Estimating population size by recapture sampling

Abstract

A design called recapture debugging is proposed to get extra information to estimate the original number of faults, N , in a reliability system. The system is observed for a fixed amount of time τ and the failures are assumed to follow an exponential law with an unknown common parameter λ. The maximum likelihood and moment estimators of N and λ are derived and compared with the existing estimators. The recapture sampling provides substantially more information and improved estimators compared to the standard experiment if τ is not small. Significance tests for testing hypotheses about N and λ are developed. Finally, for testing the system one can consider τ to be determined sequentially and we present a suitable stopping rule.