Calibration slope-governed uncertainty framework resolves method conflicts in pharmacopeial copper compliance testing of paeoniae radix alba

Despite having achieved a consensus on the copper PDE (10 µg/day) for oral preparations, major pharmacopeias (ChP, USP, EP, JP) lack uniformity in their recommended analytical protocols. For instance, a conflict exists between USP < 233 > , which designates ICP-based methods as primary, and EP Chapter 2.4.20, which accepts both AAS and ICP techniques. This lack of a unified standard thereby constitutes a key source of inter-laboratory discrepancies, particularly for concentrations near the critical 10 mg/kg compliance threshold. Pharmacopeial copper quantification near regulatory thresholds (e.g., 10 mg/kg) is challenged by method conflicts: high-sensitivity techniques (e.g., ICP-MS) amplify calibration uncertainties, while traditional methods risk false compliance. This study establishes a Linearity-Sensitivity-Uncertainty (LSU) framework to quantify slope-modulated error propagation and resolve these conflicts. Copper was quantified in Paeoniae Radix Alba certified reference material (CRM 9.60 ± 0.62 mg/kg) using microwave, wet, and dry digestion coupled with flame atomic absorption spectrometry (FAAS) or inductively coupled plasma mass spectrometry (ICP-MS). Method performance (accuracy, precision, LOD, LOQ) and measurement uncertainty (following GUM/EURACHEM) were evaluated. The LSU framework introduced the error amplification factor ( $$K=\frac{1}{b}$$ ) to quantify slope-modulated uncertainty. Microwave digestion FAAS achieved optimal accuracy at 10 mg/kg (bias: -0.03 mg/kg; expanded uncertainty $$U=0.35$$ mg/kg, $$k=2$$ ). ICP-MS, despite 1000-fold lower LOD (0.0005 mg/kg), exhibited 1.93-fold higher error amplification ( $${K}_{ICP-MS}=13.49$$ vs. $${K}_{FAAS}=7.00$$ ) due to its lower slope ( $${b}_{ICP-MS}=0.0741$$ vs. $${b}_{FAAS}=0.14288$$ ), elevating U to 3.70 mg/kg. Linearity-derived uncertainty dominated (> 98 %) the uncertainty budget. Dry ashing degraded slope integrity ( $$b$$ ↓5.5 %, RSD = 3.7 %), increasing U by 29 % and causing false-positive exceedance (10.05 > 10.00 mg/kg). Conclusion: The LSU framework reconciles sensitivity-reliability conflicts by quantifying slope-governed uncertainty propagation ( $$U\propto =\frac{1}{b}$$ ). It mandates slope-centric calibration, method-concentration zoning (FAAS for limits, ICP-MS for traces levels < 0.5 mg/kg), and slope stability criteria. This mechanistic approach reduced false-positive risk by 29 % (p < 0.01) compared to traditional methods, advancing pharmacopeial compliance testing standards.