随着深化教育评价改革的要求以及教育测量技术的发展，对教学过程进行诊断的形成性评价 (formative assessment)受到越来越多的关注。计算机化自适应认知诊断测验 (cognitive diagnostic computerized adaptive testing, CD-CAT) 是一个为每个考生量体裁衣设计个性化测验的智慧测验系统，相较于传统测验具有更高测验效率、更好的考试体验、即时诊断结果反馈等优势，能够为课堂形成性评价提供科学的测量工具。过去的数十年里，研究者为了进一步提高CD-CAT的测量精度和效率，对选题策略等方面进行了深入研究。然而CD-CAT（包括具体选题策略）的优势仅当有合适的题目来施测时才能够真正实现；这些合适的题目的集合被称为题库。
          题库设计中题库大小和构成并没有简单的答案。本研究提出服务于形成性评价的CD-CAT题库设计需要兼顾控制题库开发成本和保证测量学性质的目标。如何为特定的CD-CAT算法量体裁衣设计满足以上两个目标的最优题库是本研究尝试解决的问题。本研究提出了q-vector-and-union方法及其变式，演示了为特定CD-CAT算法设计最优题库的过程，通过模拟研究为不同属性个数、测量精度要求的变长CD-CAT设计最优题库并检验其效果。
           通过模拟研究比较不同规模、不同构成的题库表现，结果显示q-vector-and-union方法能够为特定CD-CAT算法找到满足所有类型考生的测量精度要求的最小题库。本文提出了未来研究方向以及对形成性CD-CAT设计的建议。

        With the progress of China's educational evaluation reform and the development of educational measurement techniques, formative assessment that diagnoses learning and evaluates the education quality is receiving more and more attention. Cognitive diagnostic computerized adaptive testing, CD-CAT) is a smart assessment system that tailors the optimal items to individual examinee's mastery profile. Compared with traditional tests, CD-CAT has the advantages of offering higher measurement efficiency, better testing experiences, and timely diagnostic feedback, and thus could serve as a suitable measurement tool for classroom formative assessment. In the past decades, researchers have mainly focused on developing and improving the item selection algorithms to increase the measurement efficiency of CD-CAT. However, the advantages of CD-CAT (including its item selection component) can only be realized when there are adequate items to select. This set of adequate items is called an item pool.
         There is no simple answer to the size and structure of an item pool design. This study proposed that the item pool design of CD-CAT for formative assessment purposes should balance the goal of item pool development cost control with the goal of ensuring the psychometric properties of the test. The focus of the current study is to tailor the item pool design to the specific CD-CAT algorithm in order to satisfy these two goals. Specifically, a new item pool design method, q-vector-and-union and its variation were proposed and the process of designing optimal pools for specific CD-CAT algorithms was demonstrated. A simulation study designed optimal pools and evaluated their performances for various variable-length CD-CAT conditions with different numbers of attributes, types of attribute hierarchies, and precision criteria.
           Through simulation studies in which item pools with different sizes and structures were compared, the proposed method was shown to be able to find the smallest item pool that satisfies the measurement precision needs of all kinds of examinees. Future directions were discussed and recommendations for formative CD-CAT design were provided.