  This work studies the assembly of ability estimation test forms (called
tests, for short) drawn from an item bank. The goal of fixed-from test assembly
is to generate a large number of different tests with information functions
that meet a target information function. Thus, every test has the same ability
estimation error. This work proposes a new way of test assembly, namely,
drawing tests with information functions that exceed the target. This
guarantees that every test has an ability estimation error that is less than
the error set by the target. The work estimates the number of target exceeding
tests as a function of the number of items in the test. It demonstrates that
the number of target exceeding tests is far greater than the number of target
meeting tests. A Monte Carlo importance sampling algorithm is proposed for
target exceeding test assembly.
