電腦適性化測驗的目的是藉由挑選難度與受測者能力相符的測驗試題來進行施測，進而達成專屬於受測者的個人化測驗內容。然而，對於擁有大量測驗試題的試題庫而言，電腦適性化測驗系統有兩大挑戰。其中一個挑戰為如何正確的估計測驗試題的試題難度指數；而另外一個挑戰是如何快速的挑選出最適合受測者能力水準的測驗試題。
本研究提出一個基於答題異常率的試題難度指數估計方法。受測者的能力值被直接考慮進估計的過程，也就是說，試題難度指數與受測者能力值可以被相互估計。每道測驗試題也可以獨立的進行估計。因此，試題庫可以隨時輕易地被擴充，且將可以在無需太多前測樣本的情況下，快速地估計出合理的試題難度指數。
本研究再以知識結構的概念作為受測者多重能力評估的準則，發展一個基於粒子群最佳化演算法的動態選題策略。由於粒子群最佳化演算法快速搜尋的優點與知識結構的特性，即使在擁有大量測驗試題的試題庫裡，也能快速的搜尋到最適合受測者能力水準的測驗試題。

The aim of computerized adaptive testing archives the personal test exclusively for a testee through selecting the test item with the difficulty, which is consistent with the current testee’s ability. However, for a big test item bank whit many test items, there are two important challenges to a computerized adaptive testing system. The first one is how to estimate the item difficulty indices of test items correctly; and the other one is how to locate a most suitable test item for a testee’s ability quickly.
An estimation method of item difficulty indices based on the answers abnormal rate is proposed in this study. The testees’ abilities are considered into the estimation process directly, in other words, the item difficulty indices and the testees’ abilities can be estimated mutually. Each test item can also be estimated independently. Therefore, the item bank can be expanded easily at any time, and the item difficulty indices will be estimated quickly and reasonably without too many pre-test samples.
And then, this study adopts the knowledge structure concept for multiple ability evaluation for testees, which is based on the particle swarm optimization, to develop a dynamic item selection strategy. The quick search advantage in the particle swarm optimization and knowledge structure characteristics allow the most suitable test items for a testee’s ability to be quickly identified, even in a big test item bank.

摘　　要 iv
ABSTRACT v
致　　謝 vi
目　　次 vii
表目錄 ix
圖目錄 x
第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 3
1.3 論文架構 3
第二章 文獻探討 5
2.1 電腦適性化測驗 5
2.2 知識結構 6
2.3 試題分析 7
2.3.1 試題難度 7
2.3.2 試題鑑別度 8
2.4 試題反應理論 9
2.5 粒子群最佳化演算法 12
2.6 動態選題策略 15
2.7 Kappa一致性分析 17
第三章 研究方法 20
3.1 系統架構 20
3.2 試題難度調整策略 23
3.3 PSO動態選題策略 26
3.3.1 PSO的搜尋向量 26
3.3.1.1 試題難度控制因子 27
3.3.1.2 試題比例控制因子 27
3.3.1.3 試題曝光度控制因子 29
3.3.1.4 個人試題曝光度控制因子 29
3.3.1.5 搜尋向量 30
3.3.2 PSO的速度函數 31
3.3.3 PSO的適應函數 32
3.3.4 PSO適性化測驗 33
第四章 實驗與結果討論 35
4.1 實驗一：PSO動態選題策略之成效 35
4.1.1 搜尋準確度 36
4.1.2 搜尋速度 39
4.1.3 試題重疊率 42
4.2 實驗二：試題難度指數估計方法之成效 45
4.2.1 難度調整公式性能 45
4.2.2 出題次數影響難度調整調查 49
4.2.3 測驗結果一致性分析 50
第五章 結論與未來展望 52
參考文獻 53

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