重复性极限 [latex]r[/latex] 是由重复性标准偏差 ([latex]s_r[/latex]) 得出的临界值。它表示在重复性条件下获得的两个单一测试结果之间的最大预期绝对差异，概率为 95%。通常计算公式为 [latex]r = 2.8 倍 s_r[/latex]。如果差值超过 [latex]r[/latex]，则认为结果可疑。
重复性限值（统计量）
1980
- International Organization for Standardization (ISO)
(generate image for illustration only)
The repeatability limit provides a practical tool for judging the acceptability of two test results. Its statistical foundation lies in the properties of the normal distribution. The difference between two measurements drawn from the same normal distribution with standard deviation [latex]s_r[/latex] is also normally distributed with a mean of zero and a standard deviation of [latex]\sqrt{s_r^2 + s_r^2} = \sqrt{2}s_r[/latex]. To encompass 95% of these differences, we use a coverage factor. For a normal distribution, this factor is approximately 1.96. Therefore, the 95% limit is [latex]1.96 \times \sqrt{2} \times s_r \approx 2.77s_r[/latex], which is often rounded to [latex]2.8s_r[/latex] for simplicity in standards like ISO 5725.
A more precise calculation uses the Student’s t-distribution, especially when [latex]s_r[/latex] is estimated from a small number of measurements. The formula becomes [latex]r = t_{(1-\alpha/2, \nu)} \times \sqrt{2} \times s_r[/latex], where [latex]t_{(1-\alpha/2, \nu)}[/latex] is the critical value from the t-distribution for a confidence level of [latex]1-\alpha[/latex] (e.g., 95%) and [latex]\nu[/latex] degrees of freedom used to estimate [latex]s_r[/latex]. In practice, if a lab runs two tests on the same sample and the difference is greater than [latex]r[/latex], it’s a signal to investigate potential issues like procedural errors, sample contamination, or instrument malfunction.
UNESCO Nomenclature: 1209
- 统计资料
类型
抽象系统
中断
实质性
使用方法
广泛使用
前体
- Jerzy Neyman and Egon Pearson’s development of confidence intervals in the 1930s
- The Student’s t-distribution published by William Sealy Gosset (‘Student’) in 1908
- The ISO 5725 standard on accuracy (trueness and precision) of measurement methods and results
应用
- checking the consistency of duplicate measurements in a laboratory
- defining performance specifications for analytical instruments
- quality control charts for monitoring process stability
- regulatory compliance in pharmaceutical and environmental testing
- resolving disputes between two measurements of the same sample
专利：
NA
潜在的创新想法
Related to: repeatability limit, critical difference, quality control, ISO 5725, statistical inference, confidence interval, precision, measurement.
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