  This work studies IRT-based Automated Test Assembly (ATA) of multiple test
forms (tests) that meet an absolute target information function, i.e. selecting
from an item bank only the tests that have information functions that are at a
small distance away from the target. The authors introduce the quantities
multiplicity of tests and probability of selecting a test with particular
number of items N and distance E from the target. A Grand Canonical Monte Carlo
test-assembly algorithm is proposed that selects tests according to this
probability. The algorithm allows N to vary during the simulation. This work
demonstrates that the number of tests that meet the target depends strongly on
N. The algorithm is capable of finding tests with small values of E and various
values of N depending on the need of the test constructor. Most importantly, it
can determine the optimal N for which a maximal number of tests with certain
specified small E exists.
