Reliability sampling plans are used to determine the acceptability of a product at some future point in its effective life. Whenever the life test is performed based on the measurement data, variables sampling plans can be utilized. Variables sampling plans are more efficient than the attribute sampling plans. In this paper, we propose a reliability sampling system for measurable characteristics under failure censored life testing when the life time of the product follows Weibull distribution with known shape parameter. In this proposed sampling system, the acceptance criteria do not involve the unknown scale parameter of the distribution differently from the existing sampling plans. The parameters of the proposed system are determined by using two points on the operating characteristic curve approach. To determine the optimal parameters, an optimization problem is formulated so as to minimize the average number of failures to be observed. It is also to be pointed out that the designing parameters can be done independently of the shape parameter although the operation of the system involves the shape parameter and a lower specification limit. The main advantage of the proposed system is to reduce the average failure number with desired protection.