Experiment length and sample size for negative binomial sampling

Abstract

The negative binomial distribution is a compound Poisson distribution which is useful in life-testing and other applications. The length of experiment required lo achieve a specified power when testing the average failure rate is considered, and a closed form approximation is provided. The more general question of determining the optimum combination of sample size and expciintent length tu minimize experimental cost is also considered, and an approximate closed form solution is given. These results would also be useful in other applications with negative binomial sampling.