, obj
must be a formula with no lefthand side (e.g. ~a*x+b*x^2
)
which can be evaluated in the environment x
to provide a numeric value.
The formula and expression methods first calculate derivatives for the expression or formula,
evaluate them using the supplied values of x
and then pass the resulting sensitivity
coefficients, with supplied u
, cor
or cov
to uncert.default.
The derivatives for the “GUM” method (formula and expression methods only) are algorithmic
derivatives (that is, algebraic or analytical derivatives) obtained using deriv
applied to expr
and formula
.
Numerical derivatives are computed in different ways depending on the method specified:
 For method="NUM"
, the derivatives are calculated as
(f(x+delta*u)f(xdelta*u))/(2*delta*u).
 For method="kragten"
, derivatives are calculated as
(f(x+u*sign(delta))f(x))/u.
 For method="k2"
, derivatives are calculated as
(f(x+u)f(xu))/(2*u).
"NUM"
is likely to give a close approximation to analytical differentiation provided that
delta
is appreciably less than 1 but not so small as to give step sizes near machine
precision. "k2"
is equivalent to "NUM"
with delta=1.0
. Both will give zero coefficients
at stationary points (e.g minima), leading to underestimation of uncertainty if
the curvature is large. "kragten"
uses a deliberately onesided (and large) step to
avoid this problem; as a result, "kragten"
is a poorer (sometimes much poorer) estimate of
the analytical differential but likely a better approximation to the truth.
Since these methods rely on u
, if u
is unspecified and cov
is
provided, u
is extracted from cov
(using sqrt(diag(cov))
). It is
assumed that the row and column order in cov
is identical to the order of named
parameters in x
.
Derivatives (and uncertainty contributions) are computed for all parameters in
x
. Additional parameters used in FUN
, expr
or formula
may be included in ...
; these will be treated as constants in the
uncertainty calculation.
If distrib
is missing, or if it is a list with some members missing, the distribution
is assumed Normal and distrib$name
is set to "norm"
. Similarly, if distrib.pars
or a member of it is missing, the default parameters for x$name
are
list(mean=x$name, sd=u$name)
. If the list is not named, names(x)
are used
(so the list must be in order of names(x)
).
If method="MC"
, uncert
calls uncertMC
. Distributions and
distribution parameters are required and B must be present and >1. See uncertMC
for details of distribution specification.
For other evaluation methods, the distributions are silently ignored.
An object of class ‘uncert’ or, for method="MC"
of class ‘uncertMC’.
See uncertclass
and uncertMCclass
for details.
S. L. R. Ellison s.ellison@lgc.co.uk
JCGM 100 (2008) 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. (JCGM 100:2008 is a public domain copy of ISO/IEC Guide to the expression of uncertainty in measurement (1995) ).
Kragten, J. (1994) Calculating standard deviations and confidence intervals with a universally applicable spreadsheet technique, Analyst, 119, 21612166.
Ellison, S. L. R. (2005) Including correlation effects in an improved spreadsheet calculation of combined standard uncertainties, Accred. Qual. Assur. 10, 338343.
For method="MC"
see uncertMC
and uncertMCclass
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28  expr < expression(a+b*2+c*3+d/2)
x < list(a=1, b=3, c=2, d=11)
u < lapply(x, function(x) x/10)
u.expr<uncert(expr, x, u, method="NUM")
u.expr
#Compare with default:
uncert(u=c(0.1, 0.3, 0.2, 1.1), c=c(1.0, 2.0, 3.0, 0.5))
#... or with function method
f < function(a,b,c,d) a+b*2+c*3+d/2
u.fun<uncert(f, x, u, method="NUM")
u.fun
#.. or with the formula method
u.form<uncert(~a+b*2+c*3+d/2, x, u, method="NUM")
u.form
#An example with correlation
u.cor<diag(1,4)
u.cor[3,4]<u.cor[4,3]<0.5
u.formc<uncert(~a+b*2+c*3+d/2, x, u, method="NUM", cor=u.cor)
u.formc
#A Monte Carlo example
#See uncertMC for a less linear example
u.formc.MC<uncert(~a+b*2+c*3+d/2, x, u, method="MC", cor=u.cor, B=200)
u.formc.MC

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