Post date: Feb 16, 2016 3:20:54 PM
Tolerance structures are easy to compute from a c-box. For example, if you want a 95% tolerance structure (from which you might be interested in, say, the 90th or 99th percentile as the B- or A-Basis value), the tolerance structure is a p-box formed by projecting any 95% confidence region for the parameter(s) through the distribution shape. This composition is an elementary application of probability bounds analysis. For instance, if the interval c is a 95% confidence interval for the exponential rate, then the expression "exponential(1/c)" creates a 95% tolerance structure.
In the case of the nonparametric problem, where there are no parameters to specify, the traditional Kolmogorov-Smirnov confidence bands on the distribution shape are the analogous tolerance structure for the underlying variate.