OC Curves in QC Applied to Sampling for Mycotoxins in Coffee
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1 OC Curves in QC Applied to Sampling for Mycotoxins in Coffee Geoff Lyman Materials Sampling & Consulting, Australia Florent S. Bourgeois Materials Sampling & Consulting Europe, France Sheryl Tittlemier Grain Research Laboratory, Canadian Grain Commission, Canada
2 Motivation Shipping grain to a consumer carries a risk The cargo is shipped assuming that it meets the consumer specifications (multiple quality parameters) Sampling at loading determines whether the cargo is dispatched Sampling at receipt determines acceptance of the cargo Risks to the shipper and receiver can be quantified by an OC or operational characteristic curve The OC curve is a general tool of quality control that seems to have been ignored by sampling folk
3 OC Curves What is an OC curve? The OC curve provides the probability that a lot of material will be accepted as a function of the TRUE value of the assay. Two pieces of information are needed to construct the OC curve: The distribution of the measurement uncertainty The acceptance criterion
4 OC Curves Example Coal ash content is determined with an SD of 0.1% ash and the uncertainty is normally distributed What is the risk of buying a shipment of coal having a true ash content of 10.15% when the acceptance criterion is <=10.00% ash 6.68%
5 OC Curves Example We can also look at the sellers risk. If he supplies coal at 9.9% ash, the probability that the buyer will accept the coal is 84.1% so the probability that the coal will be incorrectly rejected is % 84.1% 6.68%
6 OC Curves Reducing Risk Make the analysis more accurate Change the acceptance criterion Both these alternatives are costly The seller will ask a higher price for the cleaner coal More accurate analysis may require better sampling equipment or more replicate analyses
7 Application to Coffee Sampling for OTA OTA (Ochratoxin A) is a mycotoxin produced by moulds that grow on many kinds of foodstuffs (Durum wheat, coffee, dried fruits, grapes, maize, barley...) It can be present in extremely high concentrations on a single kernel of wheat or coffee bean (10 5 ppb) The allowable level in a lot is 5 ppb The lot can therefore be extremely heterogeneous with respect to OTA > difficult sampling
8 Application to Coffee Sampling for OTA spores OTA in mycelia?? Penicillium verrucosum on wheat
9 Application to Coffee Sampling for OTA To apply the OC curve method to coffee sampling, it is not sufficient to determine the sampling variance: THE FULL DISTRIBUTION OF THE UNCERTAINTY MUST BE KNOWN Further, the distribution usually changes with the level of contamination The work required is substantial
10 Coffee Sampling Whitakers design for OC curve development
11 Coffee Sampling Determination of assay distribution shape For each of the 25 samples, the empirical distribution function is plotted and fitted by a distribution. One family of distributions is used for all 25 fits
12 Coffee Sampling Replication permits estimation of: total variance preparation variance analysis variance subtract prep and analysis variance from total to get sampling variance At each of 25 concentrations For each variance component, regress variance against concentration
13 Coffee Sampling The total variance was modelled by a lognormal distribution (2 parameters: mean and variance) By specifying an acceptance level, an OC curve can be calculated it all looks nice and neat and complete However, there is an important flaw in this experimental plan
14 The Flaw The procedure fails to account for the distributional heterogeneity of the coffee that exists between and within sacks, or truckloads A lot of coffee consisting of say 500 sacks is far from homogeneous and there will be a substantial variance component associated with sampling from the sacks This component is probably the largest component of all!
15 Conclusion OC curves are a very useful tool for quantifying risk They must be constructed taking ALL sources of variance into account They bring a new discipline to sampling in that they demand discovery of the full distribution of uncertainty in sampling and analysis
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