Experiments do not always run successfully on all experimental units. In
the fertilizer/tobacco example above, if midway through the growth
period one of the pots is accidentally broken, then one experimental
unit has been ``lost.'' One is effectively left with a *different*
block design, with different properties than the one initiated.

The concept of *robustness* of a block design is here considered as
its ability to maintain desirable statistical properties under loss of
individual plots or entire blocks. Such a loss is catastrophic if the
design becomes disconnected. Less than catastrophic but of genuine
concern are losses in the information provided by the design, as
measured by various optimality criteria. The two elements of
`robustness_properties` accommodate these two perspectives.

The element `robust_connected` makes the statement *The
design is connected under all possible ways in which*
`number_lost` *of* `category_lost` *can be
removed.* If the reported value of `number_lost` is known to
be the largest integer for which this statement is true then
`is_max` takes the value ``true'' and otherwise takes the
value ``unknown'' (the value ``false'' is not allowed).

The element `robust_efficiencies` reports A, E, D, and MV
efficiencies for a given number (`number_lost`) of plots or
blocks (`category_lost`) removed from the design. The
efficiencies can be calculated from two different perspectives. If
`loss_measure` =``average'' then the criterion value used is
the average of all its values over all possible deletions of the type
and number prescribed. If `loss_measure` =``worst'' then the
criterion value used is the maximum of all its values over all possible
deletions of the type and number prescribed.

Balance measures have not been incorporated under
`robust_efficiencies`. This is because designed balance is
typically severely affected by plot/block loss and in ways that need
have no relation to treatment structure.

The calculations associated with the values reported here can be quite expensive.