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.