Risk Analysis for Quality Control Part 1: The Impact of Transition Assumptions in the Parvin Model

Setting quality control (QC) limits involves balancing the risk of false-positive results and false-negative results. Recent approaches to QC have focused on the assessment of false-negative results. The Parvin model is the most-used model for risk analysis. The Parvin model assumes that the system makes a transition from an in-control to an out-of-control (OOC) state but makes no further transitions after moving to the OOC state. The implications of this assumption are unclear. We used simulation experiments to compare the performance of QC systems based on no OOC transitions allowed (NOOCTA) vs systems where OOC transitions were allowed (OOCTA). The NOOCTA assumption leads to paradoxical tradeoff curves between false-positive results and false-negative results. Predictions of a false-negative result based on NOOCTA were about 10 times lower than models based on OOCTA. The most common models for QC risk analysis underestimate false-negative results. There is a need to develop better risk-based methods for QC analysis.