Designing Sampling Plans to Detect Foreign Material in Bulk Lots of Shelled Peanut1

2008 ◽  
Vol 35 (2) ◽  
pp. 159-164 ◽  
Author(s):  
T. B. Whitaker ◽  
A. B. Slate ◽  
F. G. Giesbrecht
Keyword(s):  
Binomial Distribution ◽  
Small Sample ◽  
Sampling Plan ◽  
Test Results ◽  
Foreign Material ◽  
Sampling Plans ◽  
Sample Test ◽  
The Mean ◽  
Mean Variance ◽  
Food Manufacturer

Abstract When food manufacturers specify a maximum limit for the amount of foreign material (FM) in the lot, handlers estimate the true percent FM in a commercial lot by measuring FM in a small sample taken from the lot before shipment to a food manufacturer. Because of the uncertainty (variability) in FM among samples taken from the same lot, it is difficult to obtain a precise estimate of the true FM in the lot. The objectives of this study were to (1) measure the variability and FM distribution among sample test results when estimating the true lot proportion of FM in a lot of shelled peanuts, (2) compare the measured variability and FM distribution among sample test results to that predicted by the binomial distribution, (3) develop a computer model, based upon the binomial distribution, to evaluate the performance (buyer's risk and seller's risk) of sampling plan designs used to estimate FM in a bulk lot of shelled peanuts, and (4) demonstrate with the model the effect of increasing sample size to reduce misclassification of lots. Eighty-eight samples, 9 kg (20 lb) each, were selected at random from each of six commercial lots of shelled medium runner peanuts. The percent FM (PFM), based upon number of kernels was determined for each sample. The mean, variance, and distribution among the 88 sample test results were calculated for each of the six lots. Results indicated that the variance and distribution among the 88 sample test results are very similar to that predicted by the binomial distribution. The performance of various sampling plan designs was demonstrated using the binomial distribution.

scholarly journals Sampling Hazelnuts for Aflatoxin: Effect of Sample Size and Accept/Reject Limit on Reducing the Risk of Misclassifying Lots

2007 ◽  
Vol 90 (4) ◽  
pp. 1028-1035 ◽  
Author(s):  
Guner Ozay ◽  
Ferda Seyhan ◽  
Aysun Yilmaz ◽  
Thomas B Whitaker ◽  
Andrew B Slate ◽  
...  
Keyword(s):  
Sample Size ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Food Additives ◽  
Sampling Plan ◽  
Test Results ◽  
Sampling Plans ◽  
Wide Range ◽  
Sample Test

Abstract About 100 countries have established regulatory limits for aflatoxin in food and feeds. Because these limits vary widely among regulating countries, the Codex Committee on Food Additives and Contaminants began work in 2004 to harmonize aflatoxin limits and sampling plans for aflatoxin in almonds, pistachios, hazelnuts, and Brazil nuts. Studies were developed to measure the uncertainty and distribution among replicated sample aflatoxin test results taken from aflatoxin-contaminated treenut lots. The uncertainty and distribution information is used to develop a model that can evaluate the performance (risk of misclassifying lots) of aflatoxin sampling plan designs for treenuts. Once the performance of aflatoxin sampling plans can be predicted, they can be designed to reduce the risks of misclassifying lots traded in either the domestic or export markets. A method was developed to evaluate the performance of sampling plans designed to detect aflatoxin in hazelnuts lots. Twenty hazelnut lots with varying levels of contamination were sampled according to an experimental protocol where 16 test samples were taken from each lot. The observed aflatoxin distribution among the 16 aflatoxin sample test results was compared to lognormal, compound gamma, and negative binomial distributions. The negative binomial distribution was selected to model aflatoxin distribution among sample test results because it gave acceptable fits to observed distributions among sample test results taken from a wide range of lot concentrations. Using the negative binomial distribution, computer models were developed to calculate operating characteristic curves for specific aflatoxin sampling plan designs. The effect of sample size and accept/reject limits on the chances of rejecting good lots (sellers' risk) and accepting bad lots (buyers' risk) was demonstrated for various sampling plan designs.

