Abstract: A frailty model for failure data is proposed to estimate the total number of faults in a system. The Littlewood model and Jelinski-Moranda are the two particular cases of the proposed formulation. The two-stage estimating procedure, a conditional likelihood and a Horvitz-Thompson estimator, is found to be efficient. Simulation studies are given to assess the performance of the estimator. Two examples are also presented.
Key words and phrases: Capture-recapture, conditional likelihood, fault detection, Littlewood, Jelinski-Moranda, removal experiment.