# tools:::Rd_package_title("uncertainty") tools:::Rd_package_description("uncertainty") package ## Details The DESCRIPTION file: tools:::Rd_package_DESCRIPTION("uncertainty") tools:::Rd_package_indices("uncertainty") Define an "uncertainty budget" object, including all the involved input quantities. Then estimate the output quantity object by defining a measurement model, using the "uncertainty budget" and applying an estimation method. Print or plot the output quantity estimates or create a "summary uncertainty" object to print or plot the uncertainty contributions to the output quantity described in the measurement model. ## Author(s) tools:::Rd_package_author("uncertainty") Maintainer: tools:::Rd_package_maintainer("uncertainty") ## References JCGM 200:2012. **International vocabulary of metrology—Basic and general concepts and associated terms (VIM)** JCGM 100:2008. **Guide to the expression of uncertainty of measurement** JCGM 101:2008. **Supplement 1 Propagation of distributions usign a Monte Carlo method** S.L.R. Ellison and A. Williams (2012) EURACHEM/CITAC Guide CG 4. **Quantifying Uncertainty in Analytical Measurement**, ISBN 978-0-948926-30-3. 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), unit = c("kg", "kg"), dof = c(10, 10), type = c("A", "A"), description = c("measurand mass", "sample mass"), 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", measurand_description = "ratio of masses at 20 degrees celsius", method = "GFO", alpha = 0.05)) contr.GFO <- summary(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", measurand_description = "ratio of masses at 20 degrees celsius", method = "MC", alpha = 0.05, B = 1e5)) contr.MC <- summary(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$measurand_model) plot(GFO.res, lty = 2, col = 2, add = TRUE) legend(0.7, 2.5, legend = c("Monte Carlo", "Gaussian First Order"), lty = c(1, 2), col = c(4, 2), lwd = 2, bg = "white") ## End(Not run) ## Display both uncertainty summaries ## Not run: barplot(cbind(contr.GFO$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]"), description = c("certified length of the reference gauge block", "reference gauge block cte", "mean temperature", "Delta", "difference in the cte", "difference in temperature", "mean difference in length", "d.cr", "d.dnr"), mean = c(50.000623,11.5e-6,-1e-1, 0, 0, 0, 2.15e-4, 0, 0), unit = 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), type = c("B", "B", "A", "B", "A", "A", "A", "A", "A") ), 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 = "") measurand_description = "length of end gauge block under calibration at 20 degrees celsius" # 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, measurand_description = measurand_description, 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, measurand_description = measurand_description, 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. # 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, measurand_description = measurand_description, alpha = 0.01, method = "MC", B = 1e5 ) ) u.MC # this result is not reported in the GUM ```

uncertainty-package