Integrating Statistical Process Control and Capability Analysis to Diagnose Pedagogical Variation in an Engineering Statistics Course

Abstract

Higher education engineering programs require graduates to possess strong statistical literacy for evidence-based decision-making. However, disparities in student achievement often obscure whether the pedagogical delivery is operating under stable conditions or if specific factors are introducing detrimental variation into the learning process. This study evaluates the stability and capability of the learning process within an Industrial Statistics course by applying a Quality Management System (QMS) framework to educational assessment data. The research analyzed the grades of 216 students across three evaluation instruments: quizzes, case studies, and examinations. Data was categorized according to Course Learning Outcomes (CLOs) to form consistent subgroups of n=3. Process stability was initially assessed using Statistical Process Control (SPC) with  -R control charts. Subsequently, a Process Capability Analysis (PCA) was conducted to determine whether the learning process could consistently yield outcomes meeting the defined minimum passing threshold (LSL = 50,01). The SPC analysis indicated that while the examination component achieved a state of statistical control, the quiz and case study assessments exhibited significant out-of-control variations. Furthermore, the PCA revealed systemic pedagogical deficiencies across all metrics. Both the potential (Cp) and actual (Cpk) capability indices for all evaluation instruments fell entirely below the acceptable industry threshold of 1,0. Critically, the case study component demonstrated a negative capability index (Cpk = -0.093), signifying that the mean class performance had shifted completely below the specification limit. Additionally, the examination component displayed extreme statistical variance ( = 32,794), highlighting a substantial disparity in cognitive comprehension among the cohort.