Sampling dried figs for aflatoxin - Part II: effect of sampling plan design on reducing the risk of misclassifying lots

2017 ◽  
Vol 10 (2) ◽  
pp. 99-109 ◽  
Author(s):  
H. Ozer ◽  
H.I. Oktay Basegmez ◽  
T.B. Whitaker ◽  
A.B. Slate ◽  
F.G. Giesbrecht
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sampling Plan ◽  
Export Market ◽  
Test Results ◽  
Sampling Plans ◽  
Binomial Distributions ◽  
Sample Test ◽  
Codex Standard

Because aflatoxin limits vary widely among regulating countries, the Codex Committee on Contaminants in Foods (CCCF) began work in 2006 to harmonise maximum levels (MLs) and sampling plans for aflatoxin in dried figs. Studies were developed to measure the variability and distribution among replicated sample aflatoxin test results taken from the same aflatoxin contaminated lot of dried figs so that a model could be developed to evaluate the risk of misclassifying lots of dried figs by aflatoxin sampling plan designs. The model was then be used by the CCCF electronic working group (eWG) to recommend MLs and aflatoxin sampling plan designs to the full CCCF membership for lots traded in the export market. Sixteen 10 kg samples were taken from each of 20 dried fig lots with varying levels of contamination. The observed aflatoxin distribution among the 16-aflatoxin sample test results was compared to the normal, lognormal, compound gamma, and negative binomial distributions. The negative binomial distribution was selected to model aflatoxin distribution among sample test results because it gave acceptable fits to observed aflatoxin distributions among sample test results taken from the same contaminated lot. Using the negative binomial distribution, a computer model was developed to show the effect of the number and size of samples and the accept/reject limits on the chances of rejecting good lots (seller's risk) and accepting bad lots (buyer's risk). The information was shared with the CCCF eWG and in March 2012, the 6th session of CCCF adopted at step 5/8 an aflatoxin sampling plan where three 10 kg samples must all test less than an ML of 10 µg/kg total aflatoxins to accept a dried fig lot. The 35th Session of the Codex Alimentarius Commission met in July 2012 and adopted the CCCF recommendations for the ML and the sampling plan as an official Codex standard.

Comparing the performance of sampling plans that use a single regulatory limit based upon total aflatoxins to sampling plans that use dual limits based upon B1 and total aflatoxins

2010 ◽  
Vol 3 (1) ◽  
pp. 35-44 ◽  
Author(s):  
T. Whitaker ◽  
A. Slate ◽  
J. Adams ◽  
T. Birmingham ◽  
F. Giesbrecht
Keyword(s):  
European Union ◽  
Monte Carlo ◽  
Test Results ◽  
The European Union ◽  
Sampling Plans ◽  
Tree Nuts ◽  
Study Results ◽  
Sample Test ◽  
The Mean ◽  
Aflatoxin B

The European Commission (EC) aflatoxin sampling plan for ready-to-eat tree nuts such as almonds requires that each of the three 10 kg laboratory samples must all test less than 2 ng/g aflatoxin B1 (AFB1) and 4 ng/g total aflatoxins (AFT) for the lot to be accepted. Exporters have observed that the AFB1/AFT ratio varied greatly from sample to sample and the ratio appeared to average more than 50%. Because of the concern that dual limits associated with the EC aflatoxin sampling plans may reject more lots than similar sampling plans that use a single limit based upon total aflatoxins, studies were designed with the objectives to (a) measure the distribution of AFB1/AFT ratio values using sample test results associated with testing U.S. almond lots exported to the European Union; (b) use Monte Carlo methods to develop a model to compute the effects of using dual limits based upon AFB1 and AFT on the probability of accepting almond lots; and (c) compare the probability of accepting almond lots using the current Codex aflatoxin sampling plans for tree nuts when using single limits versus the use of dual limits. The study results showed that the mean and median among 3,257 AFB1/AFT ratio values was 87.6% and 91.9%, respectively, indicating that the distribution among the ratio values was negatively skewed. Only 31% of the 3,257 AFB1/AFT ratio values are less than the mean ratio of 87.6%. Codex aflatoxin sampling plans for tree nuts using a single limit based upon total aflatoxins had the highest probability of accepting lots at all lot concentrations when compared to the probability of accepting lots with dual limits. As the AFB1 limit decreased from 90 to 50% of the total limit, the probability of rejecting lots at all concentrations increased when compared to the Codex aflatoxin sampling plans with a single limit based upon total aflatoxins.

scholarly journals Evaluating the Performance of Sampling Plans to Detect Fumonisin B1 in Maize Lots Marketed in Nigeria

2007 ◽  
Vol 90 (4) ◽  
pp. 1050-1059 ◽  
Author(s):  
Thomas B Whitaker ◽  
M Bruno Doko ◽  
Britt M Maestroni ◽  
Andrew B Slate ◽  
Bosede F Ogunbanwo
Keyword(s):  
Negative Binomial ◽  
Test Procedure ◽  
Fumonisin B1 ◽  
Sampling Plan ◽  
Regression Equations ◽  
Test Results ◽  
Energy Agency ◽  
Sampling Plans ◽  
Sample Test ◽  
Total Variability

Abstract 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.

