Processing factors uncertainty
Processing effects are modelled either by a fixed processing factor, or by a lognormal or logistic-normal distribution (depending on the distribution type of the processing type). In case of a fixed factor, the uncertainty distribution is lognormal or logistic-normal with the same mean \(\mu\) as the fixed value, and with a standard deviation \(\sigma_{unc}\) which is calculated from the specified central value \(\mu\) (or nominal) and an estimate of the p95 of the uncertainty distribution (set NominalUncertaintyUpper in the table for Processing factors).
The calculation is:
with \(f() = logit\) for the logistic-normal distribution (distribution type 1) and \(f() = ln\) for the lognormal distribution (distribution type 2). Values lower than 0.01 or higher than 0.99 (distribution type 1 only) are replaced by default values (0.01 and 0.99); this is useful computationally to avoid problems. In each iteration of the uncertainty analysis a new value is drawn from this distribution to be used as a fixed factor in the Monte Carlo calculation. In case of distribution based processing factors (describing the variability of processing factors) two uncertainties can be specified. For \(\sigma_{unc}\), specification and calculation is as before (set NominalUncertaintyUpper in the table for Processing factors).
The uncertainty about the variability standard deviation
can be specified by the UpperUncertaintyUpper value. This value is specified as the p95 upper limit on Upper. The specified value is used to derive in a iterative search the number of degrees of freedom \(\mathit{df}\) (van der Voet et al. (2009)). In the uncertainty analysis, a modified chi-square distribution with \(\mathit{df}\) degrees of freedom is used to generate new values of \(\sigma_{var}\). A very high value of \(\mathit{df}\) means little uncertainty and \(\sigma_{var}\) will be almost equal in all iterations of the uncertainty analysis. A \(\mathit{df}\) close to 0 means a large uncertainty and very different values of \(\sigma_{var}\) will be obtained in the iterations of the uncertainty analysis. The p95 upper limit on Upper is set through parameter UpperUncertaintyUpper.