In this paper, a modified double acceptance sampling plan for time-truncated life test is developed. The operating procedure of this plan is also proposed and the performance measures such as the probability of acceptance and the average sample number (ASN) are also derived. We consider gamma distribution, Weibull distribution and Birnbaum--Saunders distribution for designing the proposed plan. The optimal parameters are determined which will have minimum ASN. The efficiency of the proposed plan is also discussed over the traditional double sampling plan (DSP) and shown that the proposed plan performs better than the existing DSP. The extensive tables are provided for all the distributions and explained with the help of industrial data.