# Uncertainty Estimation and Contribution Analysis Uncertainty estimation and contribution analysis implemented by 4 methods: the Gaussian method of first, the Gaussian method of second order, the Kragten numerical method and the Monte Carlo simulation method package ## Details ||| |:--|:--| |Package:|uncertainty| |Type:|Package| |Version:|0.1.1| |Date:|2014-06-12| |License:|GPL (>=2)| Define an "uncertainty budget" object, including all the involved variables. Then estimate the "uncertainty" object by defining a measurand model, using the "uncertainty budget" and applying an estimation method. Print or plot the measurand estimates or create a "summary uncertainty" object to print or plot the uncertainty contributions to the measurand model. ## Author(s) H. Gasca-Aragon Maintainer: H. Gasca-Aragon ## References JCGM 100:2008. **Guide to the expression of uncertainty of measurement** JCGM 100:2005. **Supplement 1 Propagation of distributions usign a Monte Carlo method** EURACHEM/CITAC Guide CG 4. **Quantifying Uncertainty in Analytical Measurement** Becker, R.A., Chambers, J.M. and Wilks, A.R. (1988) **The New S Language**. Wadsworth & Brooks/Cole. ## See Also `uncertaintyBudget`, `print.uncertaintyBudget`, `uncertainty`, `print.uncertainty`, `plot.uncertainty`, `summary.uncertainty`, `print.summary.uncertainty`, `plot.summary.uncertainty` ## Examples ```r require(mvtnorm) cor.mat<- matrix(c(1,-0.7,-0.7,1),2,2) u.budget<- uncertaintyBudget(x=list(name=c("x0","x1"), mean=c(10,20), u=c(1,5), dof=c(10,10), label=c("x[0]", "x[1]"), distribution=c("normal","normal")), y=cor.mat) u.budget ## Gaussian first order estimates GFO.res<- uncertainty(x=u.budget, y=list(measurand_name="ratio.GFO", measurand_label=expression(ratio[GFO]), measurand_model="x0/x1", method="GFO", alpha=0.05)) contr.GFO<- summary.uncertainty(GFO.res) ## Monte Carlo estimates MC.res<- uncertainty(x=u.budget, y=list(measurand_name="ratio.MC", measurand_label=expression(ratio[MC]), measurand_model="x0/x1", method="MC", alpha=0.05, B=1e5)) contr.MC<- summary.uncertainty(MC.res) ## print the estimates MC.res GFO.res ## print the uncertainty summary contr.MC contr.GFO ## Displaying both estimated distributions ## Not run: plot(MC.res, col=4, xlab=MC.res$measurand_model) plot(GFO.res, lty=2, col=2, add=T) legend(0.7, 2.5, legend=c("Monte Carlo", "Gaussian First Order"), lty=c(1,2), col=c(4,2), lwd=2, bg="white") ## End(Not run) ## Display both uncertainty summaries ## Not run: barplot(cbind(contr.GFO$budget$contrib, contr.MC$budget$contrib), beside=TRUE, horiz=TRUE, main="Uncertainty contribution by method", xlab="percent Variance", names.arg=c(GFO.res$measurand_label, MC.res$measurand_label)) ## End(Not run) ########################## ## Example H.1 from GUM ## ########################## # define the uncertainty budget u.budget<- uncertaintyBudget( x=list( name=c("lambda.s", "alpha.s", "theta.bar", "Delta", "delta.alpha", "delta.theta", "d.bar", "d.cr", "d.cnr"), label=c("lambda[s]", "alpha[s]", "bar(theta)", "Delta", "delta[alpha]", "delta[theta]", "bar(d)", "d[cr]", "d[cnr]"), mean=c(50.000623,11.5e-6,-1e-1, 0, 0, 0, 2.15e-4, 0, 0), units=c("mm", "oC^-1","oC","oC", "oC^-1", "oC", "mm", "mm", "mm"), u=c(25e-6, 1.2e-6, 0.2, 0.35, 0.58e-6, 0.029, 5.8e-6, 3.9e-6, 6.7e-6), distribution=c("t","unif","unif","arcsine","unif","unif","t","t","t"), dof=c(18, 1, 1, 1, 50, 2, 24, 5, 8) ), y=diag(1, 9) ) # define the measurand measurand_name<- "lambda" measurand_label<- "lambda" measurand_model<- paste("(lambda.s*(1+alpha.s*(theta.bar+Delta+delta.theta))", "+d.bar+d.cr+d.cnr)/(1+(alpha.s+delta.alpha)*(theta.bar+Delta))", sep="") # estimate the measurand using the Gaussian First Order method (GUM) u.GFO<- uncertainty( x=u.budget, y=list(measurand_name=measurand_name, measurand_label=measurand_label, measurand_model=measurand_model, alpha=0.01, method="GFO" ) ) u.GFO # same result as reported in Table H.1 # estimate the measurand using the Gaussian Second Order method u.GSO<- uncertainty( x=u.budget, y=list(measurand_name=measurand_name, measurand_label=measurand_label, measurand_model=measurand_model, alpha=0.01, method="GSO" ) ) u.GSO # same results as reported in section H.1.6, U(99) = 93 nm, # the difference is due to rounding error. # u = 34 nm, but dof are updated to 21 instead of keeping 16. # estimate the measurand using the Monte Carlo method (GUM supplement 1) u.MC<- uncertainty( x=u.budget, y=list(measurand_name=measurand_name, measurand_label=measurand_label, measurand_model=measurand_model, alpha=0.01, method="MC", B=1e6 ) ) u.MC # this result is not reported in the GUM # estimate the measurand using the Kragten method u.Kragten<- uncertainty( x=u.budget, y=list(measurand_name=measurand_name, measurand_label=measurand_label, measurand_model=measurand_model, alpha=0.01, method="Kragten" ) ) u.Kragten # same as GFO results ```

uncertainty-package