Comparing the USDA/AMS Subsampling Mill to a Vertical Cutter Mixer Type Mill Used to Comminute Shelled Peanut Samples for Aflatoxin Analysis1

2012 ◽  
Vol 39 (1) ◽  
pp. 69-81 ◽  
Author(s):  
Thomas B. Whitaker ◽  
Andrew B. Slate
Keyword(s):  
Operating Characteristic ◽  
Test Procedure ◽  
Sampling Plan ◽  
Test Results ◽  
Test Portion ◽  
Two Samples ◽  
The Us ◽  
Sample Test ◽  
Total Variability ◽  
Very High

Abstract The US peanut industry can use up to three 21.8 kg samples per lot to determine if shelled peanut lots are acceptable or unacceptable due to aflatoxin content. If a lot is accepted by the first 21.8 kg sample (1AB≤8 ng/g) prepared with the USDA/AMS Subsampling mill (DM), then some peanut buyers request that the sheller prepare the second sample (2AB) and in some cases the 3AB sample (called special samples in the trade) with a vertical cutter mixer (VCM) type mill. These requests to specifically use the VCM instead of the DM to prepare official (1AB) and special (2AB or 3AB) samples is based in part on a perception that analytical results associated with a test portion taken from the 21.8 kg sample comminuted with a DM does not detect the full magnitude of aflatoxin in the 21.8 kg sample and that negative aflatoxin certificates (lot acceptance) are more likely to occur when samples are prepared with a DM than a VCM. Analysis of aflatoxin test results from two shellers along with Monte Carlo simulation indicate that differences between the 1AB and special sample test results are due to the use of a cut-off limit (≤ 8 ng/g associated with the 1AB) requested by the buyer as part of the acceptance criteria and not due to any bias associated with the DM. Operating characteristic curves were used to demonstrate that the performance of the USDA/AMS aflatoxin sampling plan is about the same regardless of the use of a DM or a VCM for sample preparation. The performances are similar because the DM, with an 1100 g test portion, account for only 8% of the total variability of the aflatoxin test procedure (sampling and analysis account for about 92%). A sampling plan that requires two 21.8 kg samples to test less than a limit, regardless of mill used to prepare the two samples, has a very low risk of accepting bad lots above the FDA limit of 20 ng/g, but has a very high risk of rejecting good lots, which makes for an extremely high economic burden on the sheller.

scholarly journals Strategic Asset Allocation Of Credit Guarantors

2015 ◽  
Vol 31 (5) ◽  
pp. 1823
Author(s):  
Dong-Woo Rhee ◽  
Hyoung-Goo Kang ◽  
Soo-Hyun Kim
Keyword(s):  
Public Policy ◽  
Asset Allocation ◽  
Minimum Variance ◽  
Risk Return ◽  
Out Of Sample ◽  
Sample Test ◽  
Prior Literature ◽  
The Mean ◽  
Risk Contribution ◽  
Mean Variance

<p>How to manage the portfolio of credit guarantors is important in practice and public policy, but has not been investigated well in the prior literature. We empirically compare four different approaches in managing credit guarantor portfolios. The four approaches are equal weighted, minimum variance, mean variance optimization and equal risk contribution methods. In terms of risk return ratio, the mean variance optimization model performs best in out-of-sample test. This result contrasts with previous findings against mean variance optimization. Our results are robust. The results do not change as the characteristics of guarantee portfolio vary.</p>

Bayesian two-sided group chain sampling plan for beta binomial distribution under quality regions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Waqar Hafeez ◽  
Nazrina Aziz
Keyword(s):  
Beta Distribution ◽  
Binomial Distribution ◽  
Single Point ◽  
Sampling Plan ◽  
Design Parameters ◽  
Quality Level ◽  
Consumer’S Risk ◽  
Traditional Group ◽  
Sampling Plans ◽  
Content Type

