A new test assembly algorithm based on a Monte Carlo random search is presented in this article. A major advantage of the Monte Carlo test assembly over other approaches (integer programming or enumerative heuristics) is that it performs a uniform sampling from the item pool, which provides every feasible item combination (test) with an equal chance of being built during an assembly. This allows the authors to address the following issues of pool analysis and extension: compare the strengths and weaknesses of different pools, identify the most restrictive constraint(s) for test assembly, and identify properties of the items that should be added to a pool to achieve greater usability of the pool. Computer experiments with operational pools are given.