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\footnotesize
\noindent Statistica Sinica {\bf 12}(2002), 1001-1013
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\centerline{\large\bf A FRAILTY MODEL FOR DETECTING NUMBER}
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\centerline{\large\bf OF FAULTS IN A SYSTEM }
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\centerline{Yan Wang, Paul S. F. Yip and Y. Hayakawa}
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\centerline{\it University of South Australia, University of Hong Kong and
University of Wellington}
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\begin{quotation}
\noindent {\it 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.\par
\vspace{9pt} \noindent {\it Key words and phrases:}
Capture-recapture, conditional likelihood, fault detection, Littlewood,
Jelinski-Moranda, removal  experiment. \par
\end{quotation}
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