Automated Test Assmbly using Zero-suppressed Binary Decision Diagrams

Abstract

Recently, the necessity of parallel test forms for which each form comprises a different set of items, but which still has equivalent measurement accuracy has been emerging. An important issue for automated test assembly is to assemble as many parallel test forms as possible. Although many automated test assembly methods exist, the maximum clique using the integer programming method is known to assemble the greatest number of tests with the highest measurement accuracy. However, the method requires one month or more to assemble 450,000 tests due to the high time complexity of integer programming. This study proposes a new automated test assembly using Zerosuppressed Binary Decision Diagrams (ZDD). A ZDD is a graphical representation for a set of item combinations. This is derived by reducing a binary decision tree. In the proposed method, each node in the binary decision tree corresponds to an element of an item bank and has two edges if the item (node) is contained in a uniform test. Furthermore, all equivalent nodes (having the same measurement accuracy and the same test length) are shared. Finally, this study provides simulation and actual data experiments to demonstrate the effectiveness of the proposed method. The proposed method can assemble 450,000 tests within 24 hours.