  We consider the problem of estimating the rate of defects (mean number of
defects per item), given the counts of defects detected by two independent
imperfect inspectors on one sample of items. In contrast with the setting for
the well-known method of Capture-Recapture, we {\it{do not}} have information
regarding the number of defects jointly detected by {\it{both}} inspectors. We
solve this problem by constructing two types of estimators - a simple
moment-type estimator, and a complicated maximum-likelihood estimator. The
performance of these estimators is studied analytically and by means of
simulations. It is shown that the maximum-likelihood estimator is superior to
the moment-type estimator. A systematic comparison with the Capture-Recapture
method is also made.
