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This work studies IRT-based Automated Test Assembly (ATA) of multiple testforms (tests) that meet an absolute target information function, i.e. selectingfrom an item bank only the tests that have information functions that are at asmall distance away from the target. The authors introduce the quantitiesmultiplicity of tests and probability of selecting a test with particularnumber of items N and distance E from the target. A Grand Canonical Monte Carlotest-assembly algorithm is proposed that selects tests according to thisprobability. The algorithm allows N to vary during the simulation. This workdemonstrates that the number of tests that meet the target depends strongly onN. The algorithm is capable of finding tests with small values of E and variousvalues of N depending on the need of the test constructor. Most importantly, itcan determine the optimal N for which a maximal number of tests with certainspecified small E exists.

Meeting an absolute test information target with optimal number of test items via Grand Canonical Monte Carlo simulation