The cognitive diagnostic test can be used to understand the learning effects (such as strengths and weaknesses) of learners for a specific subject area. Based on the evaluation results of the diagnostic test, instructors may suggest or give students additional material on the subject area for students who do not meet the requirements. The S-P (Student- Problem) model has been used for this purpose for a long time. However, the current S-P model pays little attention to a student's response time for each test item or for the entire question set during the test. The student's response time for each test item can be an important factor for instructors wanting to diagnose each student's individual ability in problem solving. Also, there are few computerized diagnostic test analysis systems available that are designed to support both text-diagram-based and/or multimedia-based presentation test items. In this research, we incorporate the response time, difficulty index, and discriminatory index of each test item into an S-P model during the analysis. Specifically, we employ two terms: 1) the nimbleness of thinking of a student, which can be measured based on the response time for answering each test item, and 2) the problem solving ability of a student, which can be measured based on the student's ability to solve adaptive type questions with various difficulty levels and discrimination powers. With the incorporation of these parameters, an enhanced S-P model is presented. It can be used to diagnose both time dependent information and problem solving abilities with respect to test items and test-takers. A web-based computerized system was designed and implemented based on the enhanced S-P model for both text-diagram type presentation test items and multimedia type presentation test items. Practical examples were investigated and experimental studies conducted using the cognitive diagnostic computerized system to demonstrate the rationality and applicability of the proposed enhanced S-P model.