取样方差估计值的精度与样本数目之间的关系

通过数学推导建立了取样方差估计值的精度与样本数目之间的定量关系。实验也证明,取样方差估计值的标准偏差与样本数目的平方根之积可近似为一常数。应用蒙特卡罗技术模拟随机取样,对该关系式进行了验证,并探讨了取样方差估计值的分布规律,表明其规律对于组分含量服从正态分布,均匀随机分布及多项分布总体是相似的。     

渐进取样法及其应用

提出了渐进取样法,通过样本数目的累积,使总方差估计值达到所需的精度。应用Ｍｏｎｔｅ Ｃａｒｌｏ模拟技术考察了满足一定取样精度的样本数目及其偏差。将该方法应用于散装生铁块中Ｓｉ、Ｍｎ、Ｃ、Ｓ、Ｐ含量分析的取样,结果令人满意。该项研究对于大宗货物的实际随机取样具有重要参考价值。     

组合取样的误差理论研究及其Monte Carlo模拟

基于多项分布理论,建立了组合取样方差与取样总体中各子区的大小及其组分含量之间的关系和计算公式,探讨了组合取样常数的物理意义.以颗粒物质为例,探讨了组合取样的逻辑质量单元的概念及其意义,为确定组合取样中的份样质量提供了理论依据.本文对于完善组合取样误差理论,保证组合取样的质量均具有重要意义.     

参数法和非参数法估计组合样中被测组分含量的置信区间

本文以散装生铁块的随机样本分析结果为基础,应用Ｍｏｎｔｅ Ｃａｒｌｏ模拟法考察了组合样本中Ｓｉ、Ｍｎ,Ｃ,Ｓ,Ｐ含量（或份样平均值）的分布情况,研究了组分含量的置信区间,对参数法和非参数法的结果进行了比较。结果表明,对近似符合正态分布的原始总体或当组合样中的份样数目较多时,两种方法所估计的置信区间相近。但对偏离正态分布（或ｔ－分布）的总体且组合样中的份样数目较少时,非参数法较参数法的结果更符合实际     

分层性物质的组合取样误差与份样数目之间的关系及其Monte Carlo模拟

本文从理论上研究了分层性物质的组合取样误差与份样数目之间的定量关系，表明份样数目与组合取样相对标准偏差的平方之积为一常数，称为组合取样常数，它与Ｉｎｇａｍ ｅｌｌｓ 和Ｓｗ ｉｔｚｅｒ 提出的取样常数是相似的，表示６８％ 置信度下组合取样的相对标准偏差达到１％ 时的份样数目。应用Ｍｏｎｔｅ Ｃａｒｌｏ 模拟技术对该理论进行了验证，结果令人满意。     

固体分层取样方案的最优化设计

本文首次从理论上探讨了取得量对分层取样误差的影响,提出了总取样量一定时各层的最佳取样量和最小取样方差的计算公式,从而为分层取样的最佳取样方案设计提供了理论依据。     

二元颗粒混合物按质量取样的误差研究

二元颗粒混合物的随机取样方式有两种：一是按颗粒数目取样,二是按质量取样本文对二元颗粒混合物按质量取样的误差进行了深入研究,详细分析了混合物的各种参对被测组分含量取样误差的影响,应用Ｍｏｎｔｅ Ｃａｒｌｏ技术对取样进行了模拟。以颗粒药品的二元混合物为例对按颗粒数目取样和按质量取样的误差进行了比较。此项研究对于分析取样理论和应用具有重要的价值。     

粒状物质的微观均匀度及其对取样误差的影响分析

研究物质的取样属性与以取样误差之间的关系是分析化学取样学的重要内容。从微观角度探讨了物质的理论性质及其对取样误差的影响。以碳化硅为例,考察了粒度分布、组分随粒度的变化以及均匀度因子等,分析了取样误差的来源。首次通过粒度分级成功地对碳化硅进行了分层,并对分层取样和随机取样的误差进行了分析和讨论,为制定合理的取样方案提供了有利的依据。本文的研究方法可适用于所有粒状物质的取样,同时也为分析化学取样学的深     

矿产品水分含量代表值Bootstrap模拟取样估计

在对矿产品水分含量基础统计学特征描述的基础上,采用内核密度估计对水分含量数据多态性进行了分析,根据双态分布的特点,使用Bootstrap模拟取样方法对试验样本值模拟重复取样,以多次Bootstrap模拟取样的均值与标准偏差作为矿产品水分含量有限样本代表值及标准偏差的稳健估计,实践证明Bootstrap模拟取样估计对矿产品水分含量代表值的估计是有效的,该项研究为矿产品水分含量代表值的准确评估提供了一种新方法.     

