Multinomial group testing models with incomplete identification

We study reliable multinomial probabilistic group testing models with incomplete identification. We assume that every of the pooled items has none or some of k attributes, one of them causing contamination. Any group possessing this latter attribute is discarded, while the others are collected and separated according to the attributes that were found in them. The objective is to choose an optimal group size for pooled screening so as to collect prespecified numbers of items of the various types with minimum testing expenditures. We derive exact results for the underlying distributions of the stopping times, enabling us to find optimal procedures by numerical methods.