In this paper we introduce a new scheme of censoring and study it under the Weibull distribution. This scheme is a mixture of progressive Type II censoring and self relocating design which was first introduced by Srivastava . We show the superiority of this censoring scheme (PSRD) relative to the classical schemes with respect to “asymptotic variance”. Comparisons are also made with respect to the total expected time under experiment (TETUE) as an important feature of time and cost saving. These comparisons show that TETUE(SRD) < TETUE(PSRD) < TETUE(PC2) if 0 < β < 1, TETUE(PSRD) = TETUE(SRD) < TETUE(PC2) if β = 1 and TETUE(PSRD) is the best among all the designs if β = 2 (Rayleigh distribution case).