Determination of LOD and LOQ with relative standard deviation and relative range or ratio of maximum and minimum
JIA Yunhai1, SUN Xiaofei2, ZHANG Fan3
1. Central Iron & Steel Research Institute,Beijing 100081,China; 2. NCS Testing Technology Co.,Ltd.,Beijing 100081,China; 3. China National Institute of Standardization,Beijing 100191,China
Abstract：The corresponding relative standard deviations (RSD) of limit of detection (LOD) and limit of quantification (LOQ) constitute two critical values,i.e.,RSDLOD(MAX) and RSDLOQ(MAX).In general,ten times and three times of standard deviation of the blank sample in 10 measurements are used as LOQ and LOD,respectively.At 95% confidence interval,the obtained RSD at concentration of LOQ and LOD are often larger than the theoretical value 10% or 33% of normal distribution.The McKay model for standard deviation of confidence interval was modified by Vangel.The critical value formula of RSD of small sample (K) was estimated from the RSD of normal distribution (k).It was found that when the LOQ and LOD was 10 times and 3.3 times of standard deviation of sample blank,the corresponding critical value of RSD for LOQ and LOD in ten measurements was 14% and 43%,respectively.The quantitative analysis was not available when RSD was larger than 14%,and it was undetectable when RSD was larger than 43%.When relative range (RR) was used to evaluate the precision,the corresponding critical value of RR for LOQ and LOD in two independent measurements was 28% and 84%,respectively.The quantitative analysis was not available when RR was larger than 28%,and it was undetectable when RSD was larger than 84%.The ratio of maximum and minimum (xmax/xmin) in 2~4 measurements could be used to provide the corresponding critical value for LOQ and LOD.The quantitative analysis was available when the ratio (x2/x1) was less than 1.3 in two independent measurements.The qualitative analysis was available when the ratio (x2/x1) was in range of 1.3<(x2/x1)≤2.5,while the qualitative analysis was not available when the ratio (x2/x1) was larger than 2.5.If LOQ and LOD was defined as 14.1 times and 4.65 times of standard deviation of sample blank (SB),the corresponding critical value of RSD for LOQ and LOD in ten measurements of blank sample was 10% and 30%,respectively.The quantitative analysis was not available when RSD was larger than 10%,and it was undetectable when RSD was larger than 30%.The corresponding critical value of RR for LOQ and LOD in two independent measurements was 20% and 61%,respectively.The quantitative analysis was not available when RSD was larger than 20%,and it was undetectable when RSD was larger than 61%.The quantitative analysis was available when the ratio (x2/x1) in two independent measurements was less than 1.2.The qualitative analysis was available when the ratio (x2/x1) was in range of 1.2<(x2/x1)≤1.9,while the qualitative analysis was not available when the ratio (x2/x1) was larger than 1.9.Different definition of LOD and LOQ led to different critical values of RSD and RR and (xmax/xmin).For any detection method and any testing concentration,when the RSD and number of measurements were provided,the use of RSD,RR or (xmax/xmin) ratio could be used to rapidly judge whether effective qualitative analysis or quantitative analysis could be conducted.
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JIA Yunhai, SUN Xiaofei, ZHANG Fan. Determination of LOD and LOQ with relative standard deviation and relative range or ratio of maximum and minimum. , 2021, 41(1): 1-12.
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