In traditional reliability tests for assuring the mean time to failure (MTTF) in Weibull distribution with shape and scale parameters, it is assumed that the change of lifetime is concerned with the scale parameter only. Then, Hisada et al. proposed a reliability test procedure for assuring MTTF while considering the influence of both shape and scale parameters. Their reliability test requires complete lifetime data, and the application of a censoring procedure for designing a reliability test for Weibull distribution that considers the influence of both shape and scale parameters has not been considered. In general, since reliability tests require a long testing period, the fixed-number censoring procedure is sometimes applied in order to save testing time. Therefore, in this article we consider the fixed-number censoring procedure in reliability test for assuring MTTF while considering the influence of both shape and scale parameters for Weibull distribution. We also refer to the economical design of the proposed fixed-number censoring test.