The conditional estimation of the Weibull and its related parameters are introduced. For this estimator, some interesting properties in contrast with the well known maximum likelihood estimators have been investigated. This task is done under the famous sampling plan typeii censoring scheme. Because of the complex behavior in the calculation of the likelihood function of the presented scheme in this situation without loss of generality, this problem fixed with the Gumbel (logWeibull) model. The one to one transformation between these models and it’s satisfying in their parameters able us for utilizing this alternative model. Finally, the comparison of this method and maximum likelihood estimation are provided through some numerical results.

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