稳键方差法探讨土壤取样

用稳键方差法探讨了土壤的一些分析数据的处理，稳键方差分析的优点在于可以降低异常值在统计评价中的影响，易于辨认异常值。本文自理了ｐＨ，有机质，阳离子交换量，交换性Ｍｎ，易还原态Ｍｎ等土壤分析数据，结果显示分析精度足够高而取样精度不够。     

Distribution among sample test results when testing shelled corn lots for fumonisin.

The statistical distribution known as the compound gamma function was studied for suitability in describing the distribution of sample test results associated with testing lots of shelled corn for fumonisin. Thirty-two 1.1 kg test samples were taken from each of 16 contaminated lots of shelled corn. An observed distribution consisted of 32 sample fumonisin test results for each lot. The mean fumonisin concentration, c, and the variance, s2, among the 32 sample fumonisin test results along with the parameters for the compound gamma function were determined for each of the 16 observed distributions. The 16 observed distributions of sample fumonisin test results were compared with the compound gamma function using the Power Divergence test. The null hypothesis that the observed distribution could have resulted from sampling a family of compound gamma distributions was not rejected at the 5% significance level for 15 of the 16 lots studied. Parameters of the compound gamma distribution were calculated from the 32-fumonisin sample test results using the method of moments. Using regression analysis, equations were developed that related the parameters of the compound gamma distribution to fumonisin concentration and the variance associated with a fumonisin test procedure. An operating characteristic curve was developed for a fumonisin sampling plan to demonstrate the use of the compound gamma function.     

Sampling almonds for aflatoxin, part II: estimating risks associated with various sampling plan designs

About 100 nations have established regulatory limits for aflatoxin in food and feeds. Because these limits vary widely from one country to another, the Codex Alimentarius Commission, working through the Codex Committee on Food Additives and Contaminants, has initiated work to harmonize aflatoxin limits and sampling plans for almonds, pistachios, hazelnuts, and Brazil nuts. Studies were developed to measure the uncertainty and distribution among test results for replicate samples taken from aflatoxin-contaminated almond shipments. The uncertainty and distribution information was used to develop a model to evaluate the performance of aflatoxin sampling plans so that harmonized sampling plans can be developed for almonds that reduce the misclassifying of lots in the export trade. Twenty lots of shelled almonds were sampled according to an experimental protocol in which sixteen 10 kg samples were taken from each lot. The observed aflatoxin distribution among the 16 sample test results was compared with 3 theoretical distributions. The negative binomial distribution was selected to model aflatoxin distribution among sample test results because it gave acceptable fits across all 20 observed sample distributions. By using the variance and distribution information, operating characteristics curves were developed to predict the effect of sample size and accept/reject limits on the probability of rejecting good lots and accepting bad lots.     

Evaluation of sampling plans to detect Cry9C protein in corn flour and meal

StarLink is a genetically modified corn that produces an insecticidal protein, Cry9C. Studies were conducted to determine the variability and Cry9C distribution among sample test results when Cry9C protein was estimated in a bulk lot of corn flour and meal. Emphasis was placed on measuring sampling and analytical variances associated with each step of the test procedure used to measure Cry9C in corn flour and meal. Two commercially available enzyme-linked immunosorbent assay kits were used: one for the determination of Cry9C protein concentration and the other for % StarLink seed. The sampling and analytical variances associated with each step of the Cry9C test procedures were determined for flour and meal. Variances were found to be functions of Cry9C concentration, and regression equations were developed to describe the relationships. Because of the larger particle size, sampling variability associated with cornmeal was about double that for corn flour. For cornmeal, the sampling variance accounted for 92.6% of the total testing variability. The observed sampling and analytical distributions were compared with the Normal distribution. In almost all comparisons, the null hypothesis that the Cry9C protein values were sampled from a Normal distribution could not be rejected at 95% confidence limits. The Normal distribution and the variance estimates were used to evaluate the performance of several Cry9C protein sampling plans for corn flour and meal. Operating characteristic curves were developed and used to demonstrate the effect of increasing sample size on reducing false positives (seller's risk) and false negatives (buyer's risk).     

