Determination of operating characteristic, retesting, and testing amount probabilities associated with testing for...

The relatively small perceived probability associated with retesting a food for the presence of Salmonella at low levels is often considered as one of the reasons that a confirmatory or check-analysis tends to disagree in practice with the results of an original test. Given a retesting process where a retest is only performed to confirm an original positive Salmonella test, the probability that both the original and retest will test positive for Salmonella has been traditionally determined by some as the product of the probabilities of a positive Salmonella test for the original and retest samples. When examining the probabilities associated with the retesting process, we found that our results disagreed with those based on intuitions apparently held by others concerning how these probabilities should be calculated. For Salmonella testing, operating characteristic values were computed to demonstrate the protections afforded by the Salmonella sampling plans presented in the U.S. Food and Drug Administration's Bacteriological Analytical Manual and to obtain the probability of a positive Salmonella test. The geometric distribution was examined for possible utility in determining the probabilities associated with testing amounts, i.e., the number of Salmonella tests needed to obtain a positive test.