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.

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.

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.

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 SPATIAL DISTRIBUTION AND SEQUENTIAL SAMPLING OF Brevipalpus phoenicis IN CITRUS

2016 ◽  
Vol 38 (4) ◽  
Author(s):  
WALTER MALDONADO JR ◽  
JOSÉ CARLOS BARBOSA ◽  
MARÍLIA GREGOLIN COSTA ◽  
PAULO CÉSAR TIBURCIO GONÇALVES ◽  
TIAGO ROBERTO DOS SANTOS
Keyword(s):  
Spatial Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Sampling Plan ◽  
Goodness Of Fit Test ◽  
Control Plan ◽  
Sequential Sampling Plan ◽  
Brevipalpus Phoenicis

ABSTRACT Among the pests of citrus, one of the most important is the red and black flat mite Brevipalpus phoenicis (Geijskes), which transmits the Citrus leprosis virus C (CiLV-C).When a rational pest control plan is adopted, it is important to determine the correct timing for carrying out the control plan. Making this decision demands constant follow-up of the culture through periodic sampling where knowledge about the spatial distribution of the pest is a fundamental part to improve sampling and control decisions. The objective of this work was to study the spatial distribution pattern and build a sequential sampling plan for the pest. The data used were gathered from two blocks of Valencia sweet orange on a farm in São Paulo State, Brazil, by 40 inspectors trained for the data collection. The following aggregation indices were calculated: variance/ mean ratio, Morisita index, Green’s coefficient, and k parameter of the negative binomial distribution. The data were tested for fit with Poisson and negative binomial distributions using the chi-square goodness of fit test. The sequential sampling was developed using Wald’s Sequential Probability Ratio Test and validated through simulations. We concluded that the spatial distribution of B. phoenicis is aggregated, its behavior best fitted to the negative binomial distribution and we built and validated a sequential sampling plan for control decision-making.

scholarly journals Suitability of Several Statistical Models to Simulate Observed Distribution of Sample Test Results in Inspections of Aflatoxin-Contaminated Peanut Lots

1996 ◽  
Vol 79 (4) ◽  
pp. 981-988 ◽  
Author(s):  
Thomas Whitaker ◽  
Francis Giesbrecht ◽  
Jeremy Wu
Keyword(s):  
Parameter Estimation ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Statistical Models ◽  
Negative Binomial ◽  
Estimation Method ◽  
Likelihood Method ◽  
Model Parameters ◽  
Test Results ◽  
Parameter Estimation Method

Abstract The acceptability of 10 theoretical distributions to simulate observed distribution of sample aflatoxin test results was evaluated by using 2 parameter estimation methods and 3 goodness of fit (GOF) tests. All theoretical distributions were compared with 120 observed distributions of aflatoxin test results of farmers' stock peanuts. For a given parameter estimation method and GOF test, the negative binomial distribution had the highest percentage of statistically acceptable fits. The log normal and Poisson-gamma (gamma shape parameter = 0.5) distributions had slightly fewer but an almost equal percentage of acceptable fits. For the 3 most acceptable statistical models, the negative binomial had the greatest percentage of best or closest fits. Both the parameter estimation method and the GOF test had an influence on which theoretical distribution had the largest number of acceptable fits. All theoretical distributions, except the negative binomial distribution, had more acceptable fits when model parameters were determined by the maximum likelihood method. The negative binomial had slightly more acceptable fits when model parameters were estimated by the method of moments. The results also demonstrated the importance of using the same GOF test for comparing the acceptability of several theoretical distributions.

POPULATION ASSESSMENT DURING THE LARVAL STAGE OF THE ALFALFA WEEVIL, HYPERA POSTICA (COLEOPTERA: CURCULIONIDAE)

1975 ◽  
Vol 107 (8) ◽  
pp. 785-792 ◽  
Author(s):  
J. C. Guppy ◽  
D. G. Harcourt ◽  
M. K. Mukerji
Keyword(s):  
Larval Stage ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sampling Plan ◽  
Variance Analysis ◽  
Alfalfa Weevil ◽  
Hypera Postica ◽  
Total Cost ◽  
Sample Unit

AbstractThis paper presents a sampling plan for estimating numbers of H. postica larvae in the spring growth of alfalfa. A 6-stem bouquet of foliage formed an appropriate sample unit. The pattern of counts for all four instars conformed to the negative binomial distribution, and variance analysis for 89 sets of data revealed that differences between block, plots, and quadrats generally were not significant. For moderate levels of infestation (ca. 12 larvae per bouquet), estimates with acceptable precision may be obtained by taking a single 6-stem bouquet from each of 16 randomly selected ft2 (0.9m2) quadrats within a field, at a total cost of 120 man-minutes.

