Optimized realistic economic-statistical design of memory-type control charts with Burr type XII shock model for multiple independent assignable causes
摘要
Memory-type control charts, such as EWMA charts, excel at detecting small and gradual process shifts, making them essential for manufacturing process monitoring. This study proposes a Realistic Economic-Statistical Design (RESD) framework for non-Shewhart charts that explicitly incorporates multiple independent assignable causes and assumes no new cause occurs after the first until a true alarm. The Burr XII distribution models the occurrence of assignable causes, extending the classical Lorenzen–Vance cost framework for more accurate monitoring cost estimation. Numerical results reveal that classical models underestimate expected costs in multi-cause environments by up to 173.58% (depending on Burr-XII parameters c, s, and NE/UN/HN). The proposed RESD-BurrXII EWMA model significantly mitigates this bias, achieving lower optimal expected costs E(A) than the Shewhart chart (