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This paper gives the maximum likelihood estimations of the process (or lot) average proportion $p$ of defectives and the proportion $(\alpha)$ of the population which follows a negative binomial distribution based on attribute samples that have been curtailed either with the rejection of a lot on finding the $k$th defective or with the acceptance of it on finding the $K$th nondefective. These estimates are based on inspection from a sequence of $m$ lots of inspected items. Moreover, the linear estimates of $p$ and $\alpha$ and the asymptotic variance and covariance of considered estimators are given.
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