Abstract The presence of gluten-containing grains in oat groats is not uncommon. Many countries with regulations on “gluten-free” labeling of foods, such as the US, EU and Canada, have a 20 mg/kg (ppm) limit and allow “gluten-free” claims on oat products, provided that the limit is not exceeded. The non-uniform spatial distribution of gluten-containing grains in a bulk lot poses a challenge when selecting a representative sample of oat groats from a lot to determine if the lot is within regulatory compliance limits. A probability-based method for evaluating sampling plan designs was developed. A balanced nested experimental design was used to estimate gluten concentration in 16 laboratory samples from each of 10 mini-lots of oat groats spiked with varying amounts of wheat kernels used as the gluten source. The total variance of the gluten test procedure was partitioned into the variances between laboratory samples (Vs), test portions (Vtp) and aliquots tested (Va). From regression analysis, each variance was found to be a function of gluten concentration (G): Vs = ( 100 / Ns ) 35.0880 G , Vtp = ( 1 / Ntp ) 20.0078 G and Va = ( ( 1 / Na ) 0.0264 ) G 1.5167 , where Ns is laboratory sample size in g, Ntp is test portion size in g, and Na is number of aliquots analyzed for gluten. The observed gluten distribution among samples of oat groats tended to follow gamma and negative binomial distributions compared to normal and lognormal distributions, especially at low gluten concentrations. An R program was developed using the relation of variance with gluten concentration and negative binomial distribution to compute and plot an operating characteristic (OC) curve for various gluten sampling plan designs. The OC curve was used to predict the acceptance (or rejection) probability of a bulk lot at given gluten concentration by a specific sampling plan design. The effect of change in laboratory sample size, test portion size, number of laboratory samples and manufacturer's accept/reject limit (generally lower than the regulatory limit) on the OC curve was determined.

中文翻译：

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评估用于测量燕麦碎粒中麸质的抽样计划

摘要 燕麦碎粒中含有麸质谷物的情况并不少见。许多对食品“无麸质”标签有规定的国家，如美国、欧盟和加拿大，都有 20 毫克/公斤 (ppm) 的限制，并允许燕麦产品的“无麸质”声明，前提是该限制是没有超过。在从批次中选择具有代表性的燕麦碎粒样品以确定批次是否在法规遵从性限制内时，大批量中含麸质谷物的非均匀空间分布构成了挑战。开发了一种用于评估抽样计划设计的基于概率的方法。平衡嵌套实验设计用于估计 16 个实验室样品中的麸质浓度，这些样品来自 10 个小批量的燕麦碎粒中的每一个，其中掺入了不同数量的小麦籽粒作为面筋源。面筋测试程序的总方差被划分为实验室样品 (Vs)、测试部分 (Vtp) 和测试的等分试样 (Va) 之间的差异。从回归分析中，发现每个方差都是麸质浓度 (G) 的函数：Vs = ( 100 / Ns ) 35.0880 G ，Vtp = ( 1 / Ntp ) 20.0078 G 和 Va = ( ( 1 / Na ) 0.0264 ) G 1.5167，其中 Ns 是以克为单位的实验室样本量，Ntp 是以克为单位的测试份量，而 Na 是分析面筋的等分试样数。与正态分布和对数正态分布相比，观察到的燕麦碎粒样品中的麸质分布倾向于遵循伽马分布和负二项分布，尤其是在低麸质浓度下。使用方差与面筋浓度和负二项式分布的关系开发了一个 R 程序，以计算和绘制各种面筋抽样计划设计的操作特征 (OC) 曲线。OC 曲线用于通过特定的抽样计划设计预测在给定面筋浓度下批量接受（或拒绝）的概率。确定了实验室样本大小、测试部分大小、实验室样本数量和制造商的接受/拒绝限制（通常低于监管限制）对 OC 曲线的影响。