The (T_U, T_L) simultaneous control chart is proposed by Takahashi et al., which enables us to make a multiple decision on parameters μ and σ of original normal distribution, when it is observed as attributed data (N_U, N_L) on both-sided specification limits. This cotrol chart is designed based on two assumptions in the same way of the two-way control chart as follows; (1) π_UC≒π_LC, (2) A change in a process is small. In this paper new control limits are proposed, which don't request such assumptions. The probability of the first kind of error and the power of a multiple decision based on these limits are obtained by the Monte-Carlo method and it is ascertained that new limits are more pracical compared with line limits in the previous papers.