PurposeThis paper introduces a Bayesian two-sided group chain sampling plan (BT-SGChSP) by using binomial distribution to estimate the average proportion of defectives. In this Bayesian approach, beta distribution is used as a suitable prior of binomial distribution. The proposed plan considers both consumer's and producer's risks. Currently, group chain sampling plans only consider the consumer's risk and do not account for the producer's risk. All existing plans are used to estimate only a single point, but this plan gives a quality region for the pre-specified values of different design parameters. In other words, instead of point wise description for the designing of sampling plan based on a range of quality by involving a novel approach called quality region.Design/methodology/approachThe methodology is based on five phases, which are (1) operating procedure, (2) derivation of the probability of lot acceptance, (3) constructing plans for given acceptable quality level (AQL) and limiting quality level (LQL), (4) construction of quality intervals for BT-SGChSP and (5) selection of the sampling plans.FindingsThe findings show that the operating characteristic (OC) curve of BT-SGChSP is more ideal than the existing Bayesian group chain sampling plan because the quality regions for BT-SGChSP give less proportion of defectives for same consumer's and producer's risks.Research limitations/implicationsThere are four limitations in this study: first is the use of binomial distribution when deriving the probability of lot acceptance. Alternatively, it can be derived by using distributions such as Poisson, weighted Poisson and weighted binomial. The second is that beta distribution is used as prior distribution. Otherwise, different prior distributions can be used like: Rayleigh, exponential and generalized exponential. The third is that we adopt mean as a quality parameter, whereas median and other quintiles can be used. Forth, this paper considers probabilistic quality region (PQR) and indifference quality region (IQR).Practical implicationsThe proposed plan is an alternative of traditional group chain sampling plans that are based on only current lot information. This plan considers current lot information with preceding and succeeding lot and also considers prior information of the product.Originality/valueThis paper first time uses a tight (three acceptance criteria) and introduces a BT-SGChSP to find quality regions for both producer's and consumer's risk.

Research on Reliability Assessment for the Armored Equipment Based on Multi-Source Information Fusion

2013 ◽  
Vol 760-762 ◽  
pp. 2091-2094
Author(s):  
Jian Du ◽  
Bao Jun Fei ◽  
Ying Liu ◽  
Guo Zheng Yao
Keyword(s):  
Field Test ◽  
Test Data ◽  
Information Fusion ◽  
Reliability Assessment ◽  
Small Sample ◽  
Test Results ◽  
Fuzzy Information ◽  
Source Information ◽  
Sample Test ◽  
Fusion Theory

In order to solve the problem of reliability evaluation for armored equipment, used Bayes fusion theory, combined with minimal amounts of reliability information on the field test, the paper fusioned reliability information of the same model for armored equipment, and completed the reliability assessment for a certain type of armored equipment. The test results show that the technology of multi-source information fusion can effectively solve the fusion problem of the prior fuzzy information and small sample test data, improve the accuracy of the reliability assessment, prove the feasibility and effectiveness for the multi-source information fusion in the armored equipment assessment.

scholarly journals Distribution among Sample Test Results when Testing Shelled Corn Lots for Fumonisin

2001 ◽  
Vol 84 (3) ◽  
pp. 770-776 ◽  
Author(s):  
Thomas B Whitaker ◽  
Winston M Hagler ◽  
Anders S Johansson ◽  
Francis G Giesbrecht ◽  
Mary W Trucksess
Keyword(s):  
Gamma Distribution ◽  
Gamma Function ◽  
Characteristic Curve ◽  
Test Procedure ◽  
Test Results ◽  
Significance Level ◽  
Gamma Distributions ◽  
Sample Test ◽  
The Mean ◽  
Power Divergence

Abstract 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.

Brittle Fracture in Heavy Section Welded T-Joints: Correlation Between Stress Intensity at Fracture and Small-Specimen Toughness Tests

1990 ◽  
Vol 112 (1) ◽  
pp. 53-57 ◽  
Author(s):  
W. R. Tyson ◽  
O. Vosikovsky ◽  
B. Faucher ◽  
D. J. Burns
Keyword(s):  
Stress Intensity ◽  
Residual Stresses ◽  
Fatigue Tests ◽  
Small Sample ◽  
Substantial Contribution ◽  
Test Results ◽  
T Joints ◽  
Heavy Section ◽  
Sample Test ◽  
Brittle Fractures

A fracture mechanics analysis has been made of brittle fractures encountered during a program of fatigue tests of welded plate T-joints. Fracture toughnesses are in reasonable agreement with small-sample test results, if the following factors are taken into account: a specimen size effect (with larger samples having lower toughness); existence of a substantial contribution to the stress intensity factor from residual stresses; and shakedown of residual stresses, with shakedown increasing with increasing applied stress.

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