Background Sigma measures the number of SDs (z-value) from the existing sample mean to the nearest analytical performance standard or allowable error limit. Authors and software programs often measure sigma metrics for each QC sample but use an average sigma to compare methods and select QC strategies. That practice leads to dramatic over or under-estimation of the number of errors reported and the selection of inappropriate QC strategies. Methods Data samples were created to produce sigma values of 3.0, 4.5, and 6.0. Microsoft Excel function NORMSDIST was used to convert sigma to percent to number of errors per million patients. NORMSINV was used to convert the number of errors per million patients to sigma. Results A. Six sigma represents a method with a failure rate of 0.000001% or 0.001 failures of ASP/TEa per million patients. B. Three sigma represents a method with a failure rate of 0.135 percent or 1,350 failures of ASP/TEa per million patients. C. While the average sigma value of samples A and B was 4.5s, the average error rate was 0.0675 percent or 675 failures of ASP/TEa per million patients. D. An error rate was 0.0675 percent converts with the NORMSINV function to a sigma of 3.21. E. A true 4.5 sigma method would have a failure rate of 0.00034 percent or 3.4 failures of ASP/TEa per million patients. Conclusions Sigma studies that present an average sigma value underestimate the true number of errors reported. It would be more scientifically correct to either report the number of errors reported or to report the average sigma value based on the average number of errors. Laboratory professionals should interpret sigma studies and publications cautiously if a single sigma is used to represent two or more data sets.

中文翻译：

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B-131 混合样本水平的平均西格玛水平的谬误


背景西格玛测量从现有样本平均值到最接近的分析性能标准或允许误差限的 SD（z 值）数量。作者和软件程序通常测量每个 QC 样品的 sigma 指标，但使用平均 sigma 来比较方法和选择 QC 策略。这种做法会导致报告的错误数量急剧高估或低估，并选择不适当的质量控制策略。方法 创建数据样本以产生 3.0、4.5 和 6.0 的西格玛值。 Microsoft Excel 函数 NORMSDIST 用于将 sigma 转换为每百万患者的错误数百分比。 NORMSINV 用于将每百万患者的错误数转换为西格玛。结果 A. 6 西格玛代表失败率为 0.000001% 或每百万患者 ASP/TEa 0.001 次失败的方法。 B. 3 西格玛代表失败率为 0.135% 的方法，即每百万患者 ASP/TEa 失败 1,350 次。 C. 虽然样本 A 和 B 的平均西格玛值为 4.5 秒，但平均错误率为 0.0675%，即每百万患者 ASP/TEa 失败 675 次。 D. 使用 NORMSINV 函数将错误率为 0.0675% 转换为 3.21 的西格玛。 E. 真正的 4.5 sigma 方法的失败率为 0.00034%，即每百万患者 ASP/TEa 失败 3.4 次。结论 西格玛研究提供的平均西格玛值低估了所报告错误的真实数量。报告所报告的错误数或根据平均错误数报告平均西格玛值会更加科学正确。如果使用单个 sigma 代表两个或多个数据集，实验室专业人员应谨慎解释 sigma 研究和出版物。