Abstract
We consider the group testing problem for a finite population of possibly defective items with the objective of sampling a prespecified demanded number of nondefective items at minimum cost. Group testing means that items can be pooled and tested together; if the group comes out clean, all items in it are nondefective, while a "contaminated" group is scrapped. Every test takes a random amount of time and a given deadline has to be met. If the prescribed number of nondefective items is not reached, the demand has to be satisfied at a higher (penalty) cost. We derive explicit formulas for the distributions underlying the cost functional of this model. It is shown in numerical examples that these results can be used to determine the optimal group size.
| Original language | English |
|---|---|
| Pages (from-to) | 55-72 |
| Number of pages | 18 |
| Journal | Methodology and Computing in Applied Probability |
| Volume | 6 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2004 |
Bibliographical note
Funding Information:We thank two referees for their helpful and constructive comments. We also thank Andreas H. Löpker for his help in the numerical analysis. S. K. Bar-Lev was partially supported by NWO grant no. B 61-515.
Keywords
- Cost functional
- Group test
- Incomplete identification
- Optimization
- Processing time
- Stopping time
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics