Processing factors fixed or distribution based

Processing factors can be specified as fixed factors (nominal) or as statistical distributions for the variability across samples.

The distribution is either the logistic-normal distribution for processing types with factors restricted between 0 and 1 (e.g. washing),
or the lognormal distribution the lognormal distribution for processing types with non-negative factors (e.g. drying).

Variability distribution parameters are specified indirectly via the 50th and 95th percentile. Uncertainty for processing factors can be specified using uncertainty distributions of the same form as for variability. Uncertainty distribution parameters are specified indirectly via the 95th uncertainty percentiles on the 50th and 95th variability distribution percentiles.

For distribution based processing factors specify \(f_{k,nominal}\) and \(f_{k,upper}\) (Nominal and Upper in table Processing factors). Two situations are distinguished depending on the type of transformation.

Nonnegative processing factors

Equate the logarithms of \(f_{k,nominal}\) and \(f_{k,upper}\) to the mean and the 95% one-sided upper confidence limit of a normal distribution. This normal distribution is specified by a mean

\[ln(f_{k,nominal})\]

and a standard deviation

\[ln(f_{k,upper}) – ln(f_{k,nominal})/1.645\]

Processing factors between 0 and 1

Equate the logits of \(f_{k,nominal}\) and \(f_{k,upper}\) to the mean and the 95% one-sided upper confidence limit of a normal distribution. This normal distribution is specified by a mean

\[logit(f_{k,nominal})\]

and a standard deviation

\[logit(f_{k,upper}) – logit(f_{k,nominal})/1.645.\]