Assessing and Optimizing University Students' Academic Performance via Control Charts and A Hat Relationship
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Abstract
This study applies Statistical Process Control (SPC) techniques control charts and process capability indices to evaluate and enhance the academic performance of Ibb University students taught by the researcher from 2017 to 2020 in three foundation courses: Probability Theory, Linear Programming, and Mathematical Statistics. Treating education as a measurable process, the analysis revealed general process stability, with all control charts within limits except for one year when instruction was in English instead of the native language, leading to a spike in failure rates. Once the language issue was addressed, performance improved significantly. The process capability index (Cpk = 1.333) reflects good performance with room for improvement. A nonlinear pattern, termed the "Hat Relationship," shows that success in Mathematical Statistics depends strongly on prior performance in the prerequisite courses. The results underscore the importance of reinforcing foundation-level education to ensure success in advanced subjects. The study recommends adapting industrial metrics like Cpk for educational settings and promotes the use of control charts as practical tools for monitoring and improving the learning process, thereby supporting data-driven decision-making in teaching and curriculum design.
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Statistical Process Control (SPC), Control Charts, Process Capability Index (Cpk), Educational Quality, Academic Performance, Quality Assurance in Education
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