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Frequently one has to search within a finite population for a singleparticular individual or item with a rare characteristic. Whether an itempossesses the characteristic can only be determined by close inspection. Theavailability of additional information about the items in the population opensthe way to a more effective search strategy than just random sampling orcomplete inspection of the population. We will assume that the availableinformation allows for the assignment to all items within the population of aprior probability on whether or not it possesses the rare characteristic. Thisis consistent with the practice of using profiling to select high risk itemsfor inspection. The objective is to find the specific item with the minimumnumber of inspections. We will determine the optimal search strategies forseveral models according to the average number of inspections needed to findthe specific item. Using these respective optimal strategies we show that wecan order the numbers of inspections needed for the different models partiallywith respect to the usual stochastic ordering. This entails also a partialordering of the averages of the number of inspections. Finally, the use, somediscussion, extensions, and examples of these results, and conclusions aboutthem are presented.

Information weighted sampling for detecting rare items in finite populations with a focus on security