In this paper, we propose a conditional sampling plan called conditional double sampling plan for lot acceptance of parts whose life time follows a Weibull distribution with known shape parameter under sudden death testing. A table is also developed for the selection and application of optimal parameters of the proposed plan for specified two points on the operating characteristic curve namely the acceptable reliability level and the limiting reliability level along with the producer and consumer's risks. The optimization problem is formulated as a nonlinear programming where the objective function to be minimized is the average group number and the constraints are related to lot acceptance probabilities at acceptable reliability level and limiting reliability level under the operating characteristic curve .