(Mis)Classification for in‐Control/Out‐of‐Control Decisions in Statistical Quality Control: A Case Study

ABSTRACT This case study examines decision‐making processes within a potato chip production line, where controlling the frying oil temperature is vital for maintaining product quality. The process is considered in‐control (InC) when the mean frying oil temperature is 180°C, with a standard deviation of 4°C, and out‐of‐control (OutC) when, in a rising temperature scenario, the mean shifts to 190°C. The factory had employed a likelihood ratio decision rule, classifying temperature readings above 185°C as positive (P), indicating OutC, and those below as negative (N), indicating InC. These P/N labels were further categorized into true positive (TP), false positive (FP), true negative (TN), or false negative (FN). The factory's flagging criterion, which relied on 8‐ary sequences ending with PPP from 2‐min frying cycles, resulted in an increased FP rate and frequent production interruptions. A retrospective analysis, constrained by the lack of preserved raw temperature measurements and reliant solely on categorical labels, identified six methodological weaknesses in the original classification rule. This limitation led to the development of an exploratory scoring framework based on sensitivity and specificity, calculated from the TP/FP/TN/FN composition of each 8‐ary sequence. A consistency analysis revealed that 0‐upcrossings in the moving average of the daily scores preceded 91.9% of recorded production halts, with a median lead time of 12 min, suggesting that the scoring framework holds potential for detecting OutC from categorical process data.