Estimating fault hitting rates by recapture sampling

For the recapture debugging design introduced by Nayak (1988) we consider the problem of estimating the hitting rates of the faults remaining in a system. In the context of a conditional likelihood, moment estimators are derived and are shown to be asymptotically normal and fully efficient. Fixed sample properties of the moment estimators are compared, through simulation, with those of the conditional maximum likelihood estimators. Also considered is a procedure for testing the assumption that faults have identical hitting rates; this provides a test of fit of the Jelinski-Moranda (1972) model. It is assumed that the residual hitting rates follow a log linear rate model and that the testing process is truncated when the gaps between the detection of new errors exceed a fixed amount of time.