Evaluating the performance of sampling plans to detect fumonisin B1 in maize lots marketed in Nigeria

Fumonisins are toxic and carcinogenic compounds produced by fungi that can be readily found in maize. The establishment of maximum limits for fumonisins requires the development of scientifically based sampling plans to detect fumonisin in maize. As part of an International Atomic Energy Agency effort to assist developing countries to control mycotoxin contamination, a study was conducted to design sampling plans to detect fumonisin in maize produced and marketed in Nigeria. Eighty-six maize lots were sampled according to an experimental protocol in which an average of 17 test samples, 100 g each, were taken from each lot and analyzed for fumonisin B1 by using liquid chromatography. The total variability associated with the fumonisin test procedure was measured for each lot. Regression equations were developed to predict the total variance as a function of fumonisin concentration. The observed fumonisin distribution among the replicated-sample test results was compared with several theoretical distributions, and the negative binomial distribution was selected to model the fumonisin distribution among test results. A computer model was developed by using the variance and distribution information to predict the performance of sampling plan designs to detect fumonisin in maize shipments. The performance of several sampling plan designs was evaluated to demonstrate how to manipulate sample size and accept/reject limits to reduce misclassification of maize lots.     

Evaluating the performance of sampling plans to detect hypoglycin A in ackee fruit shipments imported into the United States

Hypoglycin A (HGA) is a toxic amino acid that is naturally produced in unripe ackee fruit. In 1973, the U.S. Food and Drug Administration (FDA) placed a worldwide import alert on ackee fruit, which banned the product from entering the United States. The FDA has considered establishing a regulatory limit for HGA and lifting the ban, which will require development of a monitoring program. The establishment of a regulatory limit for HGA requires the development of a scientifically based sampling plan to detect HGA in ackee fruit imported into the United States. Thirty-three lots of ackee fruit were sampled according to an experimental protocol in which 10 samples, i.e., ten 19 oz cans, were randomly taken from each lot and analyzed for HGA by using liquid chromatography. The total variance was partitioned into sampling and analytical variance components, which were found to be a function of the HGA concentration. Regression equations were developed to predict the total, sampling, and analytical variances as a function of HGA concentration. The observed HGA distribution among the test results for the 10 HGA samples was compared with the normal and lognormal distributions. A computer model based on the lognormal distribution was developed to predict the performance of sampling plan designs to detect HGA in ackee fruit shipments. The performance of several sampling plan designs was evaluated to demonstrate how to manipulate sample size and accept/reject limits to reduce misclassification of ackee fruit lots.     

Uncertainty from sampling in measurements of aflatoxins in animal feedingstuffs: application of the Eurachem/CITAC guidelines

The duplicate method for estimating uncertainty from measurement including sampling is presented in the Eurachem/CITAC guide. The applicability of this method as a tool for verifying sampling plans for mycotoxins was assessed in three case studies with aflatoxin B(1) in animal feedingstuffs. Aspects considered included strategies for obtaining samples from contaminated lots, assumptions about distributions, approaches for statistical analysis, log(10)-transformation of test data and applicability of uncertainty estimates. The results showed that when duplicate aggregate samples are formed by interpenetrating sampling, repeated measurements from a lot can be assumed to approximately follow a normal or lognormal distribution. Due to the large variation in toxin concentration between sampling targets and sometimes very large uncertainty arising from sampling and sample preparation (U(rel) ≥ 50%), estimation of uncertainty from log(10)-transformed data was found to be a more generally applicable approach than application of robust ANOVA.