POPULATION AND MORTALITY ASSESSMENT DURING THE COCOON STAGE OF THE ALFALFA WEEVIL, HYPERA POSTICA (COLEOPTERA: CURCULIONIDAE)

1975 ◽  
Vol 107 (12) ◽  
pp. 1275-1280 ◽  
Author(s):  
D. G. Harcourt ◽  
J. C. Guppy
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sampling Plan ◽  
Mortality Factors ◽  
Alfalfa Weevil ◽  
Hypera Postica ◽  
Total Cost ◽  
Sample Unit

AbstractThis paper presents a sampling plan for estimating populations of Hypera postica (Gyll). cocoons in alfalfa, and of the principal mortality factors during this stage. The plan provides for samples in foliage and ground litter. For samples in foliage, where two-thirds of the cocoons are found, the most appropriate sample unit is a bouquet of 6 stems; for typical weevil densities, estimates with acceptable precision may be obtained by taking 25 bouquets at random from within a field. For litter samples, the appropriate sample unit is a quarter ft2 (232 cm2); acceptably precise estimates may be obtained by taking 20 such units at random from within a field. Total cost for a combined sample is 3.9 man-hours.The pattern of counts, both in foliage and ground litter, was well described by the negative binomial distribution.

SPATIAL ARRANGEMENT OF THE EGGS OF HYLEMYA BRASSICAE (BOUCHÉ), AND A SEQUENTIAL SAMPLING PLAN FOR USE IN CONTROL OF THE SPECIES

1967 ◽  
Vol 47 (5) ◽  
pp. 461-467 ◽  
Author(s):  
D. G. Harcourt
Keyword(s):  
Spatial Pattern ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Sequential Sampling ◽  
Spatial Arrangement ◽  
Sampling Plan ◽  
Chi Square ◽  
Sequential Sampling Plan ◽  
Hylemya Brassicae

Counts of eggs of Hylemya brassicae (Bouché) in cabbage did not conform to the Poisson distribution owing to a preponderance of uninfested and highly infested plants. But when the negative binomial series was fitted to the observed distribution, the discrepancies were not significant when tested by chi-square. The spatial pattern may be described by expansion of (q—px)−k with a common k of 0.95.Three methods of transformation stabilized the variance of field counts. A sequential sampling plan based on the negative binomial distribution and providing for two infestation classes was drawn up for use in control of the insect in the stem brassicas.

On Shewhart Control Charts for Zero-Truncated Negative Binomial Distributions

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Anwer Khurshid ◽  
Ashit B Chakraborty
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Control Charts ◽  
Negative Binomial ◽  
Average Run Length ◽  
Shewhart Control Charts ◽  
Binomial Distributions ◽  
Shewhart Control ◽  
Cusum Charts ◽  
Number Of Individuals

<p><span>The negative binomial distribution (NBD) is extensively used for the<br /><span>description of data too heterogeneous to be fitted by Poisson<br /><span>distribution. Observed samples, however may be truncated, in the<br /><span>sense that the number of individuals falling into zero class cannot be<br /><span>determined, or the observational apparatus becomes active when at<br /><span>least one event occurs. Chakraborty and Kakoty (1987) and<br /><span>Chakraborty and Singh (1990) have constructed CUSUM and<br /><span>Shewhart charts for zero-truncated Poisson distribution respectively.<br /><span>Recently, Chakraborty and Khurshid (2011 a, b) have constructed<br /><span>CUSUM charts for zero-truncated binomial distribution and doubly<br /><span>truncated binomial distribution respectively. Apparently, very little<br /><span>work has specifically addressed control charts for the NBD (see, for<br /><span>example, Kaminsky et al., 1992; Ma and Zhang, 1995; Hoffman, 2003;<br /><span>Schwertman. 2005).<br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p><p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>The purpose of this paper is to construct Shewhart control charts<br /><span>for zero-truncated negative binomial distribution (ZTNBD). Formulae<br /><span>for the Average run length (ARL) of the charts are derived and studied<br /><span>for different values of the parameters of the distribution. OC curves<br /><span>are also drawn.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /><br class="Apple-interchange-newline" /></span></p>

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