\[\mathrm{LOD} = \frac{3s_\text{空白}}{b},\qquad \mathrm{LOQ} = \frac{10s_\text{空白}}{b}\]\[\mathrm{LOD} = \frac{3s_\text{blank}}{b},\qquad \mathrm{LOQ} = \frac{10s_\text{blank}}{b}\]
含义Meaning
能以一定置信度区分于空白的最低浓度（LOD），以及能可靠定量的最低浓度（LOQ）。b 为校准曲线斜率（灵敏度）。
LOD is the lowest concentration distinguishable from the blank with stated confidence; LOQ the lowest reliably quantifiable. b is the calibration slope (sensitivity).
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(s_\text{空白}\) | 空白信号（或低浓度样品）的标准偏差standard deviation of the blank signal | |
| \(b\) | 校准斜率calibration slope |
推导Derivation
空白信号服从均值 \(\bar y_b\)、标准差 \(s_b\) 的分布；信号超过 \(\bar y_b + 3s_b\) 时，假阳性概率约 0.13%（单侧）。
Signals above \(\bar y_b + 3s_b\) are false positives only ~0.13 % of the time.
把信号差除以灵敏度 b 转换为浓度。
Divide by the slope to convert to concentration.
LOQ 要求相对标准偏差约 10%，故取 10s。
LOQ targets ~10 % RSD, hence 10s.
适用条件与局限Assumptions & limitations
定义有多种（IUPAC、EPA、信噪比 S/N = 3）；报告时应说明方法。基体效应使实际样品 LOD 高于纯溶剂。
Several conventions exist (IUPAC, EPA, S/N = 3); state the one used. Matrix effects raise real-sample LODs.